Presente e Futuro/

Present Status and Future Developments

Conference Proceedings Vol. 96

“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”

F. Gramegna, M. Cinausero, D. Fabris (Eds.)

SIF, Bologna 2008

THE 1f7/2 SAGA

R.A. Ricci

I.N.F.N.- Laboratori Nazionali di Legnaro and University of Padova

INTRODUCTION

This is just a personal “historical” review

concerning the evolution of nuclear spectroscopy

of the “magic” shell-model region (the 1f7/2 one)

and the corresponding experimental and

theoretical investigations to which a large part of

my scientific career and even of my human

journey was devoted.

Fig. 1: The γ-ray and γ−γ summing coincidence

spectrum and level scheme of 50Ti (left) compared with 42Ca (right).

Another important reason is that the foundation of

nuclear spectroscopy in Italy did occur at the

beginning of the 60’s when I came to Naples

back from Amsterdam where I spent one of the

most pleasant and fruitful periods of my

scientific life. It was characterized by the

experimental investigation of an impressive

number of new decay schemes due to the

possibility of producing radioactive nuclear

species with dedicated charged particle

accelerators or neutron generators and of

measuring the associated γ-rays via the only just

invented scintillation detection technique. These

researches were performed at the Philips

Cyclotron of IKO (“Instituut voor Kernphysics

Onderzoeck”) in Amsterdam and at the 14 MeV

neutron generator in Napoli in the years 1950-

1960.

The starting point of the “1f7/2 saga” was

the investigation of the 50

Ti γ-spectrum

following the β-decay of 50

Sc produced by the 50

Ti(n,p)50

Sc reaction with the 14 MeV neutrons

arising from the 400 keV Van der Graaff

accelerator [1] (see Fig. 1).

Fig.2: Cover of the experimental nuclear

spectroscopy “Bible” in the ‘60th.

151

The main experimental tool which was of

paramount importance in such investigations was

the γ-scintillation spectrometry as described in the

chapter devoted to the “Procedures for the

investigation of the disintegration schemes-

Scintillation spectra analysis” of the famous

book edited by K. Siegbahn in 1965 on “Alpha,

Beta and Gamma-Ray Spectroscopy” [2] (see

Fig. 2).

The power of such a methodology is well

illustrated in Fig. 1 by the γ-scintillation spectrum

of 50

Ti analyzed by means of the “peeling”

technique; the γ-spectrum under study was

decomposed into its single γ contributing parts by

comparison with the pulse-height distributions of

standard calibration sources (with well known

γ−ray energies) measured under the same

experimental and geometrical conditions.

The case of 50

Ti is also a typical example

of the application of the “summing technique” for

detecting γ−γ coincidences. It consists in

exploiting in a proper way the “summing effect”,

which is present in the crystal when random and

true coincidence occur between the absorbed

γ−rays and the coincident radiations are detected

within the resolving time of the detector (normally

1 μsec for a NaI(Tl) crystal coupled to a standard

pulse-height analyzer). The corresponding photo-

peaks will overlap giving rise to a summing

photo-peak whose energy is the sum of the single

γ-ray energies. The effect is emphasized by

varying the distance (i.e. the solid angle) between

the source and the detector and, in particular, by

using a geometry close to 4π, i.e. a “well-type”

crystal with the source in the well.

The 50

Ti γ-spectrum reported in Fig. 1 as

measured with the source outside and inside the

well-type crystal clearly shows the double and

triple coincidences corresponding to the cascade

γ-rays in the level scheme also reported in Fig. 1,

in comparison with that of 47

Ca (two neutrons in

the f7/2 shell).

1. THE (1f7/2)2 TWO PARTICLE SPECTRA

The 50

Ti result showed for the first time

the coincidence of the effective two-particle

interaction both for protons (1f7/2)2p and

neutrons (1f7/2)2n in the T= 1 states (0

+, 2

+, 4

+,

6+). The other states in

42Ca are of different

configuration (collective states).

Another important feature revealed was

the fact that the two-particle spectra are simpler

and easier to be recognized near 48

Ca as, for

example, 50

Ti and 48

Sc than near 40

Ca as 42

Ca

and 42

Sc [3]. In fact the information about the

effective two-body force in the f7/2 region is

really powerful since there are, in principle,

eight nuclei which can provide different types of

particle-particle, particle-hole and hole-hole

spectra. It can be seen, as I will report later that,

at a first approximation, the behavior of the T=0

and T=1 two-body spectra are in fair agreement

with the charge and symmetry independence of

the effective interaction.

It is interesting to quote here the important

observations of two pioneers in the field, who

represented for me and for the Italian groups

involved in the development of nuclear structure

studies in Italy not only very nice personal

friends but also invaluable advisors. I am

referring to Igal Talmi and Haru Morinaga1.

In his remarks on “the shell model

approach to the f7/2 shell” in the occasion of the

“famous” (let me use this expression)

International “Topical Conference on the

Structure of 1f7/2 nuclei” (Legnaro, 1971) [4],

I. Talmi argued about the persistent problem

“….why does the shell model apply at all”,

asking the question of understanding even the

title of that Conference.

In fact: “ ...If 40

Ca is very far from being

a closed shell, what sense does it make to speak

on the f7/2 shell. Still, I am happy to see that our

1 The presence of Igal Talmi today is really very

gratifying. Haru Morinaga, who has not been able to

come, still remains for us a reference person so as Bob

Van Lieshout, Aaldert Wapstra, Maurice Jean and Allan

Bromley.

152

experimental friends were not brainwashed and

still think that there is such an object. Certainly

nuclei in this region show many features which

go beyond simple f7/2 configurations, like the

existence of excited deformed states, p3/2

admixtures etc. Nevertheless, I believe that we

should still try to see the general features of the

forest in spite of the very many interesting trees in

it…………already in 42

Ca we encounter some of

these extra features. Above the first excited 2+

state there are 0+ and 2

+ states which are most

probably due to deformed core excited states. The

existence of these two states, which were even

given many years ago 4+ and 6

+ assignments,

prevented the emergence of the f7/2 picture”.

As he mentioned, that the (f7/2)n

description could work well for proton

configuration was shown by Lawson and Uretsky

[5] and this opened the way to apply this approach

also to the Calcium isotopes for neutron

configuration.

It should not be surprising that the 42

Ca

spectrum was considered a “puzzling” problem

(another one was the 42

Sc, T=0, spectrum for the

complete knowledge of the two-particle

interaction).

In the 1f7/2 shell there are simple

configurations with maximum isospin which

contain only neutrons or protons outside the

closed shells and where the shell-model

calculations are successful. A more complete

description, taking into account both protons and

neutrons were performed for the first time in the

pioneering work of McCullen, Bayman and

Zamick [6] (the so called MBZ approach).

On the other hand, in his concluding

remarks, H. Morinaga [7] mentioned that the main

problem was to compare the 1f7/2 proton and

neutron spectra on sound experimental basis. This

was of course very important for the extraction of

the “effective two-body interaction” as assumed

by I. Talmi for the calculation of energy levels

and effective operators in a single jn

configuration.

Morinaga did remind that the concept of a

single 1f7/2 shell was born already in 1948 when

Meyer and Jensen proposed the shell model but

that the first quantitative efforts started in 1955

when Ford and Levinson [8] tried to calculate

the 43

Ca spectrum taking the single-particle

energies from 41

Ca and the two-body residual

interaction from the 42

Ca spectrum, known at

that time.

After a first positive finding however:

“……there arose doubt about experimental

results on 43

Ca. Then soon after, there came

doubt on the spin assignments in 42

Ca. The β-

decay of 50

Sc was then studied but the spectrum

of 50

Ti was quite different from that of 42

Ca.

We have then studied the β-decay of 42

K and

found that the 1.836 MeV state in 42

Ca was 0+

instead of 4+ and moreover the 2.422 MeV state

was 2+. The 4+ state had to be pushed up to

2.76 MeV. But there was still uncertainty in the

β-decay of 50

Sc. That time we could not

distinguish the 6+-4

+ 0.52 MeV transition from

annihilation radiation”.

“Waiting for Godot” one could say.

And then (quoting Morinaga again):

“The final touch for the 50

Sc level scheme was

made by the Napoli group (i.e. G. Chilosi, P.

Cuzzocrea, R. A. Ricci, G. B. Vingiani) with

their 400 keV accelerator. This was one of the

most pleasant experiments I was ever involved

with. Of course the part of the spectra, the 0-2-

4-6, was very satisfactory. The same time the

problem of the foreign 0+

, 2+ in

42Ca came up.

We suspected the fact that it could only be

explained as the core-excited state, although as

experimentalists we never tried to say that this

is a seriously deformed state. This 0+ state have

been since then many times rediscovered by

clever theoretical physicists in the nuclear data

sheets”.

It is of course rewarding to notice that,

already at that time and, more precisely,

afterwards [9], the comparison of the two-

neutron spectrum of 42

Ca with the two-proton

one has been extended to the mirror 42

Ti where

not only the same 0+, 2

+, 4

+, 6

+ two particle

sequence has been observed but also 0+, 2

+ extra

(deformed ?) states as expected by the influence

153

of the 40

Ca core (less rigid than 48

Ca) [2, 9].

Perhaps the proper way to resume the interest of

the 1f7/2 nuclear region is to quote the pertinent

part of my introductory talk to the Legnaro

Conference in 1971 “Why 1f7/2 nuclei”.

.. One should also keep in mind the following

points :

a) this is a region where most of the

meaningful tests of nuclear wave functions

by means of lifetime measurements,

electromagnetic transition rates and

spectroscopic strengths are being

collected.

b) In spite of the overcoming old superstition

about the possibility of describing the

whole 1f7/2 region by the simplest pure-

configuration model, such class of nuclei,

which is confined in a “compact” area

characterized by the three “doubly-closed

shell cores”, i.e. 40

Ca, 48

Ca and 56

Ni, still

needs to be “privileged”.

As a consequence, designating them as

“the 1f7/2 nuclei” preserves some

meaning.

c) There are, in this “1f7/2” region, 49

nuclides, so far known, with 18 stable

nuclear species, so that the different types

of available reactions can, in principle, be

used to provide information on almost all

the nuclear spectra of interest”.

The “so far” known nuclei were indicated by a

“triangle” in a Z-N representation as shown in

Fig. 3, with the 3 vertices on 40

Ca, 48

Ca and 56

Ni

(see ref. [3]).

Quoting my introduction again:

“One can already draw, in this representation,

some borderlines to distinguish the “gross

features” of these nuclei. Near the 48

Ca-56

Ni line,

one has the “spherical shell-model region”; in

fac, it is known that 48

Ca (and perhaps 56

Ni) is a

better closed-shell core than 40

Ca and that the

N=28 isotones are quite well described by the

simple shell model without too many theoretical

sophistications. Following the 40

Ca-48

Ca line, we

find the Calcium isotopes, which start to display

core-excited effects, especially near 40

Ca and

open the way to deformations and rotational

like bands displayed by the nuclei following the

diagonal lines from 43

Sc to 49

Cr and from 45

Sc to 45

V”.

Fig. 3: The “1f7/2 “ nuclear region in a Z-N

representation; the borderline from 56

Ni to 46

Ca

indicates at the right-hand side the “good” shell

model nuclei. Nuclei represented with horizontal

bars display core-excitation effects; nuclei with

diagonal bars display some deformation effects; the

doubly diagonal bars indicate the presence of

rotational-like spectra.

A particular case which was emphasized in that

context was 42

Sc which was of great importance

in providing both T=0 and T=1 two-body

spectra for the 1f7/2 nuclei. The story of such a

nucleus is really interesting since one had to

wait the evolution of the experimental data

which was seriously modified as compared with

the old data (see ref. [2]).

The 42

Sc level sequence reported in Fig.

4 together with those of other well established

(1f7/2)2 nuclei refer to the data taken by W.

Kutschera et al. in 1977 [10] where the

evolution of the (1f7/2)+2

T=0,1 normalized to the

6+ levels (the less perturbed by Coulomb shift

corrections) is reported.

154

These data were summarized at the second

topical Conference on the “Physics of Medium-

Weight Nuclei” held in Florence in 1977 [11],

where also the high-spin configuration, the

electromagnetic properties, the Yrast bands and

the rotational bands in the region were reviewed.

Fig. 4: The (1f7/2)±2

T=0, T=1 spectra normalized to 6+

levels.

2. THE ENERGY SPECTRA AND THE

PRODUCTION OF NUCLEAR STATES IN

THE 1f7/2 REGION

The 1f7/2 problem in Nuclear Spectroscopy was

reviewed in 1969 in the so called “Bible” (the

definition is of Gerry Brown) of the properties of

such nuclei by P. Maurenzig and myself [12] (see

Fig. 5).

That review came from a set of

experimental data and theoretical calculations

arising from radioactive decays, stripping and

pick-up reactions, in-beam γ−ray spectroscopy,

lifetime and transition probabilities as well as

from some descriptions based on semi-

phenomenological models and few microscopic

approaches performed at that time.

The evolution of the various (1f7/2)n

spectra has been a more and more cogent test of

the model descriptions of the nuclear structure in

the region. An important piece of information was

the sequence of unperturbed single-particle and

single-hole states. Fig. 6 reports the centroids

(energies averaged over the isospin and

spectroscopic strengths) of such states as arising

from various single-particle transfer reaction

experiments [13] (see also ref. [12]).

Fig. 5: The “f7/2 Bible” in 1969

Fig. 6: Centroids of the unperturbed single-particle

and single-hole states referred to 40Ca and 48Ca

cores. The 1f5/2 - 1f7/2 splitting is often taken as ~6.3

MeV.

155

I like to mention here the important

information concerning the 1f7/2-1d3/2 energy

separations obtained by (p, 2p) knock-out

reactions at the 155 MeV synchrocyclotron in

Orsay by measuring the scattered protons at equal

angles with the help of magnetic analyzers. The

results obtained are shown in Fig. 7 where the f7/2-

d3/2 binding energies are reported together with the

excitation energies of s and d hole states in some

1f7/2 nuclei.

Fig. 7: a) Binding energies Bp of 2s1/2 nuclei, from

(p,2p) reactions; the full line connects the data

corresponding to even-even residual nuclei. The target

nuclei are indicated in the upper part of the figure.

The points indicated as 1d3/2 and 1f7/2 correspond to

the proton binding energies in the ground state of the

target nucleus; b) excitation energies E* of 2s1/2 and

1d5/2 proton-hole states in the odd nuclei reported in

a); c) excitation energies E* of 2s1/2 proton-hole

states in the even-even nuclei reported in a). The main

difference between b) and c) is due to pairing effects.

The problem of the evolution of single-

particle energies in this region is also reviewed by

B. Fornal [9] at this Conference, on the basis of

our detailed discussion (see ref. [13]) on the

variation of the 1f and 2p states with their spin-

orbit splitting in filling the 1f7/2 shell either by

neutrons or by protons. Those results already

indicated a strong residual interaction in the T=0

than in T=1 two-nucleon state, which gives rise

to a tighter binding for the protons when the

1f7/2 shell is full of neutrons.

Moreover, not only the 1f7/2 but also the

1d3/2 proton states are pushed down by the

neutron excess in the 1f7/2 shell, and this is in

agreement with the decrease of the mean charge

radius from A=40 to A=48 as observed

experimentally [14].

Since this is a very interesting topic that

I know will be quoted by Fornal in this report, I

like to recall few remarks I did in my report at

the Varenna School in 1967 [12].

“…… Once the 1f7/2 neutron shell has

been filled no important effects are observed in

filling the 1f7/2 proton shell; this could be

associated with a blocking effect of the neutron

excess.

However, all these effects are also

related to the more or less important

modification in the spin-orbit splitting. …….

This splitting……. is not seriously modified both

for neutrons (….. ~ 2 MeV for 41

Ca and 49

Ca)

and for protons (…~ 1.8 MeV for 41Sc and 55

Co,

and ~ 2.5 MeV for 49

Sc)…… The same is not

true for the spin orbit splitting concerning the 1f

state: it changes from 5.5 MeV in 41

Ca to 6.2

MeV in 47

Ca and 7.7 (or 8.7) in 49

Ca; from 5.9

MeV for 41

Sc and 49

Sc to 4.6 MeV for 55

Co. The

fact that it remains constant from 41

Sc to 49

Sc is

due to the self-binding effect in both 1f7/2 and

1f5/2 proton levels when the 1f7/2 neutron shell is

filling”. I leave any other comments to Fornal.

Concerning the more extended problem

of the (1f7/2)n configuration with n>2, an

interesting case was that of (1f7/2)+ 3

nuclei. Just

as an example I like to remind our findings for 51

V and 53

Mn [15] and their comparison with

other similar nuclei [16] . Fig. 8 shows that

comparison as reported by Talmi.

156

Fig. 8: Levels of (1f7/2)n configurations in odd nuclei.

The low-lying levels 7/2-, 5/2

- ,3/2

- are quite

well described by using the two-nucleon matrix

elements arising from the pure (1f7/2)2 interaction;

there were questions concerning the regularity of

the excitation energies with the 5/2- state lying to

low and the 3/2- state too high in

45Ca and also the

possibility of the presence of core-excitations

especially near the 40

Ca core. On the other hand

more crucial tests could be found in the

electromagnetic transitions. A case in point was

the measurement of mean lives (using the Doppler

shift attenuation method) and of branching and

multipole mixing ratios in the γ-transitions of 53

Mn [15].

The results showed that M1 transitions

between states assumed to belong to the basic

(πf7/2)-3

multiplet are retarded by factors of the order

of 10 to 100 and the E2’s enhanced by a factor of

10 in agreement with the behavior of 51

V (with

πf7/23

configuration) supporting the basic shell

model features of nuclei with a 48

Ca core.

A fundamental problem in this context is

that related with the 207

Bii207Pb decay for the

characterization of the ratio of the single particle

f7/2ip3/2 transition to the f7/2if5/2 one (E2/M1).

Fig. 9a) shows the level scheme of 207

Pb

which clearly displays the sequence of the single-

hole states in the unfilled 126 neutron shell, while

in Fig. 9b) the coincidence γ-spectrum taken via

the summing scintillation technique revealing the

γ-decay of the f7/2 level at 2341 keV to the p3/2 one

(E2 transition of 1445 keV) and to the f5/2 level

(pure spin-flip M1 transition) [17] is shown.

Fig. 9: a) Decay scheme of 207Pb following the

decay of 207

Bi. b) Sum coincidences with 2340 keV

sum energy. The inset shows the central part

enlarged.

The measured M1/E2 ratio (0.023+0.002)

showed that the M1 transition is hindered by a

factor of ~ 4. It is a clear case reported by Bohr

and Mottelson [18] in the chapter concerning the

electromagnetic moments particularly with

respect to magnetic dipole effects in single-

particle configurations.

3. DEFORMATIONS IN THE 1f7/2 SHELL

The fact that a quite general

enhancement of E2 transitions [12] was

observed in the 1f7/2 shell could indicate some

kind of deformation in the shell model states

which was also correlated to the fragmentation

of such states and to the presence of positive-

parity states. Questions arose about some

splitting of the shell-model states as arising from

157

the Nilsson diagram, due to an axially symmetric

non spherical field.

Moreover the presence of low 1/2+ and

3/2+ states interpreted as hole s1/2

- and d3/2

- hole

states in odd Scandium isotopes were interpreted

as a particular case of core excitations due to the

deformed 40

Ca core.

I will not enter into details here about the

problem of the “superconducting” behavior

(pairing force, diffuse Fermi surface) of nuclei

like 40

Ca where, as shown by stripping and pick

up reactions, the shell closure N or Z=20 does not

correspond to a sharp Fermi surface. A detailed

discussion can be found in ref. [12].

In any case the possible core excitations

could be taken into account by allowing collective

vibrations (quadrupole and octupole states) and

treating the odd-particle levels as due to the

coupling between single-particle states and the

even core excitations [19].

We were of course aware of the fact that

one should consider such an approach in the

frame of a “weak coupling” model and that, as

shown in more recent and advanced theoretical

descriptions, more configurations are needed [20]

or different coupling scheme like the Interacting

Boson Model [21] could apply.

On the other hand the phenomenology of

the nuclear properties in this region has been

extensively enlarged also by the characterization

of “collective” states as produced in inelastic

scattering experiments. I will report as an

example, the result of (p,p’) inelastic scattering in

that region, performed at Orsay with the 155 MeV

synchrocyclotron [22] .

The collective behavior is normally related

to the first 2+ levels in even-even nuclei, apart

from the shell effects. Fig. 10 shows the situation

summarized in 1969 [12] concerning the energies

and the corresponding transition enhancement

factors as a function of N of the even-even nuclei

filling the 1f7/2 shell.

The strong correlation between the

lowering of the deformation collectiveness with

the increasing of the excitation energy near the

closed shells is clear.

More interesting, and in some sense more

puzzling, was the case of 3- octupole states.

Such states cannot be interpreted in terms of

single particle excitations in the (f7/2)n

configuration since no negative parity states

may be formed by coupling two nucleons in the

1f orbit.

Fig. 10: Excitation energy E(2+) and acceleration

factor G=B(E2Ļ)/B(E2Ĺ)sp of the first level 2+ as a

function of Z and N, in the couple of nuclei f7/2. The

continuous line in the upper panel connect the

values of the parameter β2R0. Their scale is on the

right.

The more realistic assumption was to

consider them as particle-hole states (based on

the promotion of 1d-2s states of the core to the

1f-2p orbits). On the other hand they could be

referred to collective octupole vibrations

lowered in energy by the spin-orbit coupling.

The experimental results as summarized in Fig.

11 for 1f7/2 nuclei show a certain fragmentation

of such levels (in the figure the two main 3-

states are reported) which is not in good

agreement with the particle-hole model. Also

their strength decreases with the addition of

“valence” nucleons.

This does not mean that the “collective”

description is better because this strength does

not increase when the states become nearer to

158

the ground state (contrary to the 2+ states). This

behavior should be referred to the variation of

ground-state correlations approaching 48

Ca.

In conclusion, this review that I have

presented here as a kind of recollection of the

“1f7/2 saga” is only a part of a long history dealing

with very interesting aspects of the nuclear

structure investigations. And it is very rewarding

to notice today how this subject is enjoying a real

revival.

Fig. 11: Excitation energy E(3-) and acceleration

factor G=B(E3Ļ)/B(E3Ĺ)sp of the 3-

level observed in

the couple of nuclei f7/2. The vertical bars represent

the position of the levels deriving from the

configurations (f7/2)(d1/2)-1

.

4. THE REVIVAL OF (1f7/2) NUCLEI

I think that such a revival is strongly

connected with the advent of the “heavy-ion era”,

which provided the possibility of producing high-

energy, high-spin states, new nuclear species and,

at the same time, the extension and improvement

of detection techniques (γ-arrays in the on-line “in

beam” γ-spectroscopy).

The research field opened in this way also

here in Legnaro with the installation of the first

Italian heavy-ion accelerator (the XTU Tandem of

16 MV) [23] .

Moreover, the advent of the ALPI

(Acceleratore Lineare per Ioni), the new

superconducting LINAC and the new ERC

injector have provided the LNL with more

energetic beams. With heavy ions new

possibilities were open.

Fig. 12: 48

Cr level scheme; experiment vs theory

(shell model with interaction).

A special case was the production of

new isotopes in the region near the proton drip

lines (neutron-deficient nuclei). Exotic 1f7/2

nuclei are of great interest, of course, and will

contribute to new insight into nuclear structure

understanding. Among them are 48

Cr24, 45

Fe19, 46

Mn21, 48

Ni20, 49

Ni21, 50

Cr23.

Another important issue is the finding of

super-and hyper-deformed rotational bands

displaying back-bending (i.e. the inversion of

the moment of inertia).

159

Let me consider some cases in point. I

start first with the 48

Ca24 and 50

Cr26 nuclei, since

they are related to results already found in the

70’s, especially when our group was involved in a

systematic research program as the Tandem

accelerator in Munich [24] .

Figure 12 shows the γ-decay scheme of 48

Cr, which is a typical (N=Z,T=0)nucleus in the

middle of 1f7/2 shell, already far from the stability

line. It is found to be a good rotor ((Q) gives

β=0.3, where β is the deformation parameter) and

its quadrupole properties are well accounted for

by the interacting shell-model (full f-p space

reducing the valence nucleons to 1f7/2-2p3/2),

together with the excellent reproduction of the

energy levels (24)

.

Figure 13 shows the plot of the yrast band

of 48

Cr showing the back bending at J>10h, as

compared with shell-model and mean-field

calculations. The good agreement with the first is

really interesting.

Fig. 13: Back-bending plot of the yrast band of 48

Cr.

Shell-model (SM), means field (CHFB) and experiment

(Exp). (J vs Eγ).

Even more interesting is the case of 50

Cr.

Recent investigations (25)

did confirm the double

back-bending as predicted, due to the addition of

two neutrons. Also in this case the collective

behavior is accounted for by the shell-model (see

Fig. 14).

Fig. 14: Back-bending plot (J vs Eγ) of the yrast

band of 50

Cr.

The progress made with respect to the

previous experiments by the Munich-Padova-

Florence group in the 70’s is evident, in spite of

the fact that the ground-state yrast band was

already found with its collective behavior (see

ref. [24]).

Other recent results are shown in Fig. 15

a), where the T=1 isobaric triplet at A=50 is

reported [26]. It consists of the 50

Cr26, 50

Mn25

and 50

Fe24. Furthermore the f7/2 spin alignment

in the mirror (N3Z) nuclei 50

Cr and 50

Fe is

shown in Fig. 15 b), indicating the possibility of

determining the Coulomb-energy difference as

displayed by the corresponding rotational bands

[27].

160

Fig. 15: a) A=50 , T=1 isobaric triplet; b) The 1f7/2

spin alignment of A=50 mirror nuclei

So far for the 1f7/2 review I could have

mentioned other enterprises in the nuclear physics

field along my personal scientific journey

especially those concerning heavy-ion reaction

mechanisms, dissipative (deep inelastic, fusion-

fission) phenomena, clustering and ternary

processes and intermediate resonance states

induced by heavy ion at low energy and in

medium-mass nuclear region; the experiments

performed at the antiproton LEAR facility at

CERN (the OBELIX collaboration) until the

LNL-CERN collaboration in the field of ultra-

relativistic heavy-ions and the search of phase-

transition in nuclear matter, with particular

emphasis on the identification of the Quark-

Gluon-Plasma, with experiments performed at the

SPS and now in preparation at the LHC (Alice

collaboration). For this I will refer to the talks of

other colleagues and friends at this conference

to whom I want to express my deep appreciation

for this gratifying presence and participation.

In fact my scientific contribution to the

conference could be not dedicated to the

research field which has always been in my

hearth and has accompanied me for many years.

So I will leave to my young colleagues (for me

all of you, with few exceptions- the “old

friends” which means “friends for ever”- are

very young) a message that I take from the

already quoted remarks of H. Morinaga.

In ending his talk in 1971 he reported a

Confucius sentence mentioned by Akito Arima

(I will also use the original types as he did):

which means: “Preserving the old and

knowing the new”.

I don’t know if Bogdan Fornal knew that

sentence or if he read the 1f7/2 book of

1971. In any case it was a good idea and a

very appreciated gift to entitle his talk

“Admiring the old and searching for the

new” (in the fp shell)” which could be

considered as a modern version of the

Morinaga quotation of Confucius.

So I will use some Morinaga’s words as

a conclusion of my message referring to a

journey as long as 40 years:

“The way we came to the present status of

1f7/2 shell is an old story (which is familiar to

those old friends of 1f7/2 shell). Actually for

me it is a real pleasure that I could meet

those old friends. But the story is somewhat

a personal version and all the new friends of

1f7/2 shell should understand that all of us,

the old friends of f7/2 shell, have some

parallel story as mine”.

a)

b)

161

On behalf of them and as a pioneer in the field,

welcome to the “new” new friends of 1f7/2 shell

(or, if you want to be more modern, the f-p shell).

Thank you.

[1] G. Chilosi, P. Cuzzocrea, G.B. Vingiani, R.A.

Ricci and H. Morinaga; Il Nuovo Cimento vol.

XXVII, n. 1, 407, 1963

[2] A.C.G. Mitchell, R. Van Lieshout, A.H. Wapstra,

R.A. Ricci and R.K. Girgis in “α,β,γ-ray

spectroscopy” edited by K. Siegbahn, North

Holland, Amsterdam 1965

[3] R.A. Ricci “Why 1f7/2 nuclei” in Proceedings of

the Int. Conf. on the Structure of 1f7/2 nuclei,

Legnaro 1971, Editrice Compositori Bologna

1971, p. 1

[4] I. Talmi, see ref. [3], p. 511

[5] R.D. Lawson and J.L. Uretsky: Phys. Rev. 106,

1369 (1957); see also R.D. Lawson, ref. 3, p. 520

[6] J.D. McCullen, B.F. Bayman and L. Zamick: Phys.

Rev. 134, B515 (1964); see also L. Zamick, ref.

[3], p. 9 ; see also J.N. Ginocchio and J.B. French;

Phys. Lett. 7, 137 (1963)

[7] H. Morinaga: see ref. [3], p. 529

[8] K. Ford and C. Levinson: Phys. Rev. 99, 792

(1955); 100, 1, 13 (1955)

[9] Cfr. B. Fornal, contribution to this conference:

“That problem was dealing with the incoming

extensive investigation on the coexistence of

single-particle and collective states in this nuclear

region which, from the experimental point of view,

has been and still is at the origin of an impressive

set of measurements and data, especially after the

advent of the nuclear structure studies with heavy-

ion reactions. I am spending some time in

reminding you these details but they are a sort of

“milestones” of the 1f7/2 story and it is what I want

to tell you also as an appropriate acknowledgement

of those pioneering works”.

[10] See W. Kutschera in Proc. of the EPS Int. Conf.

on the “Physics of Medium-Weight Nuclei”,

edited by P. Blasi and R.A. Ricci, Florence 1978,

Editrice Compositori, Bologna 1978, p. 120 [11] See R.A. Ricci “Introductory talk” in Proc.

quoted in ref. [10].

[12] R.A. Ricci and P. Maurenzig: Rivista del Nuovo

Cimento 1, 1, 1969, p. 291; see also R.A. Ricci:

Proc. Int. School of Physics, Course XL,

Varenna 1967, Ac. Press. Rend. SIF, 1969

[13] R.A. Ricci: Proc. Int. School of Physics “E.

Fermi”, Course CLIII, edited by A. Molinari, L.

Riccati, W.M. Alberico, M. Morando, 2003,

IOS Press Amsterdam, p. 627

[14] See e.g.: B.F. Baymann: Proc. Int. School of

Physics “E. Fermi”, Course XL,Varenna 1967,

Ac. Press New York 1969, p. 404

[15] See F. Brandolini, A. Brusegan, C. Signorini

and R.A. Ricci, Il Nuovo Cimento 7.1, 1972, p.

xxx; see also ref. [12] and P. Maurenzig

[16] I. Talmi, Proc. Of the Int. School “E. Fermi”,

Varenna 1976, Course LXIX, edited by A. Bohr

and R.A. Broglia, North Holland 1977, p. 352

[17] G. Chilosi, R.A. Ricci, J. Touchard and A.W.

Wapstra, Nucl. Phys. 53, 1964, 23

[18] A. Bohr and B. Mottelson, Nuclear Structure,

Vol. 1 (New York, Amsterdam) 1969, p. 343,

Table 3-3

[19] See A. De Shalit, Phys. Rev. 122, 1961, p.

1530; see also the discussion of the “center of

gravity theorem in nuclear spectroscopy”

reported in ref. [13]

[20] See A. Covello Proc. Int. School of Physics “E.

Fermi”, Course CLIII, Varenna 2002 , edited

by A. Molinari and L. Riccati (IOS Press)

2003, p. 79

[21] See F.Iachello, as ref.. [20], p. 1

[22] R.A.Ricci, J.C. Jacmart, M. Liu, M. Riou and

C. Ruhla: Nucl. Phys. A91, 1967, 609

[23] See: R.A.Ricci, Nuovo Cimento A, 81, 1994, 1;

C. Signorini, G.P. Bezzon, F. Cervellera, P.

Spolaore and R.A. Ricci, Nucl. Instr. And

Methods, 220, 1984, 30; see also R.A. Ricci,

Nucl. Instrum. Methods A, 328, 1993, 355

[24] See C. Signorini: in Proc. of the Int. School of

Physics “E. Fermi”, Course LXII, edited by H.

Faraggi and R.A. Ricci (North Holland) 1876, p.

499; and H. Morinaga ibidem, p. 351

[25] See S.M. Lenzi et al., Phys. Rev. C60, 1989,

1303; see also S.M. Lenzi, Proc. Int. School “E.

Fermi”, Varenna 2007, to be published; see also

B. Fornal, in ref. [9]

[26] S.M. Lenzi et al., Z. Phys. A354, 1996, 117;

C.E. Asvensson et al, Phys. Rev. C, 58, 1998,

R2621

[27] S.M. Lenzi et al. Phys. Rev. C60, 1999, 1303

162

ADMIRING OLD AND SEARCHING FOR NEW

IN THE fp SHELL

Bogdan Fornal

Institute of Nuclear Physics, Polish Academy of Sciences, Krakow, Poland

INTRODUCTION

The f7/2 nuclei have always been a greatscientific passion of Professor Ricci and itwas just this passion that, already in the six-ties, lead him to very extensive studies of nu-clei with 20≤Z, N≤28. The results collectedin the course of those investigations werepublished by R. A. Ricci and P. R. Mau-renzig in the paper entitled ”The f7/2 Prob-lem in Nuclear Spectroscopy” [1], sometimescalled: ”The Bible on f7/2 Nuclei”. Fora nuclear spectroscopist this review articleis invaluable - it offers a fantastic guidancethrough the labyrinths of nuclear structurenot only restricted to the f7/2 shell. Alsoin my presentation, I will use it as a basefor elaborating on one of the central issuesof modern nuclear spectroscopy - the issueconcerning evolution of the single particlestates in energy when mowing toward exoticnuclei.

One of the most striking characteristicsof nuclear structure are magic nucleon num-bers: 2, 8, 20, 28, 50, 82, and 126. Magicnumbers arise from non-uniformities of thequantum states distribution in energy, be-cause those non-uniformities form the shellsseparated by the energy gaps − completefilling of the shells occurs at magic num-bers of nucleons. The existence of the shellsreflects the fact that nucleons occupy welldefined orbitals and this, in turn, tells usthat they move in a well defined average po-tential. Theoretical picture of a nucleus inwhich the single particle states are calcu-

lated in an average potential well with ad-dition of a spin-orbit term, was developedby Maria Goeppert-Maier and Hans Jensenin 1949 (they were awarded for it the NobelPrize in 1963).

It has been widely discussed of what hap-pens to the arrangement of the single par-ticle levels established for nuclei along thestability valley, when going toward exoticregions of the nuclidic chart. In particu-lar, it is not obvious whether the classicalmagic numbers are valid away from the sta-bility line. It is remarkable that the prob-lem of the single particle states evolutionalong isotopic or isotonic chains of nucleiwas addressed and deeply discussed alreadyin ”The Bible on f7/2 Nuclei”, i.e., fourdecades ago. Let us now focus our attentionon the region of nuclei in which the f7/2,p3/2, f5/2, and p1/2 orbitals are being filledand let’s try to see what one can say aboutthe locations of these single particle states.Figure 1 displays a portion of the historicalpicture from Prof. Ricci’s talk in Varenna in1969 [2], in which he illustrates the results ofan extraordinary analysis of the single par-ticle state behavior in energy in nuclei from40Ca to 48Ca and then from 48Ca to 56Ni.

An extended representation of that pic-ture, supplemented by additional informa-tion from Ref. [2] and from the studies ofneutron orbitals along the N = 28 istones,is shown in Figure 2. It is clear that thechanges of relative positions of the orbitalsare huge even though only very limited re-gion of nuclei is examined. For example,

Conference Proceedings Vol. 96“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”F. Gramegna, M. Cinausero, D. Fabris (Eds.)SIF, Bologna 2008

163

FIG. 1: Portion of Fig. 11 from Ref. [2] show-ing the changes in energy of proton single par-ticle states in the fp shell from 41Sc to 49Sc.

near the doubly magic 56Ni the three neu-tron single particle states p3/2, p1/2 and f5/2

are very close to each other, whereas near48Ca they are well separated in energy andtheir spacing is of similar size as that be-tween f7/2 and p3/2, the latter being respon-sible for the shell closure in 48Ca.

Such an observation could have pointed tothe presence of subshell closures associatedwith the filling of the p3/2 orbital, i.e., atN = 32 and, possibly, with the filling of thep1/2 state, i.e., at N = 34 in neutron-richnuclei. However, the issue did not receivemuch attention at the time, as the structureof neutron-excessive nuclei with Z ∼ 20 ap-peared to be out of reach.

SUBSHELL CLOSURE AT N = 32

First information on the possible exis-tence of an N = 32 subshell closure forneutron-rich nuclei just above 48Ca came

FIG. 2: Evolution of proton and neutron single-particle energies (relative to the 2p3/2 state),

when moving from 41Sc to 49Sc, and from 49Cato 57Ni.

in the eighties. The phenomenon was sug-gested by A. Huck et al. [3] who tentativelyidentified a candidate for the 2+

1 state in52Ca with an excitation energy of 2563 keVthat is significantly higher than the corre-sponding 2+ energy in 50Ca. However, theconsiderable uncertainty associated with thespin and parity assignments to this state (in52Ca) did not give much credence to the is-sue. Further indication of development of anenergy gap at N = 32 in neutron-rich nucleiarose from the systematic variation of theE(2+

1 ) energy for the chromium (Z = 24)isotopes, which was found to reach a max-imum in 56Cr32 [4]. At that point, it wasobvious that crucial information on the oc-currence of the N = 32 subshell gap shouldbe provided by data on the yrast structuresof the Z = 20−22 species with N ∼ 32, butthese nuclei are again very neutron rich and,until very recently, their structure was com-pletely unknown. This situation, however,was going to change.

In a series of past experiments, we haveshown that the yrast spectroscopy of hard-

164

to-reach neutron-rich nuclei, populated inheavy-ion multi-nucleon transfer reactions(at energies 15-25% above Coulomb bar-rier), can be studied successfully in γγ co-incidence measurements with a thick target[5–7]. Production of neutron-rich species inthese processes is possible due to a tendencytowards N/Z equilibration of the di-nuclearsystem formed during collision. Usually,in the studied reactions the projectile hadlower N/Z ratio than the target nucleusand, as a result, production of species moreneutron-rich than the light colliding part-ner was favored. Taking into account theseconsiderations, the bombardment of thick208Pb and 238U targets with a 48Ca beamseemed to offer good prospects in reachingnuclei with larger neutron excess than 48Ca,i.e., neutron-rich titanium, scandium andcalcium isotopes.

Two experiments were performed at Ar-gonne National Laboratory employing a48Ca beam from the Argonne Tandem Lin-ear Accelerator System (ATLAS) and thegermanium multidetector array GAMMAS-PHERE, which consisted of 101 Compton-suppressed Ge detectors. During the firstrun, a 305 MeV beam was focused on a50 mg/cm2 208Pb target. In the second,the projectile energy was 330 MeV and a50 mg/cm2 238U target was used. Gamma-ray coincidence data were collected with atrigger requiring three or more Compton-suppressed γ rays to be in prompt coinci-dence. Energy and timing information forall Ge detectors that fired within 800 ns ofthe triggering signal was stored. The beam,coming in bursts with ∼0.3 ns time width,was pulsed with ∼400 ns repetition time,providing clean separation between promptand isomeric events. A total of 8.1×108 and2.3×109 three- and higher-fold events wererecorded in the first and second measure-ments, respectively. Conditions set on the

γγ time parameter were used to obtain var-ious versions of prompt and delayed γγ andγγγ coincidence matrices and cubes cover-ing γ-ray energy ranges up to ∼4 MeV.

In γ-ray spectroscopic studies of the deep-inelastic reaction products, identification ofan unknown sequence of γ rays to a spe-cific product may be possible by using thecross-coincidences with transitions in reac-tion partners. In the case of the 48Ca+208Pbsystem, complementary products in binaryreactions leading to Ti isotopes are Hg nu-clei, but a given Ti product is in coincidencewith several Hg partners because of neu-tron evaporation from the fragments afterthe collision. The situation is illustrated inFigure 3, where the spectrum arising from asum of double gates on known transitions in196Hg is presented. This spectrum, accord-ing to expectations, displays known linesfrom 50Ti, 51Ti and 52Ti, which are part-ners to 196Hg associated with 10, 9 and 8evaporated neutrons, respectively. Furtherinspection of the spectrum revealed also thepresence of unknown gamma rays at ener-gies 1002, 1237, 1495 and 1576 keV. Thesegamma rays were observed also in the spec-tra gated on transitions from the Hg iso-topes with A=197-200 which indicated thatthey originate from the titanium products.It seemed very likely that the new transi-tions occur in the Ti isotopes with massesA>52.

Pursuing this hypothesis we applied theidentification method based on the γ-ray cross-coincidence intensities. For the50,51,52Ti reaction products, the mean massAav(Hg) of the complementary mercuryfragments was determined from the Hg γ-ray intensities measured in coincidence withthe γ rays of that particular Ti isotope. Thesame procedure of calculating the Hg meanmass was applied also to newly found 1237,1495 and 1576 keV Ti lines. The results are

165

FIG. 3: Part of a coincidence γ-ray spectrumfrom the 48Ca+208Pb reaction gated on pairs ofyrast transitions in 196Hg showing gamma raysbelonging to Ti partners.

illustrated in Figure 4, where the Aav(Hg)as a function of A(Ti) is shown. The datapoints corresponding to the known gammarays from 50,51,52Ti nuclei exhibit a smoothcorrelation. The Aav(Hg) for the new tran-sitions fit nicely into this pattern, if one as-signs the 1237 and 1576 keV gamma rays to53Ti and the 1495 keV gamma ray to 54Ti.

FIG. 4: Plot of average mass Aav(Hg) ofcomplementary Hg fragments against Ti prod-uct mass A(Ti) deduced from γ-ray cross-coincidence intensities. See text for details.

The suggestion that the 1495 keV line isa transition in 54Ti, was fully supported by

the data from an experiment performed atMichigan State University (National Super-conducting Cyclotron Laboratory), in whicha beta-decay measurement of the 54Sc par-ent produced in fragmentation of a Kr beam,was studied. The MSU measurement iden-tified the first two gamma-ray transitions in54Ti: 2+→0+ with energy of 1495 keV and4+→2+ with energy of 1002 keV [8].

Using the 1495 keV transition as a ”start-ing point” in the analysis of γγ coincidencedata, we could establish the yrast structurein the 54Ti nucleus up to an energy of ∼6.5MeV. The details of the procedure are re-ported in Ref. 8 and the experimental levelscheme of 54Ti is shown in Figure 5a. Thelow lying yrast sequence is dominated by the2+, 4+ and 6+ states, members of the πf2

7/2

multiplet. The higher yrast excitations arisefrom the configurations involving streachedcoupling of the two f7/2 protons and promo-tion of a neutron to the p1/2 and f5/2 singleparticle states.

As we have just seen, valuable results onnew yrast excitations in the 54Ti isotopewere obtained following deep inelastic reac-tions between a thick 208Pb target and a305 MeV 48Ca beam. However, no infor-mation on 56Ti could be derived from thisdata set. It was then decided to investigatethe 48Ca+238U system instead, in order totake advantage of the larger neutron reser-voir provided by the 238U target. The largerN/Z ratio of 1.59 for the latter target com-pared to the corresponding value of 1.54 for208Pb, was viewed as hope for a productdistribution extending significantly towardsmore neutron-rich nuclei, including the 56Tiisotope of interest here.

At first, it should be recognized that inthe case of the 238U target, the target-likeproducts of deep-inelastic processes mostlyundergo fission. Thus, an identificationbased on cross-coincidence relationships be-

166

FIG. 5: Level schemes constructed for 54Ti and56Ti.

tween gamma rays from reaction partners,such as that performed for the 48Ca + 208Pbsystem reported earlier, is not possible. In-stead, another method for identifying thestarting transitions has to be applied. In thecase of 56Ti, a starting point for the analy-sis was provided by a β-decay study of the56Ti parent, 56Sc [9, 10], which identified a2+→0+ γ ray with an energy Eγ=1127 keV.

A search aimed at finding transitions feed-ing this 2+ excitation, i.e., being in coinci-dence with the 1127 keV line in the 48Ca+ 238U coincidence data set, displayed onlytwo, mutually coincident γ rays with en-ergies of 1161.0 and 690 keV. Taking intoaccount that deep-inelastic reactions pref-erentially populate yrast states, an assign-ment of the 1161 and 690 keV γ rays tothe 4+→2+ and 6+→4+ transitions is thenstraightforward. These two transitions lo-cate the 4+ and 6+ levels at excitation en-

ergies of 2290 and 2980 keV, respectively, asindicated in the level scheme of Figure 5b.

Let us take a look at the new findingsin 54,56Ti from the perspective of system-atics of the lowest yrast excitations in theeven Ti nuclei that is shown in Fig. 6.The observed features of yrast structure of54Ti, such as the relatively high energy ofthe 2+

1 state and the energy spacings be-tween the Jπ = 0+, 2+, 4+, 6+ excitationssimilar to those in the N = 20 42Ti andN = 28 50Ti magic isotopes, are charac-teristic for a magic nucleus and fully sup-port the existence of the N=32 subshell clo-sure in neutron-rich species close to Z = 20.This new subshell closure can be attributedto the existence of a sizeable energy gapbetween the νp3/2 and higher lying νp1/2,νf5/2 orbitals for neutron-rich nuclides hav-ing Z<24. Such a scenario is in line with thesingle particle state arrangement reportedby Prof. Ricci in Ref. [2] (Fig. 2.).

FIG. 6: Systematics of the πf27/2 2+, 4+, and

6+ states in even-even Ti isotopes.

Our spectroscopic finding regarding thethree lowest yrast states 2+, 4+ and 6+ in54Ti, which mirror the 2+, 4+ and 6+ ar-rangement in 50Ti, was associated with alot of excitement. Similar excitement musthave experienced also the researchers who

167

located the first three yrast states in 50Tiand found that their energies are almostidentical to those in 42Ti. Among the pi-oneers who explored for the first time thestructure of 50Ti was Professor Ricci. Infact, the first data on the lowest excitationsin 50Ti were obtained by the group of theItalian physicists G. Chilosi, P. Cuzzocrea,G. B. Vingiani, R. A. Ricci and H. Morinagain Napoli in 1962 (they used beta decay ofthe 50Sc parent produced by irradiation of atitanium matallic foil with 14 MeV neutronsfrom the AN 400 accelerator) [11]. As onecan see, it took more than forty years to ex-tend the knowledge on yrast excitations inthe Ti isotopes by 4 neutrons. On this oc-casion, it is also worth to note that in addi-tion to the 50Ti and 54Ti isotopes, membersof the pure f2

7/2configuration are known in

other two magic nuclei: 42Ca and 42Ti. Thepresence of a pure configuration of two iden-tical nucleons on the same high-spin orbitalin four different nuclei is a unique featurein the nuclidic chart. Figure 7 shows theselowest excitations in 42Ca, 42Ti, 50Ti and54Ti − all they are remarkably similar interms of the energy spacings. Apparently,to a good approximation the interaction ofthe two f7/2 nucleons does not depend nei-ther on the isospin nor on the doubly closedcore.

LARGE-SCALE SHELL-MODEL

CALCULATIONS

Recently, it became possible to performshell model calculations in the full fp shelland our new data on the structure ofneutron-rich nuclei may serve as a test-ing ground for various interactions. Letus recall two Hamiltonians developed forthe fp shell: a new interaction, labeledGXPF1A, that was worked out by Honma et

al. [12], and another empirical Hamiltonian

FIG. 7: The πf27/2 2+, 4+, and 6+ states in

two-valence-nucleon nuclei.

constructed for nuclei in the fp-shell, namedKB3G [13]. As shown in Figure 8, thefull fp-shell model calculations employingthe GXPF1A and KB3G Hamiltonians aresuccessful in describing the yrast structurein 54Ti - particularly good agreement pro-vides the GXPF1A interaction and the re-sults from this Hamiltonian often were usedas guidance for the spin-parity assignmentsproposed in the measured level scheme.

Figure 9 compares the results of the fullfp shell-model calculations with the twoHamiltonians to the available data on the2+

1 energies for the Cr, Ti and Ca isotopicchains. Both interactions give a good de-scription of the variations in the experimen-tal 2+

1 energies near N = 28 and N = 32.However, there is a striking discrepancy be-tween the two types of calculations in 54Ca,for which no measured value is available: theGXPF1A Hamiltonian predicts the 2+ en-ergy at very high value, ∼3 MeV, whereasthe KB3G interaction gives for it a valueslightly above 1 MeV.

Differences in the predictions of the twoHamiltonians regarding the 2+

1 location inthe 54Ca nucleus can be associated with dif-ference in the effective single particle ener-

168

FIG. 8: Comparisons between shell-model cal-culations with the GXPF1A and KB3G Hamil-tonians and data for 54Ti.

gies of the νp3/2 and νp1/2 orbitals withrespect to the νf5/2 state in neutron-richnuclei. According to the the GXPF1AHamiltonian the magnitude of this separa-tion in heavy Ca isotopes is large, whereasthe KB3G interaction produces rather smallspacing. As mentioned earlier [2] and shownin Fig. 2, studies of the location of single-particle states in 49Ca pointed to a size-able (∼2 MeV) energy gap between thetwo higher lying neutron orbitals p1/2 andf5/2 - this observation gives support to theGXPF1A predictions. From a broader per-spective, the issue is of special importancebecause the presence of the νp1/2−νf5/2 en-ergy gap could possibly produce a subshellclosure associated with the filling of the p1/2

state, i.e., at N = 34 in neutron-rich nu-

FIG. 9: Systematics of the 2+

1 energies inthe even Cr, Ti and Ca isopes compared tothe results of shell-model calculations with theGXPF1A and KB3G interactions.

clei. To verify this hypothesis, the magni-tude of the energy separation between thef5/2 and p1/2 orbitals in neutron-rich Ca iso-topes needed to be derived from experimen-tal data, although one should be aware thatthis task represents a significant challengeas the states involving the f5/2 neutron inisotopes such as 51,53Ca are rather difficultto reach.

169

IS THERE AN ENERGY GAP

BETWEEN νp1/2 AND νf5/2?

Using again the thick target γγ coinci-dence data from GAMMASPHERE for thesystems 48Ca+208Pb and 48Ca+238U, andanalyzing the observed production yields forthe 48−56Ti isotopes, it became clear that,particularly in reactions on the 238U tar-get, Ca isotopes with masses up to 51 orhigher had to be present in the data set withcross sections sufficient to examine in detailthe coincidence relationships required to es-tablish significant level schemes. This con-clusion was supported further by the factthat coincidence events were observed be-tween known gamma rays emitted in thebeta decay of 51Ca. Firm identification ofgamma rays in the 51Ca case was, how-ever, very difficult because of a rather lowproduction rate and the limited informa-tion on the location of the yrast states pro-vided by the 51,52K beta-decay measure-ments. The help came from a new, inde-pendent experiment in which the same re-action, 48Ca+238U, was studied, but witha thin target and gamma rays were de-tected in coincidence with reaction prod-ucts identified in a magnetic spectrome-ter. In this second measurement, the sameprojectile-target combination, 48Ca+238U,was investigated at the Laboratori Nazion-ali di Legnaro using the ALPI acceleratorand the CLARA+PRISMA detection setup[14–16]. In this case, the 330-MeV 48Cabeam was impinging on a 238U target of 600µg/cm2 thickness, placed in the center of theCLARA germanium detector array consist-ing of 24 Compton-suppressed clover detec-tors. The PRISMA magnetic spectrometer,used to identify product nuclei, was posi-tioned at 53 degrees with respect to beamdirection, i.e., in the vicinity of the grazingangle. The spectrometer was set up for the

detection of nuclei close in mass to the pro-jectile and the event trigger required the de-tection in coincidence of a single gamma rayin CLARA and an ejectile at the PRISMAfocal plane.

Prior to the present investigations, theonly information available on the 51Ca nu-cleus originated from the beta decay studyof neutron-rich 51K and 52K by Perrot etal. [17]. Excited states at 1718, 2377, 2934,3460, 3500 and 4493 keV were proposed, butonly the 3460-keV level was tentatively as-signed 7/2− spin and parity quantum num-bers. The analysis reported here startedfrom the gamma-ray spectrum measured bythe CLARA array in coincidence with 51Caproducts; the latter is presented in Figure10. Among the gamma lines found in thespectrum appear three transitions with re-spective energies of 2378, 2934 and 3462 keVwhich had been observed earlier in beta de-cay. Other weak lines in the spectrum ofFig. 10 must also belong to 51Ca, but theirordering and mutual coincidence relation-ships could not be established due to the lowstatistics of the gamma-gamma-ejectile co-incidence data. In this situation, the set ofgamma-ray coincidence data obtained withthe thick target at GAMMASPHERE pro-vided crucial complementary information.

In thick target experiments only gammarays emitted from stopped products appearin the spectra as sharp lines (with the widthpractically equal to the intrinsic energy res-olution of the germanium crystal). As aresult, one can display only those gammatransitions, for which the cumulative emis-sion time is comparable or longer than theproduct stopping time (typically of the or-der of 1 ps). This feature poses a limitationon this experimental technique. However,since deep-inelastic processes populate pref-erentially yrast states, the associated halflives involved are often long enough to ex-

170

FIG. 10: Gamma-ray spectrum measured in thethin-target experiment with a gate on 51Ca re-action products identified at the focal plane ofthe PRISMA spectrometer.

plore level sequences up to moderate spin.Using the GAMMASPHERE data set, we

examined the gamma-ray spectrum gated onthe 2378 keV transition, which is the mostprominent gamma line observed in coinci-dence with the 51Ca products. The inspec-tion of the spectrum revealed a series ofweak peaks, potential candidates for gammarays in 51Ca. However, only two out of thosecandidates satisfied the condition of beingpresent also in the 51Ca product gated spec-trum: these were 1466 and 1942 keV lines.Subsequently, a double gate set on the 1466and 2378 pair of gamma rays in the promptγγγ cube displayed the 476 and 311 keVlines both also seen in coincidence with the51Ca product. On the basis of those findingsand other coincidence relationships we wereable to construct an extended level schemefor 51Ca that is shown in Figure 11.

The level scheme established in thepresent work for 51Ca is compared in Fig. 11with the results of shell-model calculationswith the GXPF1A interaction. Based onthe fact that deep-inelastic processes, usedhere to produce the nuclei of interest, pop-ulate preferentially the yrast and near-yraststates, taking into consideration the decay

FIG. 11: Comparison between shell-model cal-culations with the GXPF1A Hamiltonian anddata for 51Ca.

pattern, and guided by the results of theshell model calculations we made tentativespin-parity assignments. Of special interestis a state identified at 4320 keV with a spin-parity assignment of 9/2− which is expectedto involve the promotion of a neutron intothe νf5/2 orbital - the relative location inenergy of that orbital near Z ∼ 20 playsa decisive role in the presence or absenceof a significant N = 34 shell gap in 54Ca.With the character of the 9/2− excitation in51Ca established, the opportunity arises toinspect in detail the behavior of the exper-imental and calculated states with configu-rations involving the νf5/2 orbital along anextended isotonic N = 31 chain, as detailedspectroscopic information is also availablefrom Refs. [18, 19] for 53Ti and 52Sc. Figure12 displays the partial level schemes of thethree nuclei and compares the states of in-terest with the results of shell model calcula-tions with the GXPF1A and KB3G interac-tions. The yrast states containing the νf5/2

171

orbital in their main configuration are: the4320-keV, 9/2− level in 51Ca, the 3603-keV,8+ state in 52Sc, and the 21/2− level at 6056keV in 53Ti. For the GXPF1A Hamilto-nian, the agreement between the experimen-tal and the calculated values is very good inthe heaviest isotone. However, the devia-tion between the data and the results of thecalculation, increases slightly in 52Sc, andbecomes even larger for 51Ca. In turn, theKB3G calculations underestimate the 9/2-energy in all three cases by several hundredsof keV. Thus, the observed behavior of thestates with predominant f5/2 configurationsuggests that the f5/2 in Ca nuclei is locatedat higher energy than the value given by theKB3G Hamiltonian, but, on the other hand,this energy might be somewhat smaller thanthat predicted by the GXPF1A interaction.The results, however, do not rule out thepresence of a sizeable gap at N = 34, leav-ing the experimental determination of thisfeature as an interesting challenge.

OUTLOOK

By identifying yrast states in the heavyTi isotopes, we have established the pres-ence of a new subshell closure at N = 32 inneutron excessive nuclei. We have also ob-tained information on the energy separationbetween the νp1/2 and νf5/2 neutron or-bitals in the neutron-rich Ca isotopes, whichdoes not exclude the existence of a sizeableenergy gap at N = 34. Even though theseare only the first steps in exploration of theneutron-rich territory, we already see thatin the new regions of nuclear chart the sin-gle particle structure may be different withrespect to that known in the vicinity of thestability valley. The studies along this lineare particularly important for nuclear astro-physics, because it is the structure of ex-otic nuclei that strongly determines the r-

FIG. 12: Comparisons between experiment andshell-model calculations with the GXPF1A andKB3G Hamiltonians for states involving excita-tions of a νf5/2 neutron in the N = 31 isotones51Ca, 52Sc and 53Ti.

process path. Obviously, to advance theinvestigations one needs radioactive beamfacilities, one also will have to use newexperimental techniques. It is very likelythat one of the most effective methods forstudying the structure of neutron-rich exoticspecies will be the gamma-ray spectroscopyof deep-inelastic reactions products. Lab-oratori Nazionali di Legnaro with the al-ready available instruments like PRISMAand with the ongoing SPES project aimedat development of radioactive beams, may

172

become one of the world centers for such in-vestigations.

The present excellence of LNL owes verymuch to Professor Ricci. On the occa-sion of today’s celebration, I would like towish You, Professor, that always continuesYour passion for nuclear spectroscopy andother fields of nuclear physics, Your pas-sion for science which, as You said to theyoung people during the lecture in Varennain 2003, ”is a great intellectual adventure ofhumankind on one hand and a school of crit-icism, freedom and tolerance on the other”.The outstanding role of science in bringingthose ideas closer to life was proven manytimes in the history. One of the best ex-amples is the work of Nicolaus Copernicus.In the Book 1 of his opus ”De revolution-ibus orbium coelestium” (the manuscript ofwhich is located in the Jagiellonian Libraryin Krakow) one finds a sentence that soundsvery familiarly in the context of our discus-sion: ”All the good arts serve to draw man’smind away from vices and lead it towardbetter things”. The concepts of those ”bet-ter things”, which include ”criticism, free-dom and tolerance” were rooted very deeplyat LNL by Professor Ricci, other Professors,and their Followers and have served as abase for developing many fruitful collabo-rations. The collaboration between the In-stitute of Nuclear Physics PAN in Krakowand LNL is a very good example of it.

ACKNOWLEDGMENTS

The results presented in this lecture havebeen obtained in the frame of collaborationsthat gathered researchers from many insti-tutions. The list of the names includes:R. Broda, W. Krolas, T. Pawlat, and J.Wrzesinski from IFJ PAN Krakow, Poland;R.V.F. Janssens, S. Zhu, M.P. Carpenter,D. Seweryniak et al. from ANL Argonne,

USA; P. Mantica, B.A. Brown et al. fromMSU East Lensing, USA; M. Honma fromthe University of Aizu, Japan; T. Otsukafrom the University of Tokyo, Japan; P.J.Daly, Z.W. Grabowski from Purdue Univer-sity, USA; S. Beghini, M. Cinausero, L. Cor-radi, G. De Angelis, F. Della Vedova, E.Farnea, E. Fioretto, A. Gadea, B. Guiot,S. Lunardi, N. Marginean, P. Mason, G.Montagnoli, D.R. Napoli, F. Scarlassara, A.M. Stefanini, D. Seweryniak, S. Szilner, C.A. Ur, J. J. Valiente-Dobon, G. Viesti etal. from INFN di Legnaro, INFN Sez. DiPadova, and from Padova University.

[1] R. A. Ricci, and P. R. Maurenzig, Riv.Nuovo Cim. 1, 291 (1969).

[2] R. A. Ricci, Proceedings of the Interna-tional School of Physics ”Enrico Fermi”,Course XL, edited by M. Jean and R. A.Ricci (Academic Press) 1969, p. 80.

[3] A. Huck et al., Phys. Rev. C 31, 2226(1985).

[4] J. I. Prisciandaro et al., Phys. Lett. B510,17 (2001).

[5] R. Broda, J. Phys. G 32, R151 (2006).[6] B. Fornal et al., Acta Phys. Pol. B 26, 357

(1995).[7] W. Krolas et al., Nucl. Phys. A724, 289

(2003).[8] R. V. F. Janssens et al., Phys. Lett. B546,

55 (2002).[9] S. N. Liddick et al., Phys. Rev. Lett. 92,

072502 (2004).[10] S. N. Liddick et al., Phys. Rev. C 70,

064303 (2004).[11] G. Chilosi, P. Cuzzocrea, G. B. Vingiani,

R. A. Ricci and H. Morinaga, Nuovo Cim.27, 86 (1963).

[12] M. Honma, T. Otsuka, B. A. Brown, andT. Mizusaki, Eur. Phys. J. A 25 suppl. 1,499 (2005); M. Honma, T. Otsuka, B. A.Brown, and T. Mizusaki, Phys. Rev. C 65,061301(R) (2002).

[13] A. Poves, J. Sanchez-Solano, E. Caurier,F. Nowacki, Nucl. Phys. A694 (2001), 157

173

(2001).[14] A. M. Stefanini et al., Nucl. Phys. A701,

217c (2002).[15] A. Gadea et al., Eur. Phys. J. A 20, 193

(2004).[16] S. Szilner et al., Phys. Rev. C 76, 024604

(2007).

[17] F. Perrot et al., Phys. Rev. C 74, 014313(2006).

[18] B. Fornal et al., Phys. Rev. C 72, 044315(2005).

[19] B. Fornal et al., Phys. Rev. C 77, 014304(2008).

174

REACTION MODELS FOR EXOTIC NUCLEI

Angela Bonaccorso ∗

Istituto Nazionale di Fisica Nucleare, Sez. di Pisa,

Largo Pontecorvo 3, 56127 Pisa, Italy.

I. INTRODUCTION

Nuclear reaction theory has experienceda great revival in the last twenty years fol-lowing the large increase in quantity as wellas quality of experiments with exotic beams.Exotic nuclei are located away from the sta-bility valley and have large differences inthe number of neutrons and protons. Theirvalence particle separation energies Sn aresmaller than the average 8 MeV expectedin nuclear matter. In the extreme case ofhalo nuclei such as several beryllium andlithium isotopes (11Be,12Be,14Be,11Li), Sn

can be even less than 1 MeV. As a conse-quence as much as 10% of the total reactioncross section is due to just one channel: 1nor 2n breakup. Therefore, out of necessity

(N. Orr), breakup has been the most stud-ied reaction for very weak beams and theone for which several new models have beendeveloped.

In this short review I will first present themechanisms which lead to breakup and therelative observables that are measured. Foreach of them a description will follow of themost recent advances in the models used fortheoretical calculations.

∗In collaboration with C.A. Bertulani, G.Blanchon, D.M. Brink, F. Carstoiu, A. Garcıa-Camacho, A.A. Ibraheem, J. Margueron,N.Vinh Mau.

II. CROSS SECTION

Most theoretical methods used so far todescribe breakup rely on a basic approxi-mation to describe the collision with onlythe three-body variables of nucleon coordi-nate, projectile coordinate, and target coor-dinate. Thus the dynamics is controlled bythe three potentials describing nucleon-core,nucleon-target, and core-target interactions.Often the projectile-target relative motion istreated semiclassically by using a trajectoryof the center of the projectile relative to thecenter of the target R (t) = bc + vtz withconstant velocity v in the z direction and im-pact parameter bc in the xy plane. This ap-proximation makes the formalism applica-ble for incident energies above the Coulombbarrier. Along the semiclassical trajectorythe amplitude for a transition from a nu-cleon state ψi bound in the projectile, to afinal continuum state ψf , is given by [1,2]

Afi =1

ih

∫ ∞

−∞

dt〈ψf (r, t)|V (r,R(t))|ψi(r, t)〉,

(1)

where V is the interaction responsible forthe transition which will be specified in thefollowing. The probabilities for differentprocesses can be represented in terms of theamplitude as dP/dξ =

∑

|Afi|2δ(ξ − ξf )

where ξ can be momentum, energy or anyother variable for which a differential crosssection is measured.

Direct one-particle re-arrangment reac-tions of the peripheral type in presence ofstrong core-target absorption can be de-scribed by an equation like [2–5]

Conference Proceedings Vol. 96“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”F. Gramegna, M. Cinausero, D. Fabris (Eds.)SIF, Bologna 2008

175

dσ−n

dξf= C2S

∫

dbc

dPbup(bc)

dξfPct(bc), (2)

(see Eq. (2.3) of [3]) and C2S is the spec-troscopic factor for the initial single par-ticle state. The core survival probabilityis defined in terms of a S-matrix functionof the core-target distance of closest ap-proach bc. A simple parameterisation isPct(bc) = |Sct|

2 = e(− ln 2exp[(Rs−bc)/a]). Ittakes into account the peripheral nature ofthe reaction and naturally excludes the pos-sibility of large overlaps between projectileand target. The strong absorption radius

Rs ≈ 1.4(A1/3p + A

1/3t ) fm is defined as the

distance of closest approach for a trajectorythat is 50% absorbed from the elastic chan-nel and a=0.6 fm is a diffuseness parameter.The values of Rs thus obtained agree withina few percent with those of the Kox param-eterization [6].

III. BREAKUP MECHANISMS

Based on the time dependent amplitudeEq.(1) and the classical projectile-targettrajectory of relative motion given above,in Ref. [4] we considered the breakup of ahalo nucleus like 11Be consisting of a neu-tron bound to a 10Be core in a collisionwith a target nucleus. The system of thehalo nucleus and the target was describedby Jacobi coordinates (R, r) where R is theposition of the center of mass of the halonucleus relative to the target nucleus andr is the position of the neutron relative tothe halo core, and the coordinate R is as-sumed to move on a classical path. TheHamiltonian of such a system is H = TR +Tr+Vnc (r)+Vnt (β2r + R)+Vct (R − β

1r) ,

with β1 and β2 the mass ratios of neutronand core, respectively, to that of the projec-tile. TR and Tr are the kinetic energy oper-ators associated with the coordinates R andr and Vcn is a real potential describing theneutron-core final state interaction. Vcn was

neglected under the hypothesis that the ob-servables measured and calculated did notdepend significantly on it. In Sec.V we willdiscuss cases in which such an interactiondominates instead the measured data. Thepotential V2 = Vnt + Vct describes the inter-action between the projectile and the tar-get. It is a sum of two parts depending onthe relative coordinates of the neutron andthe target and of the core and the target.Both Vnt and Vct are represented by com-plex optical potentials. The imaginary partof Vnt describes absorption of the neutronby the target to form a compound nucleus.It gives rise to the stripping part of the halobreakup we will describe in Sec. IV. Theimaginary part of Vct describes reactions ofthe halo core with the target. The poten-tial Vct also includes the Coulomb interac-tion between the halo core and the target.This part of the interaction is responsiblefor Coulomb breakup. In fact the Coulombforce does not act directly on the neutronbut it affects it only indirectly by causingthe recoil of the charged core.

Since the mass ratio β1 is small for ahalo nucleus with a heavy core (β1 ≈0.1 for 11Be) the Coulomb potential wasapproximated by the dipole term in Ref.[4]. Then, making an eikonal approxima-tion for the neutron final state ψf (t) =exp (ik · r − iεkt/h) exp

(

− 1ih

∫ ∞

t V2 (r, t) dt)

,the amplitude became

Alm (k,bc ) =1

ih

∫

d3rdte−ik·r+iωt

×e( 1

ih

∫

∞

tV2 (r,R(t) )dt )

×V2 (r,R(t) )φlm (r) (3)

where ω = (εk − εi) /h and φlm is the ra-dial part of the neutron initial wave func-tion. k is the neutron-core relative momen-tum vector in the final state. The corre-sponding energy is εk, while εi is the initialstate binding energy. Eq. (3) is appropri-ate to calculate the coincidence cross sectionAp → (Ap − 1) + n.

176

The components Vnt and Vct of V2 aretreated differently because of the long rangeof the Coulomb interaction. The neutron-target interaction is strong and has a shortrange. We assumed that the interactiontime τ for this part of the interaction is veryshort in the sense that ωτ is small comparedwith unity. On the other hand the longrange Coulomb interaction between the halocore and the target is weaker and changesmore slowly. The way to treat it is discussedin the next subsection.

A. Coulomb breakup

Introducing the notation Vc = ZcZte2,

Vv = ZvZte2 and VC = (Zv + Zc)Zte

2, withZv = 0, 1 for a neutron and for a protonrespectively, the Coulomb potential can bewritten as

V (r,R) =Vc

|R − β1r|+

Vv

|R + β2r|−

VC

R.

(4)

Here β1 can be also the mass ratio ofthe proton to that of the projectile. InRef. [7] we have shown that the Coulombphase χeff (bc, r, k) =

∫

dteiωtVC(r, t)/h.which is solvable in the dipole approxima-tion, can similarly be calculated with thewhole multipole expansion if a screeningterm is added and subtracted to the poten-tial, suct that it can be written as V (r,R) =

Vsh(r,R) + Vlo(r,R) = VC [( e−γ|R−β1r|

|R−β1r|−

e−γR

R )+(− 1−e−γ|R−β1r|

|R−β1r|+ 1−e−γR

R )]. The term

Vsh contains the singularity at R=0 but de-cays quickly with the impact parameter. Onthe other hand, Vlo, well-behaved at the ori-gin, accounts for the long-range characterof the Coulomb potential. When inserted inthe integral for χeff , these two terms can betreated in different ways if the parameter γis big enough. In this case, as done in [4]

with the nuclear potential, Vsh can be con-sidered in the sudden approximation, yield-ing a phase χsudd(bc, r) =

∫

dtVsh(r, t)/h,whereas Vlo needs to keep the whole timeevolution description, but, being weak,it can be approximated to first orderχpert(bc, r, k) =

∫

dteiωtVlo(r, t)/h. There-fore the Coulomb phase becomes a sum oftwo terms χeff (bc, r, k) = χsudd(bc, r) +χpert(bc, r, k), both of them depending uponthe screening parameter γ. In order forthis approximation to be valid, the screen-ing term γ needs to be sufficiently largeas to ensure that the range of Vsh re-mains short enough, and that Vlo doesnot become too large. This is nextachieved by taking just γ = ∞, in whichcase χsudd = 0, and χeff = χpert =2VC

hv

(

eiβ1ωz/vK0(ωbc/v) − K0(ωR⊥/v))

.

0 5 10 15

ε (MeV)

1

10

100

1000

σ (

mb)

FIG. 1. Integrated breakup cross-section for ahypothetical 34Si beam against Pb at 70 A.MeVas a function of the neutron separation energy.Different initial parameters: circles (squares)are for Coulomb (nuclear) breakup from an ini-tial s-wave; diamonds (triangles) for Coulomb(nuclear) breakup from a d-wave; pluses (stars)for Coulomb (nuclear) breakup from an initialf-wave. Nuclear breakup is the sum of diffrac-tive and stripping contributions.

B. Sudden limit and all-order treatment

Aiming for an all-order formalism, in [4]it was shown that a possible way to achieve

177

this is to use the sudden approximation,subtract the first order term, which divergesfor large impact parameter, and then toadd a first order term calculated in time-dependent perturbation theory. The sud-den limit (ω → 0) must be therefore takenin the above expression for χeff , yielding

χsuddeff = 2VC

hv log bc

R⊥. Following a procedure

analogous to that of [7], the Coulomb phasefor the proton is shown to be [8]

χp =2

hv(Vce

iβ1ωz/vK0(ωbc/v)

− VCK0(ωR⊥/v)

+ Vve−iβ2ωz/vK0(ωbv/v)). (5)

Since VC = Vc + Vv, Eq. (5) can be writ-ten as χp = χ(β1, Vc) + χ(−β2, Vv) whereχ is the χeff of the previous section andbv = bc + r⊥ is the proton impact pa-rameter with respect to the target. TheCoulomb phase is therefore the sum of twoterms: one of them describes the recoil ofthe core whereas the other accounts for thedirect proton-target Coulomb interaction.Of course, in the case of the neutron thelatter vanishes and the phase reduces to theone derived in [7]. It is easy to see that theexpansion of χeff to first order in r yieldsthe well known dipole approximation to thephase: which only differs from the neutronbreakup case in the different constant fac-tor, which is now (Vcβ1 − Vvβ2) instead ofVcβ1 of Ref. [7].

The probability amplitude can be writtenas the sum of three contributions. The recoilterm,

Arec =∫

dre−ik·rφi(r)(

ei 2Vc

hvlog bc

R⊥ − 1

− i2Vc

hvlog

bc

R⊥+ iχ(β1, Vc)) , (6)

where, according to the discussions in [4,7],the sudden limit has been used in order toinclude all orders in the interaction. The di-rect proton Coulomb interaction term Adir

which has the same form as Eq.(6) but withthe substitution Vc →Vv, β1 → −β2 andbc →bv. The nuclear part is given by

Anuc =

∫

dre−ik·r(

eiχnt(bv) − 1)

φi(r),

(7)

which is the eikonal form of the diffrac-tive nuclear breakup with the neutron-target phase χnt(bv) =

∫

dzVnt(bv, z)/(vh).Finally the expression for the differentialcross-section is

dσ−n

dk=

1

8π3

mk

h2

∫

dbc |Anuc + Adir + Arec|2

× |Sct(bc)|2. (8)

-150 -100 -50 0 50 100 150

p|| (MeV/c)

2

4

6dσ

/dp || (

mb/

(MeV

/c))Exptot, nuc-Cou, exc, dipoletot, nuc-Cou, gs, dipoletot, nuc-Cou, excited statetot, nuc-Cou, gs

FIG. 2. Calculated momentum distributionof 7Be fragments after proton-removal from 8Bagainst Pb at 936 MeV/A. Both dipole and fullmultipole results are shown for the ground stateand first excited state. Calculations accordingto Sec. III and Ref.[8] where more details canbe found. Data are from Ref.[17].

In a number of papers higher order ef-fects [9] and proton breakup have been dis-cussed, among which we recall Refs. [10–12].Some works have also addressed the prob-lem of asymmetry in the core parallel mo-mentum distribution after proton knockout[13,14]. The fact that this asymmetry comesfrom high order terms can be directly ex-tracted from our formalism. If the Coulombpart of the amplitude is simply expanded tofirst order in χ, it can be written, in terms

178

of the one-dimensional Fourier transform inz−direction of the initial wave function φi,as

ACou ≃2

hv

∫

dr⊥e−ik⊥·r⊥

× (VcK0(ωbc/v)φi(r⊥, kz − β1ω/v)

− VCK0(ωR⊥/v)φi(r⊥, kz)

+ VvK0(ωbv/v)φi(r⊥, kz + β2ω/v)).

(9)

Thus the Coulomb breakup probabilityamplitude can be regarded as a coherentsum of three terms, each of which contains ashifted z−Fourier transform. The shifts arein opposite directions, β1ω/v and −β2ω/v,but they are not visible directly in the calcu-lated momentum distributions as ω dependson k itself. Moreover, the 1/v factor indi-cates that the asymmetry decreases as thebeam energy increases. In the dipole ap-proximation, however, the amplitude doesnot contain any asymmetry for the mo-mentum distribution as it involves squaremodulii of φi(r⊥, kz) separately. Hence wehave confirmed analytically that the asym-metry in Coulomb breakup parallel momen-tum distributions is due to the presence ofhigher multipole terms, in agreement withearlier works [9,13,14]. However, the pres-ence of the nuclear interaction introduces aninterference that does depend on the signof kz and thus an additional asymmetry tothat due to higher multipole terms in theCoulomb interaction.

We then present two applications of theformalism just discussed. Fig. 1 showscalculations of absolute cross sections forCoulomb and nuclear breakup, according tothe formalism of Secs. II and III, for a heavyexotic projectile 34Si. It intends to demon-strate the feasibility of nuclear breakup ex-periments on heavy targets when the initialneutron separation energy and angular mo-mentum become large. In this way it shouldbe possible to avoid the asymmetries and

deviations from the eikonal model found insome experiments [15,16]. Fig. 2 comparesdata [17] for proton breakup to calculationsfrom our new model [8] shortly describedabove.

IV. TRANSFER TO THE

CONTINUUM

In Ref. [2] the transfer to the contin-uum method (TC) to calculate the nuclearbreakup was introduced in a way that madenumerical calculations relatively easy. Fur-thermore it was shown that breakup givesrise to a stripping cross section σstr and adiffractive breakup cross section σdiff whichare distinguishable experimentally depend-ing on whether the removed neutron is de-tected in the final state or not. The eikonalapproximation to Eq.(1) has been alreadygiven for the diffraction term by Eq.(7). Ex-tending it to the stripping term of the nu-clear breakup [18,19], one derives [20] thetotal one nucleon removal probability

dP−n(bc)

dkz∼

1

2π

∫ ∞

0

dbv|φi(bv − bc, kz)|2

× [|(1 − e−iχ(bv))|2 + 1 − |e−iχ(bv)|2 ], (10)

where e−iχ(bv) is the eikonal form of the neu-tron (proton) target S-matrix already dis-cussed in Sec.III. Notice that in this expres-sion the exact initial state wave function ap-pears, therefore Eq.(10) is valid for a neu-

tron as well as for a proton. |φi(bv−bc, kz)|2

is the longitudinal Fourier transform ofthe initial state wave function. The totalbreakup probability is obtained from the in-tegral of Eq.(10) involving I(kmin

z , kmaxz ) =

∫ kmaxz

kminz

dkz |φi(bv − bc, kz)|2. If the integral

could be extended to ±∞, it would just bethe longitudinal density, and the formulaefor the TC and eikonal model would becomeidentical. In fact in this limit the removalcross section reduces to

179

σ−n = C2S

∫

d2bc

∫

d3r|φi(bv − bc, z)|2

×[

|(1 − S)|2 + 1 − |S|2]

|Sct(bc)|2 (11)

which is consistent with the breakup crosssection originally obtained by Yabana andcollaborators [21]. Notice that Eqs.(10) and(11) are consistent with Eq.(7).

To see how accurate the sudden approx-imation is, the integral I(kmin

z , kmaxz ) was

calculated in Ref. [19] under various condi-tions of angular momentum, neutron bind-ing energy in the projectile, and projectilevelocity. For values of the parameters of in-terest there can be a rather large reductionfor small values of the neutron transverseradius in the projectile, |bv −bc|. However,the approximation becomes increasingly ac-curate as the transverse radius is madelarger. Another sudden model for Coulomband nuclear breakup was presented in Ref.[22] and compared to the present approach.

V. PROJECTILE FRAGMENTATION

We call projectile fragmentation the elas-tic breakup (diffraction dissociation) dis-cussed above, when the observable stud-ied is the neutron-core relative energy spec-trum. This kind of observable has beenwidely measured in relation to the Coulombbreakup on heavy target. Results on lighttargets have also been presented [23]. Thesedata enlighten the effect of the neutron fi-nal state interaction with the core of origin,neglected in the previous sections, while ob-servables like the core energy or momentumdistributions enlighten the effect of the neu-tron final state interaction with the target.

Projectile fragmentation has also beenused experimentally with two neutron haloprojectiles [24]- [41]. In this case it has beensuggested that the reaction might proceedby the simultaneous emission of the two neu-trons or by successive emissions [24]. The

successive emission can be due to a mecha-nism in which one neutron is stripped by theinteraction with the target, as in the one-neutron fragmentation case, while the otheris left behind, for example in a resonancestate, which then decays. This mechanismhas been described by the sudden approx-imation in Ref. [25] under the hypothesisthat while the first neutron is stripped, thesecond neutron is emitted at large impactparameters with no final state interactionwith the target. The emission can be ex-pected sequential if the two neutrons are notstrongly correlated.

If the two neutrons are strongly correlatedthey will preferentially be emitted simulta-neously. If the neutron which is not detectedis stripped while the other suffers an elas-tic scattering on the target, then in bothcases to first order in the interaction theneutron ends-up in a plane wave final state[2]. It can then re-interact with the corewhich, for example, is going to be 10Be inthe case of the one-neutron halo projectile11Be, while it will be 12Be in the case of theprojectile fragmentation of 14Be, since 13Beis not bound or 9Li in the case of the pro-jectile fragmentation of 11Li, since in thiscase 10Li is not bound. Experiments with a14B projectile [26] have also been performed,in which the n-12Be relative energy spec-tra have been reconstructed by coincidencemeasurements. In such a nucleus the valenceneutron is weakly bound, while the valenceproton is strongly bound. Thus the neutronwill probably be emitted in the first step andthen re-scattered by the core minus one pro-ton nucleus. The projectile-target distancesat which this kind of mechanism would berelevant are probably not so large to neglectthe effect of the neutron-target interaction.

A. Inelastic excitation to the continuum.

To first order the inelastic-like excitationscan be described again by the time depen-

180

dent perturbation amplitude Eq.(1) [1,2]. Inthis section also, the potential V (r,R(t)),which is the interaction responsible for theneutron transition, moves past on a constantvelocity path as described in the previoussections. The radial part φi(r) of the singleparticle initial state wave function ψi(r, t)is calculated in a potential VWS(r) which isfixed in space. The coordinate system andother details of the calculations can be foundin Ref. [27]. In the special case of exoticnuclei the traditional approach to inelasticexcitations needs to be modified. For ex-ample the final state can be eigenstate of apotential V1 modified with respect to VWS

because some other particle is emitted dur-ing the reaction process as discussed in theintroduction.

0 1 2 3ε

f (MeV)

0

10

20

30

40

50

dσ/d

εf

(m

b/M

eV)

Sums1/2 to s1/2s1/2 to p3/2s1/2 to p1/2s1/2 to d5/2s1/2 to d3/2CoulombConvolutionExp.

FIG. 3. n-10Be relative energy spectrum, in-cluding Coulomb and nuclear breakup for the re-action 11Be+12C → n+10Be+X at 69 A.MeV.Only the contributions from an s initial statewith spectroscopic factor C2S= 0.84 are calcu-lated. The triangles are the total calculated re-sult after convolution with the experimental res-olution function. The dots are the experimentalpoints from Ref.[23].

The final state interaction might also havean imaginary part which would take intoaccount the coupling between a continuumstate and an excited core. The first or-der time dependent perturbation amplitudethen reads

Afi =1

ihv

∫ ∞

−∞

dxdydz φ∗f (x, y, z)φi(x, y, z)

eiqzV (x − bc, y, q), (12)

where V (x − bc, y, q) =∫ ∞

−∞dzV (x −

bc, y, z)eiqz, and we changed variables andput z′ = z − vt or t = (z − z′)/v, q =εk − εi/hv. In this section εk is the neutron-core relative energy in the final state.

0 1 2 3ε

f (MeV)

0

20

40

60

80

dσ/d

εf

(m

b/M

eV)

FIG. 4. Sum of all transitions from the s ini-tial state with εi=-1.85 MeV (solid line) for thereaction 14Be+12C → n+12Be+X . Experimen-tal points from H. Simon et al. [31] for the samereaction at 250 A.MeV. Dashed line is the fold-ing of the calculated spectrum with the experi-mental resolution curve.

The target represented by V perturbs theinitial bound state wave function and allowsthe transition to the continuum by transfer-ring some momentum to the neutron. Thenit is enough to choose a simplified form ofthe interaction, such as a delta-function po-tential V (r) = v2δ(x)δ(y)δ(z). The value ofthe strength v2 ≡ [MeV fm3] used in the cal-culation is taken equal to the volume inte-gral of the appropriate neutron-target inter-action. It is clear that while in the suddenapproach the initial and final state overlapis taken in the whole coordinate space, irre-spective of the target and of the beam veloc-ity, here the overlap of the initial and finalwave functions depends on the core-targetimpact parameter. The neutron is emittedpreferentially on the reaction plane and the

181

z-component, being along the relative veloc-ity axis is boosted by a momentum q.

0 0.5 1 1.5 2 2.5 3ε

f (MeV)

0

50

100

150

200

dσ/d

εf

(m

b/M

eV)

Exp. data from [2]31% s 45% p 31% s 45% p with exp. conv31% s 45% p without d

5/2

31% s 45% p without d5/2

with exp. conv.

FIG. 5. n-9Li relative energy spectrum, forthe reaction 11Li+12C → n+9Li+X at 264A.MeV. Only the contributions from an s and pinitial state with experimental spectroscopic fac-tors [46] C2S= 0.31 and 0.45 respectively andseparation energy 0.3 MeV are included. Thethin solid curve is the total calculated result.The thick solid curve curve is after convolutionwith the experimental resolution function. Thethin dashed curve is the calculation without thed-resonance while the thick dashed curve is thesame calculation after convolution. The sym-bols with error bars are the experimental pointsfrom Ref.[31]. Calculations are normalised tothe data

Due of the strong core absorption dis-cussed in Secs. 2 and 3 these calculations arealso performed using the asymptotic formof the initial and final state wave functions.Introducing the quantization condition ac-cording to Ref. [2] the probability spectrumreads

dPin

dεk

=2

π

v22C2

i

h2v2

m

h2k

1

2li + 1

× Σmi,mf|1 − Smi,mf

|2|Imi,mf|2. (13)

The generalization including spin is given inAppendix B of Ref. [27] and |Imi,mf

|2 is

|I|2 =∣

∣

∣γk

i

2ili

∫ ∞

−∞

dzeiqzh(1)li

(iγr)h(−)lf

(kr)

×Yli,mi(θ, 0)Ylf ,mf

(θ, 0)∣

∣

∣

2

. (14)

The quantity S = e2i(δ+ν) is an off-the-energy-shell S-matrix representing the finalstate interaction of the neutron with theprojectile core. It depends on a phase whichis the sum of δ, the free particle n-core phaseshift, plus ν the phase of the matrix elementI, Eq.(14). Some examples of our calcula-tions [27] are shown in Figs. 3, 4 and 5and compared to recent data. See also Ref.[28]. Finally we refer to two books [42,43]and recent reviews [44,45] in which furtherdiscussion and bibliography can be found.

VI. CONCLUSIONS AND OUTLOOK

The field of Rare Isotopes Studies is veryactive, growing steadily and rapidly. Somerecent achievements in reaction models forneutron and proton breakup from exoticbeams have been presented. From the struc-ture point of view, in the search for thedripline position, a very important role isplayed by the study of nuclei unstable byneutron emission. On the other hand in-creasing the mass of the projectiles pro-duced we are going to face the problem ofenvisaging new experiments to study them.These two are among the most importantsubjects which need to be adressed andfurther developed in the near future andfor which some suggestions have been pre-sented.

[1] K. Alder and A. Winther, ElectromagneticExcitation, North-Holland, 1975.

[2] A. Bonaccorso and D.M. Brink, Phys. Rev.C 38 (1988) 1776; Phys. Rev. C 43 (1991)299; Phys. Rev. C 44 (1991) 1559.

[3] A. Bonaccorso, Phys. Rev. C 60 (1999)054604.

[4] J. Margueron, A. Bonaccorso and D.M.

182

Brink, Nucl. Phys. A 703 (2002) 105; Nucl.Phys. A 720 (2003) 337.

[5] R. A. Broglia and A. Winther, Heavy IonReactions, Benjamin, Reading, Mass, 1981.

[6] S. Kox et al., Phys. Rev. C 35 (1987) 1678.[7] A. Garcıa-Camacho, A. Bonaccorso and

D.M. Brink, Nucl. Phys. A 776 (2006) 118.[8] A. Garcıa-Camacho, G. Blanchon, A.

Bonaccorso and D.M. Brink, Phys. Rev. C76 (2007) 014607.

[9] H. Esbensen, G.F. Bertsch and C. Bertu-lani, Nucl. Phys. A 581 (1995) 107.

[10] J.H. Kelley et al., Phys. Rev. Lett. 77

(1996) 5020 and references therein.[11] K. Hencken, G. Bertsch and H. Esbensen,

Phys. Rev. C 54 (1996) 3043.[12] A. Bonaccorso, D. M. Brink and C. A.

Bertulani, Phys. Rev. C 69 (2004) 024615..[13] H. Esbensen and G.F. Bertsch, Nucl. Phys.

A 600 (1996) 37; Phys. Rev. C 59 (1999)3240; Nucl. Phys. A 706 (2002) 383.

[14] B. Davids et al., Phys. Rev. Lett. 81 (1998)2209; Phys. Rev. C 63 (2001) 0654806.

[15] J. Enders et al., Phys. Rev. C 65 (2001)034318.

[16] A. Gade et al., Phys. Rev. C 71 (2005)051301.

[17] D. Cortina-Gil et al., Nucl. Phys. A 720

(2003) 3.[18] A. Bonaccorso and F. Carstoiu, Phys. Rev.

C 61 (2000) 034605.[19] A. Bonaccorso and G.F. Bertsch, Phys.

Rev. C 63 (2001) 044604.[20] A. Bonaccorso and D.M. Brink, Phys. Rev.

C 57 (1998) R22; Phys. Rev. C 58 (1998)2864.

[21] K. Yabana, Y. Ogawa and Y. Suzuki, Nucl.Phys. A 539 (1992) 295.

[22] F. Carstoiu, E. Sauvan, N.A. Orr, A.Bonaccorso. Phys. Rev. C 70 (2004)054602.

[23] N. Fukuda et al., Phys. Rev. C 70 (2004)054606.

[24] F.M. Marques et al., Phys. Rev. C 64

(2001) 061301(R). N.Orr, Prog. Theor.Phys. Suppl. 146 (2003) 201.

[25] G.F. Bertsch, K. Hencken and H. Es-bensen, Phys. Rev. C 57 (1998) 1366.

[26] J.L. Lecouey, Few Body Syst. 34 (2004) 21.

[27] G. Blanchon, A. Bonaccorso, D.M. Brink,A.Garcıa-Camacho and N. Vinh Mau.Nucl. Phys. A 784 (2007) 49.G. Blanchon, A. Bonaccorso, D.M. Brink,and N. Vinh Mau. Nucl. Phys. A 791

(2007) 303.[28] G. Blanchon, A. Bonaccorso and N. Vinh

Mau, Nucl. Phys. A 739 (2004) 259.[29] M. Thoennessen et al., Phys. Rev. C 59

(1999) 111; Phys. Rev. C 60 (1999) 027303.[30] M. Labiche et al. Phys. Rev. Lett. 86

(2001) 600.[31] H. Simon et al., Nucl. Phys. A 791 (2007)

267.[32] A.A. Korsheninnikov et al., Phys. Lett. B

343 (1995) 53.[33] G.F. Bertsch and H. Esbensen, Ann. Phys.

(N.Y.) 209 (1991) 327.[34] I.J. Thompson and M.V. Zhukov, Phys.

Rev. C 53 (1996) 708.[35] N. Vinh Mau and J.C. Pacheco, Nucl.

Phys. A 607 (1996) 163.[36] J.C. Pacheco and N. Vinh Mau, Phys. Rev.

C 65 (2002) 044004.[37] P. Descouvemont, Phys. Lett. B 331

(1994) 271; Phys. Rev. C 52 (1995) 704.[38] A. Adachour, D. Baye and P. Descouve-

mont, Phys. Lett. B 356 (1995) 445.[39] D. Baye, Nucl. Phys. A 627 (1997) 305.[40] T. Tarutina, I.J. Thompson, J.A. Tostevin,

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N. Vinh Mau, Phys. Rev. C 60 (1999)027303.

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[43] Y. Suzuki, R. G. Lovas, K. Yabana, K.Varga. Structure and Reactions of LightExotic Nuclei. Taylor and Francis Eds.2003.

[44] L.F. Canto, P.R.S. Gomes, R. Donangelo,M.S. Hussein, Phys. Rep. 424 (2006) 1.

[45] B. Jonson, Phys. Rep. 389 (2004) 1.[46] S.N. Ershov et al., Phys. Rev. C 70 (2004)

054608.

183

Conference Proceedings Vol. 96

“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”

F. Gramegna, M. Cinausero, D. Fabris (Eds.)

SIF, Bologna 2008

NUCLEAR STRUCTURE AT EXTREME CONDITIONS THROUGH γ SPECTROSCOPY

MEASUREMENTS

S. Leoni, A. Bracco, F. Camera

University of Milano and I.N.F.N. sez. Milano

INTRODUCTION

The study of the nucleus at the limits of angular momentum, temperature and neutron/proton number is one of the central topics currently addressed with selective Ȗ-spectroscopy measurements. In these extreme regimes nuclear structure studies are probing nuclear shapes and their evolution, the influence of thermal environments on low-lying modes, collective rotation and giant resonances.

In this contribution we present selected studies of the collective response of the atomic nucleus at extreme conditions, making use of nuclear reactions with stable/radioactive ions. In particular, the nuclear rotation at high spin values and moderate excitation energy is used to study the transition between order and chaos, while the temperature and isospin degrees of freedom are investigated in connection with giant dipole resonances and pygmy states in exotic nuclei.

THE ORDER-TO-CHAOS TRANSITION

IN THE WARM ROTATING NUCLEUS

It has been shown, both experimentally and theoretically, that the atomic nucleus displays properties typical of an ordered system at temperature T = 0 [1], and of a chaotic systems at the compound nucleus level [2]. The transition between order and chaos can be studied through the analysis of the γ-decay of warm rotating nuclei produced at high spins and moderate excitation energy by fusion reactions between heavy ions, with typical beam energies of 5 MeV/A. In fact, after rapid evaporation of light particles, warm rotating nuclei de-excite emitting long sequences of γ transitions, ending up in discrete regular rotational bands when the nuclear temperature of the system is almost zero. Therefore, by detecting the largest number of γ-rays emitted by the excited nucleus, nuclear

structure properties can be investigated as a function of angular momentum and excitation energy. This can be achieved by the use of high-efficiency HpGe-array spectrometers (such as EUROBALL [3] or AGATA [4] in the near future), consisting of more than 100 Ge crystals in 4π geometry around the reaction center, usually combined with other types of detectors.

By constructing γ−γ spectra from the measured Eγ energies of high-fold γ cascades (see figure 1), one can distinguish between the contribution from the COLD region of regular decay at T=0 (“ridges”) and from the WARM region above ≈ 1 MeV internal excitation energy (“valley”). This is where the nuclear rotation becomes damped and the rotational decay is fragmented over a large number of states with an energy spread Γrot ≈ 200 keV, as a consequence of the rapidly increasing level density and of the presence of a residual two-body interaction mixing the nuclear states [5].

Fig. 1: Example of a region of a γ−γ spectrum of a warm rotating nucleus (168Yb), showing the different contributions from the COLD regular decay at zero temperature (ridges) and from the WARM region of rotational damping (valley), where the transition between order and chaos is expected to take place.

168YbRIDGES(COLD-Order)

VALLEY (WARM-Onset of Chaos)168Yb

RIDGES(COLD-Order)

VALLEY (WARM-Onset of Chaos)168Yb

RIDGES(COLD-Order)

VALLEY (WARM-Onset of Chaos)

185

The study of such ridge-valley landscape can

be used to investigate the transition between order and chaos in terms of a gradual vanishing (at T≠0) of the selection rules associated with the quantum numbers at T = 0, such as K (the projection of the angular momentum on the symmetry axis). In this respect, the deformed nucleus

163Er is an ideal case, being characterized

by a number of rotational bands having low-K (K=5/2) and high-K (K=19/2) values [6]. The nucleus

163Er has been populated by the reaction

18O +

150Nd, at Ebeam = 87, 93 MeV, and its

subsequent γ-decay has been detected using the EUROBALL array at the IReS Laboratory (France). The

150Nd target was made of a stack of

two thin foils for a total thickness of 740 μg/cm2

and the corresponding maximum angular momentum reached in the reaction has been calculated to be 40 and 45 h, for the two different bombarding energies. Figure 2 shows examples of 60 keV wide projections, perpendicular to the Eγ1 = Eγ2 diagonal of experimental matrices of 163

Er, gated by transitions among states with low-K (K=5/2) and high-K (K=19/2) quantum numbers [7,8]. The spectra, showing the typical ridge-valley structure resulting from the γ-decay of a deformed rotating nucleus, have been first analyzed by statistical analysis methods [9].

Fig. 2: 60 keV wide projections on the Eγ1-Eγ2 axis of experimental matrices of 163Er, at the average transition energies Eγ = 900 and 960 keV. Panels a) and b) (c) and d)) show spectra obtained from γ−γ matrices gated by low-K (high-K) configurations of 163Er. The smooth curves represent the interpolation of the data by a two-component spectral function [8].

The analysis of the fluctuations of the events collected in the γ−γ spectra allows to estimate the number of bands (named paths, Npath) both in the ridge and valley region, through the relation

being Neve, μ1 and μ2 the number of events

and the first and second moment of the distribution of counts in a given sector [9]. In the previous expression P

(2) is a correction factor

taking into account the finite energy resolution of the detection system. The analysis is typically performed in a two-dimensional energy region where a rotational band contributes in average with one transition, namely ΔEγ×ΔEγ = 4h2

/ℑ(2)×4h2/ℑ(2)

, being ℑ(2) the

effective

dynamic

moment of inertia of the rotational bands. As

shown in the top panel of figure 3, a total number of ~40 discrete excited bands is found to populate the ridge structures of

163Er, half of

which of high-K nature. On the contrary, many more bands, of the order of 10

3-10

5, are found to

populate the valley region, with large differences between low-K and high-K states, being the latter ~10 times fewer, as shown in the bottom panel of figure 3. This suggests that the K-quantum number is at least partially conserved up to moderate excitation energies, of the order of ~1.5 MeV above yrast (corresponding, in the bottom panel of figure 3, to transition energies Eγ ~1.1 MeV), where the rotational motion is damped. At higher excitation energies (namely for Eγ > 1.1 MeV) more similar number of bands are obtained for low-K and high-K gated spectra, pointing to a vanishing of selection rules on K and to the onset of a chaotic regime, in which quantum numbers and selection rules loose their meaning.

The previous results are supported by the analysis of the correlations between spectra gated by different K-states, which can be evaluated in terms of covariance of the spectrum fluctuations [7]. As reported in ref. [7], the covariance analysis of the valley region shows strong similarities/correlation between the high-K and low-K gated distributions at the highest transition energy values, indicating a gradual transition to a chaotic regime around 1.5 MeV of internal energy.

The experimental results shown in figure 3 are well reproduced by the shell model of ref. [10]

d)c)

-1 00 0 10 0

2 0

3 0

4 0

Eγ 1- Eγ2 [keV]

High K

960 keV

15 0

20 0

25 0

Low K

960 keV

a) b)

2 0 0

2 5 0

3 0 0

3 5 0

103

Co

un

ts

L ow K

900 keV

-1 0 0 0 10 0

3 0

4 0

5 0

6 0

Eγ1 - Eγ 2 [keV]

103 C

ou

nts

Hig h K

900 keV

)2(

1

2 1

PN

N evepath ×

−=

μμ

186

which combines a cranked mean-field and a residual two-body interaction, together with a terms taking into account the angular momentum carried by the K-quantum number. According to the model, K-mixing is induced by the interplay of the Coriolis and residual interaction, and it is found to gradually increase until a complete violation of the K-quantum number is reached above 2-2.5 MeV of internal energy, in good agreement with the experimental findings.

Fig. 3: Results of the statistical analysis of the ridge and valley regions of the experimental γ−γ matrices of 163Er. The top panel shows the number of discrete excited bands at T=0, obtained from the fluctuation analysis of the ridge structures of the total spectrum (triangles) and from spectra gated by Low-K and High-K structures (open symbols). The bottom panel gives instead the results of the statistical analysis of the corresponding valley regions, providing information on the regime of strongly interacting bands at ~1.5-2 MeV internal excitation energy [7]. In both panels the lines give the prediction from the cranked-shell model calculation of ref. [10].

The spectral shape of the ridge-valley structure of the γ−γ spectra (see figure 2) can also been used to extract the rotational damping with Γrot [8], which is related to the evolution of the nuclear system towards complexity. Figure 3 shows the values obtained for the rotational damping width, by interpolating the ridge-valley event distribution of the total γ−γ spectrum of 163

Er, by a two component function (smooth curves in figure 2). The damping width is also found to depend on the K value, being ∼ 200 keV for low-K and ∼ 150 keV for high-K states, in agreement with the calculation of the model [10], giving further support to the conservation of K up to moderate excitation energies [11].

Fig. 4: Experimental values of the rotational damping width Γrot, as extracted from the spectral shape analysis of the total γ−γ spectrum of 163Er [11]. Predictions from cranked shell model calculations are shown by the full line [10].

DAMPING MECHANISM OF THE GIANT

DIPOLE RESONANCE IN HOT NUCLEI

The Giant Dipole Resonance (GDR) is a collective excitation of the nucleus in which proton and neutron oscillate with opposite phase. By studying the γ-decay of the GDR it is possible to investigate highly excited nuclei and to explore the basic nuclear structure properties at finite temperature and angular momentum, such as nuclear shapes and thermal effects [12]. In particular, the dependence of the GDR width on temperature and angular momentum provides information on the evolution of the nuclear shapes and on the damping mechanism of this collective state.

There are still open problems concerning the

temperature dependence of the width of the GDR

30 40

100

200

300

Spin [h]

Γ rot [

keV

]

163Er

30 40

100

200

300

Spin [h]

Γ rot [

keV

]

163Er

Eγ [keV]Eγ [keV]

Warmrotation

Low K

High K

10K

Warmrotation

Low K

High K

10

Warmrotation

Low K

High K

10KK

Valley

187

at T > 2.5 MeV. In fact, while, in general, the measured GDR width is well described within the thermal fluctuation model (TFM) [13] for T < 2 MeV, at higher temperature the situation is more complex, also due to the presence of sizable pre-equilibrium emissions which significantly cool down the nuclear system before its thermalization [14]. This implies a correction to the initial compound excitation energy at which the giant dipole resonance is emitted. To properly understand the behaviour of the GDR width with temperature it is therefore important to fix unambiguously the compound excitation energy, namely, experimental data are required which do not contain pre-equilibrium contributions, whose subtraction is model dependent.

An experimental campaign focused to the

measurement of the width of the GDR built on excited nuclei with mass A~130 and with temperature in the range 2-4 MeV has been performed at Legnaro National Laboratory of INFN, making use of the GARFIELD array [15] combined with large volume BaF2 detectors of the HECTOR set up [16] and with two Position Sensitive Parallel Plate Avalanche Counter telescopes (PSPPAC). In this way, high energy γ-rays from the decay of the GDR were measured in coincidence with light charged particles (to identify the possible presence of pre-equilibrium emission and to properly define the compound nucleus temperature) and with evaporation residues (to select the fusion-evaporation channel). Two different reactions were employed, producing the same

132Ce compound

nucleus at excitation energy 100, 150 and 200 MeV: a symmetric one, using a

64Ni beam at

300, 400 and 500 MeV on a 68

Zn target, and an asymmetric one with an

16O beam at 130 and 250

MeV on a 116

Sn target [17]. In this way the pre-equilibrium contribution predicted, in the oxygen case, by Kelly et al. [14] has been measured.

In figure 5 the α particle spectra measured at Θ

= 74° in both the symmetric 64

Ni and asymmetric 16

O reactions are displayed, in the case of beam energy 500 and 250 MeV, respectively. For the two reactions the excitation energy deduced from kinematics is the same, being equal to 200 MeV. While the α particle spectra corresponding to the 64

Ni-induced reaction show a spectral shape in agreement with a statistical emission from a fully thermalized compound system (red curve), in the case of the

16O beam a sizable pre-equilibrium

contribution is observed, as deduced from the

excess yield which is particularly intense at forward angles. As a consequence, the study of the GDR width at different temperature has been restricted to the symmetric

64Ni-induced reaction,

which does not require any correction related to pre-equilibrium effects.

Fig. 5: Measured α-particle spectra at the detection angle Θ = 74° for the 16O-induced reaction (Elab=250 MeV) (right panel) and for the

64Ni-induced reaction

(Elab=500 MeV) (left panel). The solid line corresponds to statistical model calculations assuming emission from a fully thermalized compound system at the kinematical value of the excitation energy common to the two reactions (E*=200 MeV)[17].

Figure 6 shows the high energy γ-ray spectra

measured in coincidence with the recoiling residual nuclei from the symmetric reaction induced by the

64Ni beam at the 3 different

excitation energies. The full lines give the best fitting statistical model calculations performed using the computational code DCASCADE of ref. [18,19] and folded with the response function of the BaF2 array, calculated using the GEANT libraries [20]. The calculations assume a single Lorentzian strength function centered at EGDR = 14 MeV (as in ref. [21]) and a value of the energy-weighted sum rule (EWSR) corresponding to 100% of the Thomas-Reiche-Kuhn formula. The insets of the figure show the GDR spectra linearized according to the procedure described in ref. [17], together with the corresponding best fitting calculated spectrum (full lines) obtained by treating the Lorentzian width and centroid as free parameters.

The nuclear temperature of the compound

nucleus associated with the GDR decay has been calculated with the expression

0 50 100 150

Eα [MeV]

106

105

104

103

102

counts

[arb

. un.]

0 50 100 150

Eα [MeV]0 50 100 150

Eα [MeV]0 50 100 150

Eα [MeV]0 50 100 150

Eα [MeV]

106

105

104

103

102

counts

[arb

. un.]

0 50 100 150

Eα [MeV]0 50 100 150

Eα [MeV]

188

dE

EdT

))((ln(

1

ρ=

as discussed in ref. [22,23], being ρ(E) the

density of levels, which in this case has been described according to the Reisdorf formalism [24]. The value used for the level density parameter a (MeV

-1) linearly increases between

A/9 and A/10 for E* < 100 MeV, between A/10 and A/11 for 100 < E* < 170 MeV, while it is equal to A/12.5 for E* > 170 MeV.

Fig. 6: The measured (filled points) and calculated

statistical model (full drawn lines) high energy γ-ray

spectra for 132Ce at excitation energy of 200, 150

and 100 MeV [17].

Figure 6 shows the measured values of the

GDR width in comparison with results of different theoretical predictions based on the thermal fluctuation model of the nuclear shape [13]. The error bar on the width is the statistical error connected to the fitting procedure. The horizontal bar represents instead the average temperature range associated to 75% (lower value) and 25% (upper value) of the γ-ray yield. The neglected yield in the average corresponds to the decay at the end of the compound nucleus (CN) cascade which is not sensitive to the GDR width because of its spectral shape.

Within the thermal shape fluctuation model the GDR strength function is calculated by averaging the line shape corresponding to the different possible deformations. The averaging over the distribution of shapes is weighted with a Boltzmann factor

where F is the free energy and T the nuclear temperature [13]. At each deformation point the intrinsic width Γ0 of the resonance was chosen equal to the zero temperature value, namely 4.5 MeV, as it was generally done to reproduce the existing majority of data at T < 2.5 MeV. This calculation is shown in figure 6 by the thin continuous line. It is found that the predicted increase does not reproduce the present experimental data. Moreover, the expected increase seems to follow rather well the deformation increase of the compound nucleus induced by temperature. This is also shown in the figure with a dashed line, representing the average deformation of the nucleus obtained by the thermal fluctuation model (scale on the right vertical axis). A possible explanation for the discrepancy between the data and the TFM model at T > 2.5 MeV could be related to the fact that the effect of the lifetime of the compound nucleus plays a role at these temperatures, as originally suggested by Ph.Chomaz et al. [26]. In fact, taking also into account the compound nucleus lifetime much better agreement between data and theory is obtained, as shown in figure 7 by the thick full drawn line. In the present calculation, the CN total lifetimes were calculated with the statistical model, and the obtained lifetime values have been added to the GDR intrinsic width Γ0, before performing the averaging over nuclear shapes [26].

Fig. 7: Comparison between measured (black points) and calculated GDR width [17]. The thick continuous line shows the predictions of the thermal shape fluctuation model with the inclusion of the compound nucleus (CN) lifetime. The thin continuous line indicates the results of shape fluctuations alone. The dashed line shows the average deformation < β > calculated by the thermal fluctuation model [13].

132Ce132Ce

)/),(exp(),( TFP γβγβ −∝

5 10 15 2010

-1

100

101

102

103

104

5 10 15 20 5 10 15 20 25

5 10 15 20

0,04

0,08

5 10 15 20

0,04

0,08

5 10 15 20

0,08

0,16

E*=200MeV

Yie

ld [

arb

.un

.]

Eγ [MeV]

E*=150MeV

Eγ [MeV]

E*=100MeV

Eγ [MeV]

[arb

.un

.]

Eγ [MeV]

[arb

.un

.]

Eγ [MeV] [a

rb

.un

.]

Eγ [MeV]

189

From the results presented in figure 6 one can conclude that, in agreement with the expectation of the theory [12], for T > 2 MeV there is no room for a significant increase of the intrinsic width Γ0 with temperature [27], unless one unrealistically neglects the CN lifetime contribution to the total width.

PYGMY DIPOLE RESONANCE

IN NEUTRON RICH SYSTEMS

Most of our current understanding of nuclear structure results from the study of reactions between stable nuclei, which until now have allowed to produce ~3000 radioactive nuclides, at quite low values of excitation energy and angular momentum . The availability of beams of unstable ions [27] has recently opened up the possibility to explore the properties of the atomic nucleus far away from the stability line, gaining access to a much wider region of exotic, loosely bound nuclear systems, at the limit of the proton and neutron binding energy. The study of nuclei far away from stability is important not only for a full comprehension of the nuclear many-body system, but also for their astrophysical implications, not least the nucleosynthesis of the heavy elements in the stellar environment. In this respect, one of the topic mostly discussed at present is the evolution of the Giant Dipole Resonance strength from stable to exotic, weakly bound, nuclei with extreme neutron to proton ratio, in connection with the existence of the so called Pygmy Resonance (PR) or soft mode [28-30]. This mode of excitation arises from the vibration of the less tightly bound valence neutrons against the residual core and according to different type of calculations, it is expected to appear as a redistribution of the strength towards lower excitation energies, well below the giant resonance region. It is also found that the details of this redistribution depend significantly on the effective forces used in the calculations. Moreover, according to G. Goriely [31], the pygmy resonance strength can have a striking impact on the calculated r-abundance of the elements since it can significantly change the neutron capture process in the r-process nucleosythesis.

In the case of stable nuclei extensive work was made with photon scattering experiments in different regions of mass [32,33] and in general it was seen that the low energy E1 strength increases with increasing N/Z ratio, as expected

from a neutron-skin vibration. For nuclei far from stability the pygmy dipole resonance was investigated with Coulomb break up reactions for the

20-22O and

132-134Sn nuclei [34,35]. Coulomb

excitation followed by gamma decay was instead measured so far only in the case of

20O [36]. In

contrast with the break up technique the measurement of γ-decay following Coulomb excitation allows to search for strength at energies also below the particle separation energy.

Among the unstable neutron-rich nuclei

68Ni

represents a good case to search for pygmy structures being among the experimentally accessible exotic nuclei with the present radioactive beam facilities. Recently, Vretenar et al. [30] have applied the relativistic random phase approximation to predict the evolution of the isovector dipole response in nuclei with a large neutron excess, and their results for the case of the medium-heavy Ni isotopes are shown in figure 8. It is found that the low-energy dipole strength distribution increases with the neutron excess, in agreement with non relativistic Random Phase Approximation calculation by Colò et al. [29].

Fig. 8: The isovector dipole strength distribution for 4 different isotopes of Ni nuclei as predicted by D. Vretnar et al. using the Relativistic Random Phase Approximation approach [30]. The dashed lines separate the region of the giant resonances from the low-energy region around 10 MeV (pygmy region).

The study we report here concern the

measurement of the γ-decay following Coulomb excitation of a

68Ni beam at 600 MeV/A, energy

at which the dipole excitation dominates over the other excitation modes. This is shown in figure 9,

190

where the cross sections for electromagnetic excitation of different collective states as a function of beam energy is given, in the case of a medium mass nucleus on a Au target [37].

Fig. 9: The cross section for electromagnetic excitation for different collective states as a function of beam energy, for medium mass nuclei on a Au target [37].

As one can see in the figure, the dipole cross section increases as the beam energy increases, opposite to the behaviour of the quadrupole cross section. One can than conclude that it is important in a Coulomb excitation process to have the highest possible beam energy in order to ensure to excite mainly dipole states.

The experiment has been performed at the GSI Laboratory (Darmstadt), where

68Ni has been

produced from the fragmentation of 86

Kr at 900 MeV/A from the UNILAC-SIS with an intensity of ∼ 10

10 particle per spill. The spill length was

approximately 6 seconds long with a period of 10 seconds. The primary beam was focused on a Be target 4 g thick and the

68Ni ions were selected

using the Fragment Separator (FRS) facility. The beam cocktail arriving on the

197Au target (3

g/cm2 thick) had an intensity of ∼4 10

4 events

per spill, out of which approximately 30% were 68

Ni isotopes, as can be seen in figure 10. A total of ∼3 10

7 events of

68Ni have been finally

collected after 6 days of beam time [38]. The γ-ray emission from Coulomb excited

68Ni

has been measured using the RISING array [39] located after the FRS spectrometer. The particle identification setup after the target is performed by the CATE calorimeter [40] placed approximately 1.5 m after the target and at 0°.

Fig. 10: The beam cocktail arriving on the secondary target as measured after the FRS. In the x-axis is plotted the Z of the incident isotopes while in the y axis the A/Q ratio is indicated. The strongest spot in the center is relative to

68Ni.

In the present experiment, the calorimeter

consisted of nine position sensitive Si detectors coupled to four 6 cm thick CsI arranged to equally share the intensity of the incident beam. High and low energy γ-rays have been measured using 15 HPGe clusters of the EUROBALL array [3], 7 HPG segmented clusters from the MINIBALL array [41] and 8 BaF2 from the HECTOR array [16] located at different angles.

The upper panel of figure 11 shows the spectrum obtained by the CATE calorimeter requiring incoming

68Ni ions. The achieved

energy resolution (4.4% for Si and 1.2% for CsI detectors) is found to be sufficient to discriminate between different masses and charges. In the bottom panel of figure 11, the Time of Flight spectrum of the BaF2 detectors are shown, with and without the condition of a 68

Ni event detected in CATE. As one can see, such condition eliminates completely almost all background except for the γ flash coming from CATE, arriving ∼12 ns after the prompt peak.

The measured high energy γ-rays spectra in the HpGe cluster detectors and in the BaF2 of the RISING setup are shown in figure 12, top and middle panel. Only the

68Ni events before and

after the target have been selected with the additional condition on the prompt time of flight peak and on the overall RISING γ- multiplicity equal to one. A peak structure is observed in both the Doppler corrected spectra, at ≈10-11 MeV, where theoretical calculations predict the low energy peak associated to the pygmy resonance component, as displayed in the bottom panel of figure 12.

191

Fig. 11: The E-ΔE spectrum acquired with the CATE calorimeter, in coincidence with incoming 68Ni isotopes, is shown in the top part. The bottom panel shows instead the Time of Flight spectrum of BaF2 detectors, before and after the requirement of a 68Ni event in the CATE calorimeter [40].

In the figure, the lines superposed to the

experimental spectra correspond to accurate GEANT [20] simulations of a 10.8 MeV incident γ-ray in the corresponding detector. In the inset of the figure the peak structure observed in the HpGe clusters and BaF2 detectors is shown, after subtracting a background with an exponential-like shape. A similar peak structure at 10-11 MeV, although not well defined as in the case of the HpGe Clusters and BaF2 detectors, is also observed in the γ-ray spectrum from the MINIBALL array which, being placed closer to the target, suffers of a higher background [40].

One can than conclude that, even though the statistic is low and the background is high, a coherent scenario is observed in the different type of detectors of the RISING setup, namely a peak structure between 10-11 MeV, at the place where different theoretical calculations predict an excess of E1 strength associated to a pygmy dipole response. This results represent the first evidence of the pygmy resonance in a measurement using the virtual photon scattering technique, therefore opening possibilities for more systematic studies in the future.

Fig. 12: The high-energy γ-ray spectra measured in the BaF2 detectors and in the EUROBALL cluster detectors are shown in the top and middle panel. The theoretical calculated 68Ni dipole strength is displayed in the lower-right panel [41]. The continuous line superimposed to the experimental spectra are the results of GEANT simulation of the peak line shape of a 10.8 MeV γ-ray.

CONCLUSION

In this contribution we have presented three selected examples of nuclear structure studies at extreme conditions of angular momentum, temperature and N/Z ratio, making use of γ-spectroscopy measurements.

The first is the study of the transition between

order and chaos in the warm rotating nucleus. By comparing γ coincidence spectra gated by low-K

8 10 12 140

10

20

30

40

50

60

5.0 7.5 10.0 12.50

5

10

15

20

25

8 10 12 140

10

20

30

40

50

60

5.0 7.5 10.0 12.50

5

10

15

20

25

8 10 120

2

4

6

Co

un

ts

HPGe-Cluster

Energy [MeV]

Energy [MeV]

Energy [MeV]

Cou

nts

Energy [MeV]

Baf2 Hector

arb

.units

Theory

G. Colò et al.

192

and high-K structures in the nucleus 163

Er, a gradual vanishing of selection rules on the K quantum number is observed with increasing temperature, suggesting a smooth transition between order and chaos at internal excitation energy ∼1.5 MeV. The experimental results are in good agreement with theoretical predictions based on cranked shell model calculations at finite temperature, taking also into account the angular momentum carried by the K quantum number.

The second topic concerns the study of the dependence of the width of the Giant Dipole Resonance with temperature, in the high temperature regime above 2.5 MeV. This is were sizable pre-equilibrium emission may be present, making it more difficult to unambiguously define the excitation energy of the compound nucleus. For this purpose, the GDR decay of the hot

132Ce

nucleus produced in symmetric 64

Ni-induced reactions, free from pre-equilibrium effects, has been studied in the temperature region 2.5-4.1 MeV. The measured Giant Dipole Resonance width shows an almost linear increase with temperature, in good agreement with predictions from the fluctuation model including also the lifetime of the compound nucleus.

As a last topic, the search for the pygmy resonance in the exotic neutron rich nucleus

68Ni,

using the relativistic Coulomb excitation technique, is discussed. The measured γ-ray spectrum shows a peak centered around 10-11 MeV, corresponding to an enhanced strength as compared to the tail of the standard GDR Lorentzian function. Such an excess is also predicted by different type of calculations and it is interpreted as due to the oscillation of the neutron skin against the inert proton-neutron core. This represents the first observation of a pygmy resonance with virtual photon scattering technique, therefore opening the possibility for more systematic studies in the future.

ACKNOWLEDGMENTS

The authors wish to thank the EUROBALL, GARFIELD and RISING collaborations which made possible the technical developments of the various setups and the realization of the experiments here discussed. Fruitful discussions with the nuclear structure theory group of the University of Milano, of the Niels Bohr Institute of Copenhagen and of the Japanese University of Niigata are also acknowledged.

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[20] R.Brun et al., CERN Report No.CERN

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29.

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194

Conference Proceedings Vol. 96

“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”

F. Gramegna, M. Cinausero, D. Fabris (Eds.)

SIF, Bologna 2008

THE SPES PROJECT:

AN ISOL FACILITY FOR NEUTRON-RICH BEAMS

G.Prete, on behalf of the SPES Collaboration

INFN Laboratori Nazionali di Legnaro

INTRODUCTION

SPES is an INFN project to develop a

Radioactive Beam facility as an intermediate step

toward EURISOL. The Laboratori Nazionali di

Legnaro (LNL) was chosen as the site for the

facility construction.

The LNL capability to play a role in this

research field is related to the presence of the

superconducting linac ALPI, able to re-accelerate

exotic ions at up to 10÷11 MeV/u, the well

consolidated know-how in linac construction, the

existing detectors and the related know-how.

Moreover, the necessary real estate is available

thanks to the extension of the Laboratory site

(more than a factor two in area with respect to

the actual size). Primary services and new

infrastructures, like a 40 MW power station, are

currently under implementation.

OVERVIEW OF THE SPES PROJECT

The main goal of the proposed facility is to

provide an accelerator system to perform

forefront research in nuclear physics by studying

nuclei far from stability. The SPES project is

concentrating on the production of neutron-rich

radioactive nuclei with mass in the range 80-160.

The emphasis to neutron-rich isotopes is justified

by the fact that this vast territory has been little

explored, at exceptions of some decay and in-

beam spectroscopy following fission. Therefore,

reactions in inverse kinematics will allow a new

class of data to be obtained.

The Rear Ion Beam (RIB) will be produced by

ISOL technique using the proton induced fission

on a Direct Target of UCx. The proton driver is a

Cyclotron with variable energy (15-70 MeV) and

a maximum current of 0.750 mA upgradeable to

1.5 mA and splitted on two exit ports.

The second goal of the facility is achieved by the

use of the second high energy proton beam and

developing an accelerator based Neutron Facility

by the high proton current produced with the

TRASCO injector, that is in an advanced

construction phase and it is able to deliver a

proton beam of 30 mA 5 MeV. The Neutron

Facility has two main applications: the

development of a Boron Neutron Capture

Therapy (BNCT) installation to perform research

in the treatment of cancer and an irradiation-

facility (LENOS) for material research and cross

section measurements. The expected neutron

beam has a fluence of thermal neutrons of 109 n

cm-2

s-1

and a rate of fast neutrons of 1014

n s-1

.

The radioactive beams, in selected forms, are

also valuable tools for biological and medical

research in the field of cancer therapy.

The most critical element of the SPES project

is the Direct Target. Up to day the proposed

target represent an innovation in term of

capability to sustain the primary beam power.

The design is carefully oriented to optimise the

radiative cooling taking advantage of the high

operating temperature of 2000 oC.

An extensive simulation of the target behaviour

has been performed to characterize the thermal

properties and the release process. Experimental

work to bench mark the simulations was carried

out at HRIBF, the Oak Ridge National

Laboratory ISOL facility (USA).

The production target will be designed following

the ISOLDE and EXCYT projects and special

care will be devoted to the safety and

195

radioprotection of the system. According to the

estimated level of activation in the production

target area of 1013

Bq a special infrastructure will

be designed. The use of up-to-date techniques of

nuclear engineering will result in a high security

level of the installation. The radiation

management and the control system will be

integrated and redundancies will be adopted in

the design.

The isotopes will be extracted and ionized at +1

with a source directly connected with the

production target. Several kinds of sources will

be used according to the beam of interest. A laser

source will be implemented in collaboration with

INFN-Pavia with the aim to produce a beam as

pure as possible.

The selection and the transport of the exotic

beam at low energy and low intensity is a

challenging task. Techniques applied for the

EXCYT beam will be of reference for the beam

diagnostic and an online identification station

will be part of the diagnostic system.

To optimize the reacceleration, a Charge Breeder

will be developed to increase the charge state to

+N before to inject the exotic beam in the

Bunching RFQ and PIAVE Superconductive

RFQ which represents the first re-acceleration

stage before the injection in ALPI.

Fig. 1: The SPES layout with the new facility connectd to the existing Tandem-Alpi-Piave complex.

The expected beam on experimental target will

have a rate on the order of 108-10

9 pps for

132Sn,

90Kr,

94Kr and 10

7-10

8 pps for

134Sn,

95Kr with

energies up to 9-11 MeV/u.

The SPES lay-out is shown in Fig. 1. The area

on the left side has to be constructed to house the

cyclotron proton driver, the two RIB targets, the

high intensity proton linac with neutron facility

and the target development laboratory. An

extension building for the second proton beam

from the cyclotron is planned but out of the

scope of the present project.

RARE BEAM PRODUCTION

The evaluation of the in target yield for physics

experiment at SPES has been determined starting

from the production yield (fission fragment

distribution), which was calculated mainly

through a Monte Carlo simulation based on

transportation model MCNPX [1]. This

simulation allows a detailed 3D definition of the

system to be analysed and a full transport

calculation starting from the proton distribution

[2]. The proton fission cross-section, is obtained

from the experimental data and from the

MCNPX calculations using the Bertini model

[3], and benchmarked with others models

(CEM2k, ISALBEL). The target is designed with

the aim to reach a fission rate of about 1013

fission/s, considering this number a challenge.

As far as the final beam current is considered, a

very crucial point is linked to short-life time of

radioactive isotopes which are produced in the

target: the target plus ion source system have to

be built considering with a great care the

properties related to the release and the

efficiency of the system.

The important step for a radioactive beam is the

overall efficiency of the target-source system

plus the efficiency linked to the post-accelerator

configuration: the evaluation of the intensity of

some radioactive beam species, interesting for

the nuclear physics community, has been

performed and validated through the existing

experimental data.

The final radioactive beam current depends on

the efficiencies of several chemical-physical

processes and beam transport elements For ISOL

facilities, the total efficiency is extremely case

dependent and lies between 10-2

to 10-6

. To give

an evaluation of the final beam the exotic species

must be followed all along their path.

196

The exotic species are produced inside the target

as neutral atoms and are extracted in a gas fase

due to the high operating temperature of the

target (2000oC). This process is governed by the

release efficiency: that is the diffusion process in

the uranium carbide grains, the effusion in the

container and the injection in the ion source. As

soon as the atoms are in the ion source they

should be ionized +1 to be extracted and injected

in the transport system; this process is controlled

by the source ionization efficiency. For an

efficient reacceleration it is necessary to increase

the charge state of the ions. This is done by the

Charge Breeder which increases the charge state

from +1 to +N with a breeding efficiency.

Finally, the overall efficiency of the transport

and post-accelerator system (the efficiency of the

separator and finally the transport efficiency

through the post accelerator up to the

experimental set up) must be considered.

All these parameters strongly affect the final

current, but the target efficiency itself is a very

complicated stuff.

The diffusion in the material is a complicated

phenomenon, which is not completely known

especially when the material is at high

temperature: it strictly depends on the material

structure and on the temperature at which the

material is maintained. [4]

A statistical approach is used to describe the

effusion of atoms inside the target powder. After

the diffusion the atoms follow a random walk up

to exit the container following the effusion

process. Experimental data available from

ISOLDE at CERN [5], HRIBF at ORNL [6] and

PNPI at Gatchina (RU) [7] have been used.

Table 1: Target release parameters for some species

The final results of our calculation indicate a

release time of 1 s for Sn isotopes and 10 s for Kr

for the chosen target configuration, mainly due to

the diffusion time, as reported in Table1.

The production rates of exotic beam on the

experimental target were evaluated taking into

account the following efficiencies as well as the

total release fraction of each isotope.

The assumed +1 and +1/+N ionization

efficiencies are 90% (+1) and 12% (+1/+N)

respectively for Kr and Xe, but only 30% (1+)

and 4% (1+/n+) respectively for Zn, Sr, Sn, I and

Cd. These values are obtained by the SPIRAL2

project and are expected for an optimized

extraction in which the source is specifically

designed for each beam. In some case the use of

an ECR source is required.

The Linac ALPI transmission efficiency is

considered 50%.

Using these quantities an evaluation of the beam

current on target, which can be obtained with the

new SPES facility, are then shown in Fig. 2 for

some isotopes.

Fig. 2: Beam on target: Intensities calculates considering emission, ionization and acceleration efficiencies (see text) for different isotopes

In Table 2 we report, for sake of comparison,

some world-wide facilities looking to the fission

rate and to the power deposited in the production

target.

SPES is located to a high production rate of

fission fragments similar to Spiral2. Nevertheless

a comparison with Spiral2, from the point of

view of driver, layout and cost, is doubtful as the

driver of the Spiral2 facility is oriented to the

production of high intensity stable beams and in

this sense the two facilities cannot be compared

at all.

element Diff.

time

(s)

Nr

of

Coll.

Eff.

Time

(s)

Release

Time

(s)

T1/2

(s)

TRF

(%)

132Sn 1 10

5 0.2 1.2 40 98

133Sn 1 10

5 0.2 1.2 1 40

Kr 10 105 0.1 10 1 15

Beam on Target

1.00E+00

1.00E+01

1.00E+02

1.00E+03

1.00E+04

1.00E+05

1.00E+06

1.00E+07

1.00E+08

1.00E+09

1.00E+10

70 80 90 100 110 120 130 140 150

mass

inte

ns

ity

(s

ec

-1)

Series1

132Sn

Ga

KrSr

AgIn

Sn Cs

197

Table 2: Comparison between several ISOL facilities.

PROTON DRIVERS

The driver for the primary proton beam impinging on the UCx fission target is the commercially available cyclotron Cyclone C70 from IBA.

The C70 cyclotron (see Fig. 3) is currently under commissioning in Nantes (ARRONAX project) with the purpose of radioisotopes production for radiochemistry and oncology [8].

As reported in Table 3, the accelerator is equipped with two external ion sources (a multicusp and an ECR) so as to produce 4 types of particles, in particular high intensity, variable energy H

- (30 ÷ 70 MeV, 750 μA).

The 5 MeV, 35 mA proton beam necessary for the operation of the 150 kW beryllium target of the BNCT neutron source and the LENOS neutron facility will be provided by an off resonance ECR source (TRIPS) followed by a RFQ. The TRIPS source was transferred from LNS to LNL at the end of 2005 [9].

Table 3: Cyclotron C70 beam characteristics

Fig. 3: The C70 cyclotron

Installation was completed in late July 2006

and beam extraction was succesfully tested in September 2006 [10].

The RFQ, initially developed for the TRASCO project, has two working regimes, pulsed and cw.

The operating frequency is 352.2 MHz, with the design choice of using a single 1.3 MW klystron already used at LEP. The RF power will be fed by means of eight high power loops.

The RFQ structure consists of six modules 1.18 m long each made of OFHC copper. The vacuum ports are on the first and fourth segments and the couplers on the other four. Particularly challenging are the very tight mechanical tolerances (20 μm) necessary for the purity of the accelerating mode (as required by beam dynamics) that have to be kept in presence of a

Primary

beam

Power

on

target

target Fissions per

sec

ISOLDE p 1GeV

2 microA

0.4

KW

Direct

Convert.

4· 1012

spallation

HRIBF p 40MeV

10 microA

Up-grade:

20 microA

0.4

KW

Direct

4·1011

TRIUMF p 450MeV

(250 MeV

in target)

40 μA

Up-grade:

70 μA

10

KW

17

KW

Direct

spallation

EXCYT

13C

45AMeV

0.5

KW

Direct

Light ions by

direct

reactions

4 108 8Li

(9·106

extracted)

SPIRAL2 d 40 MeV

5 mA

200

KW

Convert. 1013- 1014

SPES-

Direct

Target

p 40 MeV

200 μA

8 KW Direct

1013

Accelerated

beam

Extracted

Energy

(MeV)

Beam

Intensity

(μA)

Exit Ports

H-

D-

4He

2+

HH+

30 ÷ 70

15 ÷ 35

70

35

750

50

70

50

Dual

Dual

Single

Single

198

large power density. To date, the first two modules (RFQ1 (see Fig.

4) and RFQ2) underwent the complete construction cycle and the remaining four modules (RFQ3, RFQ4, RFQ5 and RFQ6) were pre-braze assembled and RF characterized and are ready for brazing at CERN [11].

Fig. 4: RFQ1 after completing construction

REACCELERATION

The linear accelerator ALPI, with a β range between about 0.04 and 0.2 and CW operation, represents an ideal re-accelerator for the radioactive beams. Radioactive ions can be accelerated above the Coulomb Barrier with high efficiency, and with a quasi-continuous time structure well suited for experiments. A time structure suitable for TOF measurements can be implemented by a low energy bunching system.

ALPI underwent a number of significant upgrades, in recent years, which made it a world-class facility in heavy ion stable beam accelerators and which will represent an important added value for its use as a RIB accelerator as well. Alpi has an equivalent acceleration voltage of 40 MV and may accelerates heavy ions in the region of Tin at energies between 6 and 13 AMeV according to their charge state (19+ or 40+ respectively).

To allow the reacceleration with ALPI a new bunching RFQ will be developed and the PIAVE Superconductive RFQ, which represent the actual injector from the ECR heavy ion source, will be moved to accept the low energy exotic beam.

CONCLUSION

The SPES facility is expected tu run the first exotic beam in 2013. Before starting the construction the R&D program will continue for key development subsystems to receive adequate answers; such items like control system final

target design and proton driver analysis, will be completely mature in about one year.

At the same time the detailed design and the procedure needed for the construction authorization will be implemented.

Design and construction of the complete facility will require 4 years, with the installation and commissioning of parts of the machine beginning immediately after the completion of the buildings and related infrastructures. Critical parts as RIB target and high current RFQ are in advanced construction stage and will be ready for laboratory test before the building construction. The implementation of the ALPI re-accelerator is already scheduled starting from the current year.

The evaluated budget is in the order of 43-48 Meuro, compatible with the INFN Road Map for the Nuclear Physics development.

[1] J.S. Hendricks et al., MCNPX vers. 2.5.e, LA-UR-04-0569 (2004) [2] A. Andrighetto, S. Cevolani and C. Petrovich Proceedings of 5

th Italy- Japan Symposium,

Napoli, November 3-7, 2004, p. 409 [3] A. Andrighetto, S. Cevolani, C. Petrovich Europ. Journal of Physics A25 (2005) 41 [4] J. Crank, The Mathematics of Diffusion, Clarendon Press (1956). [5] See web site: www94.web.cern.ch/ISOLDE and private communication [6] K. Carter, presentation at the 1

st Workshop on

Actinide Target Development, April 27-29, 2006, Vancouver Canada [7] M. Barbui et al., LNL Annual Report 2006, p.182 [8] J. Martino et al., and L. Medeiros Romao et al., Proceedings of the 18

th International

Conference on Cyclotrons and their Applications (CYCLOTRONS 2007) September 30, October 3, Giardini Naxos, Italy (www.lns.infn.it/Cyclotrons2007) [9] E. Fagotti et al., LNL Annual Report 2005, p. 150 [10] E. Fagotti et al., LNL Annual Report 2006, p. 189 [11] A. Palmieri et al., LNL Annual Report 2006, p. 193

199

Conference Proceedings Vol. 96

“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”

F. Gramegna, M. Cinausero, D. Fabris (Eds.)

SIF, Bologna 2008

NUCLEAR COLLISIONS AND THE LOW DENSITY NUCLEAR

EQUATION OF STATE

J. B. Natowitz1

and

L. Qin1, K. Hagel

1, R. Wada

1, Z. Chen

1, P. Sahu

1, S. Kowalski

2,

S. Shlomo1, M. Barbui

3, D. Fabris

3, M. Lunardon

3, S. Moretto

3, G. Nebbia

3, S. Pesente

3, V. Rizzi

3,

G. Viesti3, M. Cinausero

4, G. Prete

4, T. Keutgen

5, Y. El Masri

5 and Z. Majka

6

1 Cyclotron Institute, Texas A&M University, 2 Silesia University, 3 Dipartimento di Fisica and

INFN Padova, 4 INFN Laboratori Nazionali di Legnaro, 5 Universit´e Catholique de Louvain , 6

Jagellonian University

INTRODUCTION

The opportunity to present a lecture on nuclear

reaction dynamics at the Workshop in Honor of

the 80th Birthday of Professor Renato Angelo

Ricci is itself an honor and a pleasure. Thanks to

a nearly 20 year collaboration with scientists

from Legnaro National Laboratory and the

University of Padova I have had a first hand

opportunity to observe the major impact that this

Laboratory has had on nuclear science and, in

particular, the legacy of Professor Ricci in

setting the course for this very successfiul

program. I congratulate Professor Ricci on his

Birthday and on his scientific acheivements,

many of which are covered in greater detail in

other contributions to this symposium. In

reviewing the progress in nuclear reaction

dynamics over the course of the time that the

Legnaro Lab has been active, I can not help but

recall that our early picture of heavy ion (HI)

collisions, as summarized in Fig. 1 which was

shown at many reactions meetings in the 1960’s,

was indeed a quite limited one.

Much of this simplified view could, of course,

be attributed to the relative youth of the HI field

and to the relatively low energies of the available

heavy ion accelerators at that time. Even so, a

concentrated program of experimental and

theoretical efforts soon resulted in significant

extensions of the simple models and a much

greater understanding of the richness of the HI

collisions and their ability to produce and explore

nuclei at the extremes of angular momentum and

excitation energy and to uncover a rich array of

new structural features. It is not possible in this

limited format to address the many different

works in these areas, so, by way of example,

Fig. 2 presents some results from just one area of

early reaction studies, that of HI fusion reactions

This is an area where the Padova and Legnaro

scientists have made many important

contributions.

Fig. 1: Simple HI Reaction Classification - 1960’s

With the advent of more powerful

accelerators and detector arrays, a much better

appreciation of the reaction landscape was soon

201

developed from a large body of HI reaction

experiments and theoretical models. A more

recent summary of reaction mechanism types is

contained in Fig. 3. Notably, as the beam

energies pass through the Fermi Energy domain,

near 38 MeV/u, a significant change occurs in the

dominant reaction mechanisms, from the

relatively gentle low energy collisions to more

violent collisions which can produce large

thermal and compressional shocks and large

fluctuations in the interacting nucleonic matter.

Fig. 2: Fusion limits and Nuclei at Extremes of Angular Momentum

Fig. 3: A more modern classification of heavy ion

induced nuclear reactions presented as a function of

both impact parameter b and laboratory beam

energy per nucleon of the projectile.

In recent years our own group has actively

pursued several avenues of investigation of

heavy ion reactions focused on understanding the

dynamical evolution [1-3], the degree of

equilibration [1-4], the possibility of critical

disassembly in near Fermi energy collisions [5-

7], the derivation of information on the equation

of state from nuclear caloric curve measurements

[8-10] and determination of symmetry energies

of low density nuclear gases [11].

Understanding the nuclear matter equation of

state over a wide range of temperature and

density is important in both the nuclear and

astrophysical context. In the latter, knowledge of

specific heats and the density dependence of the

symmetry energy are crucial to understanding

Fusion Limits and Nuclei at Extremes of Angular Momentum

R. Grover et al, 1965

202

collapse of supernovae and the properties of

neutron stars resulting from supernova collapse

[12.13]. The initial compression and the thermal

shock in Fermi-Energy heavy ion collisions lead

naturally to the production of nucleonic matter at

varying temperatures and densities which are

interesting in this context. To illustrate the large

fluctuations in density which may be produced,

we present, in Fig. 4, results of AMD

calculations [14] for the system 64

Zn + 124

Sn.

Fig. 4: Density profiles from Antisymmetrized

Molecular Dynamics calculations for collisions of

47A MeV 64Zn with 124 Sn targets. Results are shown

for times ranging from collision to 300 fm/c for

impact parameters ranging from 0.3 to 3.3 Fermis

Conceptually our studies may be understood

by reference to Fig. 5, where the schematic

trajectory of a near-Fermi energy collision

between normal density nuclei is depicted in

temperature-density space. For comparison, the

theoretical phase diagram for infinite nuclear

matter is also depicted on this diagram. It is that

equation of state which one hopes to probe in

collisions which lead to different trajectories in

the Rho-T plane.

Fig. 5: Nuclear collisions of normal density nuclei

create short lived, initially compressed and excited

systems, which expand and cool. During this process,

the properties of the expanding system may be

manifested in the matter flow, in caloric curves and

in the energy spectra, yield patterns and nature of

produced species which emerge from the collision

zone.

Most of our studies are made using the

TAMU NIMROD detector, a 4π charged particle

telescope array inside a 4π neutron calorimeter

[15] in collaboration with colleagues from

Legnaro National Laboratory, the University of

Padova and the Jagiellonian University in

Krakow. (See Fig. 6). Recently, the detection

characteristics of NIMROD have been

considerably enhanced with additional Si wafer

detectors and improved ionization detectors.

The features of NIMROD place us in an

excellent position to take advantage of the

TAMU Accelerator upgrade [16], presently

underway.

In addition to a picture of the NIMROD

Detector, Fig. 6 includes a typical two-

dimensional array depicting the observed

relationship between charged particle

multiplicity and neutron multiplicity in

NIMROD for the reaction 47AMeV 64

Zn + 197

Au. The plot evidences a distinct correlation in

which increasing charged particle multiplicity is

associated with increasing neutron multiplicity.

Exploring The Nuclear Matter Phase

Diagram With Collisional Heating

• .

•

203

Fig. 6: Left- The NIMROD Detector. Right-Plot of

charged particle multiplicity vs neutron multiplicity

for the reaction 47A MeV 64Zn + 197Au.

Although there are significant fluctuations

reflecting both the competition between decay

modes and the detection efficiencies, these

correlations and transverse energy measurements

provide a means for selecting the most violent

collisions.

2. EQUATION OF STATE STUDIES

Since the light particle emission which occurs

during the collisions carries essential information

on the early dynamics and on the degree of

equilibration at each stage of the reaction, we

have emphasized investigations of nucleon and

light cluster emission to obtain a more detailed

experimental picture of the pre-equilibrium,

thermalization and disassembly phases of such

reactions. The kinematic features and yields of

emitted light particles and clusters can been

exploited to probe the nature of the intermediate

system and information on the EOS can be

extracted. Much of our work utilizes coalescence

model based techniques to follow the time

evolution of the reaction [17-18] and references

therein]. Using NIMROD we have made

comprehensive studies of the reaction dynamics

for a number of heavy ion induced reactions in

the Fermi energy domain.

MCP

MN

One theme of our recent work has been the

extensive comparisons of our experimental

results with predictions of an anti-symmetrized

molecular dynamics model code (AMD) [14].

Direct observables, such as multiplicity

distributions, charge distributions, energy spectra

and velocity distributions, are reproduced

reasonably well by the AMD calculations [1] and

such comparisons have proved to be particularly

useful in elucidating the underlying reaction

dynamics and in differentiating between

dynamically driven and thermodynamically

driven processes. With these techniques, we have

explored the dynamic and thermal evolution and

degree of equilibration achieved and extracted

heat capacities of nuclei at temperatures

comparable to those encountered in supernovae,

key sites of nucleo-synthesis of elements heavier

than Fe [1-10]. We have also determined nuclear

symmetry energies at low densities comparable to

those of the neutrino-sphere in supernova

explosions [11,19,20]. In the following we

discuss these last results and proposed extensions

of this work in more detail.

204

LIGHT PARTICLE CLUSTERIZATION IN

NUCLEAR MATTER AT VERY LOW

DENSITY

Reliable understanding of the nuclear EOS over a

range of densities remains a very important

requirement in nuclear astrophysics. Several

extensive calculations and existing tabulations,

based on varying nucleon-nucleon interactions

serve as standards for a wide variety of

astrophysical simulations [21,22]. At low

densities and high temperatures strong alpha

clustering of the matter is predicted. Such

clusterization can be expected in low density

nuclear matter, whether it be gas or the surface of

an expanded high temperature nucleus.

In a recent theoretical paper, Horowitz and

Schwenk have reported the development of a

Virial Equation of State (VEOS) for low density

nuclear matter [19]. This equation of state,

derived from experimental observables should be

“model-independent, and therefore to set a

benchmark for all nuclear equations of state at

low densities.” Its importance in both nuclear

physics and in the physics of the neutrino sphere

in supernovae is emphasized in the VEOS paper

[19].

Fig. 7: Virial equation of state results ( solid lines) at

T = 2, 4 and 8 MeV are compared to those of two

other theoretical models. The present Virial model

does not include heavier nuclei is not expected to be

adequate above the point where the Shen Calculation

peaks.

An important feature of the VEOS is the natural

inclusion of clustering which leads to large

symmetry energies at low baryon density. These

results are compared to those of other

calculations in Fig. 7.

We recently adapted our investigations of the

nucleon and light cluster emission that occurs in

near Fermi energy heavy ion collisions [1-10] to

probe the properties of the low density

participant matter produced in such collisions

[11]. The reactions of 35 MeV/nucleon 64

Zn

projectiles with 92

Mo and 197

Au target nuclei

were studied. The analysis employed the

isoscaling technique which assumes that for two

systems with similar temperatures but different

N/Z ratios, the ratio of yields of a particular

isotope in the two systems may be expressed as

Y2(Z,N)/Y1(Z,N) = Ce – (ĮN + βZ) /T

where C is a constant. For systems of

temperature T, a comparison of such ratios for a

number of isotopes allows extraction of the

parameters Į and β which can be related to the

symmetry energy [23-26]. The data provide

experimental evidence for a large degree of

alpha clustering resulting from nucleon

coalescence in this low density matter, in

agreement with theoretical predictions [11, 19,

21, 22, 27-29]. For nuclear gases with average

proton fraction, Yp ~0.44, and densities at and

below 0.05 times normal nuclear density and

varying temperatures experimental symmetry

energy coefficients of 9 – 14 MeV have been

derived using the isoscaling method.

The resultant symmetry energy

coefficients are plotted against density in Fig. 8

where they are compared to those which are

predicted by the Gogny effective interaction and

to the 31.6 x (Δ/Δ0)1.05

dependence suggested by

a recent analysis of isospin diffusion data [30].

These symmetry energies reported in Fig. 8 are

far above those obtained in common effective

interaction calculations and reflect cluster

formation, primarily of alpha particles, not

included in such calculations. They are in good

205

agreement with those calculated in the VEOS

treatment of reference 19. A detailed description

of this work may be found in reference 11.

Stimulated by these data, Schwenk and his

collaborators have since improved the VEOS

model with the addition of 3H and

3He cluster

coefficients [20].

Fig.8: Derived symmetry energy coefficients as a

function of baryon density. Solid diamonds indicate

results using densities of column 4 in Table 1 of ref

[30]. Solid line indicates the variation predicted by

the Gogny interaction. The dotted line represents the

function 31.6 x (Δ/Δ0)1.05 .

To the best of our knowledge our analysis is the

only one which employs experimentally

determined numbers for all quantities occurring

in the isoscaling relationship and does so as a

function of ejected particle velocity. This

analysis at low density is made possible because

at such low density the chemical equilibrium

model of Albergo et al. should be applicable

[31]. Extracting information at higher densities is

clearly desirable but requires a more

sophisticated analysis. This is made clear from a

number of theoretical results [ 27-29] .

For example, in Fig. 9 and Fig. 10 we present

results of Beyer et al. and of Roepke et al. who

have calculated the in-medium binding energies

of clusters as a function of temperature and

density. As seen in Fig. 9 for a temperature of 10

MeV, the free binding energies of the clusters (at

0 on the density axis) decrease with increasing

density and reach 0 at a point known as the Mott

density. This point is temperature dependent as

seen in Fig. 8 where Mott lines for, d, t nd alpha

particles are represented. This disappearance of

the cluster binding energy in medium is closely

related to the peaks in the calculated alpha mass

fractions seen in Fig. 7.

Fig. 9: In medium binding energies of light

clusters

Using this model, G. Roepke has made

calculations of the low density symmetry energy

for comparison to our experimental results [29].

The agreement between the two is fair, however

we are continuing to discuss these results and G.

Roepke is presently making more complete

calculations which may allow us to push the

experimental analyses to higher densities where

the simple extreme low density chemical

equilibrium model is not appropriate.

0

10

20

30

40

0,001 0,01 0,1 1Rho

Es

ym

M

eV

Esym ShenDens Corr

Gogny

^1.05

206

Fig. 10: Symmetry energies at low density. Points-

Theoretical results of G. Roepke are compared to

experimental results of Kowalski et al. Line-

homogeneous matter calculation by Roepke et al.

In order to pursue this effort of taking the

in medium modifications into account and

broaden the density range over which the

symmetry energies are experimentally

determined we have carried out a series of

experiments in which the reactions of 112

Sn and 124

Sn with a wide range of projectiles, ranging

from p to 64

Zn, all at the same energy per

nucleon, 47Mev/u, could be studied. The

systems chosen for this study, the PhD thesis of

LiJun Qin, were :

1

H + 112

Sn,124

Sn

2

H + 112

Sn,124

Sn 4

He + 112

Sn,124

Sn

1 0

B + 112

Sn,124

Sn

20

Ne + 112

Sn,124

Sn 40

Ar + 112

Sn,124

Sn

64

Zn + 112

Sn,124

Sn

In this series of experiments different collision

systems should lead to different average

densities, The analysis is nearing completion. By

careful comparisons of the yields, spectra and

angular distributions observed for particle

emission from these different systems we are

attempting to cleanly separate early emission

resulting from nucleon-nucleon collisions from

that resulting from evaporation from the

thermalized system and obtain a much cleaner

picture of the dynamic evolution of the hotter

systems. Information on the symmetry potential

included in mean field can then be extracted

from comparison of the data with results of the

dynamic transport model calculations (and

statistical afterburners) using QMD and AMD

models [14, 32] or, guided by such QMD and

AMD calculations, using empirical techniques

such as isoscaling for systems with different

N/Z ratios (see above). Below we present some

preliminary results from this work.

REACTION TOMOGRAPHY

Fig. 11 contains invariant velocity plots of the

yields of p and 4He emitted in the reaction

64Zn+

124Sn as a function of their parallel and

transverse velocities in the laboratory frame.

Fig. 11: Invariant velocity plots for protons (top) and

alpha particles (bottom) emitted in the most violent

collisions of 47A MeV 64Zn + 124Sn.

207

To construct these plots, the data from the

discrete detector rings were smoothed by

assignment of the position for a particle detected

in a given discrete detector according to the

angular distribution function generated with the

source fitting parameters. The plots reveal some

strong similarities for the two different systems,

related to the similar dynamic particle emission

in the two systems.

Within the framework of such velocity

representations it is possible to explore various

quantities, derivable from the particle yields.

||V

||V

Vpar cm/ns

Vp

erp

cm/n

s

Significant Temperature Evolution

with Particle Velocity

Relatively Small Changes

with Projectile Size

10B + 124Sn

20Ne + 124Sn

40Ar + 124Sn

64Zn + 124Sn

Fig. 12: Chemical equilibrium temperatures.

Thus, in Fig. 12 the THHe double isotope ratio

temperatures for reactions of four different 47

MeV/u heavy ion projectiles with 124

Sn are

compared.

For the 64

Zn projectile, Fig. 13 presents a very

preliminary representation of the symmetry free

energies, derived from isoscaling analyses for

the 112

Sn and 124

Sn targets.

Fig. 13: Symmetry free energy in velocity space. See

text.

ACKNOLEDGEMENTS

This work was supported by the United States

Department of Energy under Grant # DE-FG03-

93ER40773 and by The Robert A. Welch

Foundation under Grant # A0330.

[1] R. Wada et al., Phys.Rev. C 69 (2004)

044610.

[2] J. Wang et al., Phys.Rev. C 75 (2007)

014604.

[3] J. Wang et al., Phys.Rev. C 72 (2005)

024603

[4] Y. G. Ma et al., Phys.Rev. C 69 (2004)

031604.

[5] Y. G. Ma et al., Phys.Rev. C 71 (2005)

054606.

[6] Y. G. Ma et al., Nucl.Phys. A749 (2005)

106.

[7] J.B. Natowitz et al., Phys.Rev. C 66 031601

(2002).

[8] J. B. Natowitz et al., Phys.Rev.Lett. 89

(2002) 212701.

[9] J.B. Natowitz et al., Phys.Rev. C 65 034618

(2002).

[10] J. Wang et al., Phys.Rev. C71 (2005)

054608.

208

[11] S. Kowalski et al., Phys.Rev. C 75 014601

(2007).

[12] D. Arnett, “Supernovae and

Nucleosynthesis”, Princeton University

Press, Princeton, NJ, 1996.

[13] J. M. Lattimer and M. Prakash, Phys.

Rept. 333 (2000) 121.

[14] A. Ono, Phys. Rev. C 59 (1999) 853.

[15] TAMU Cyclotron Institute Report,

2006-07

[16] http://cyclotron.tamu.edu/

[17] J.Cibor et al., in "Isospin Physics in Heavy-

Ion Collisions at Interm.Energies",

Eds.Bao-An Li and W. Udo Schroeder,

NOVA Science Publishers, Inc.

(New York), (2001), p 283.

[18] K Hagel et al., Phys.Rev. C 62, (2000)

034607-1

[19] C.J. Horowitz and A. Schwenk,

Nucl. Phys. A 776 (2006) 55.

[20] E. O'Connor et al., arXiv:nucl-th/0702044

to appear in Phys. Rev. C (2007).

[21] H.Shen et al., Nucl.Phys. A637, (1998)

435; Prog.

Theor. Phys. 100 (1998)1013.

[22] J.M. Lattimer and F.D. Swesty, Nucl.

Phys. A535 (2001) 331.

[23] M. B. Tsang et al., Phys. Rev. Lett. 86,

(2001) 5023.

[24] M. B. Tsang et al., Phys.Rev. C 64

(2001) 041603.

[25] A.S. Botvina et al., Phys.Rev. C 65

(2002) 044610.

[26] Akira Ono et al., Phys.Rev. C 68

(2003) 051601.

[27] http://www.arxiv.org/find/nucl-th/1/au:

+Shen_H/0/1/0/all/0/1

M. Beyer et al., Phys.Lett. B488 (2000)

247.

[28] M. Beyer et al., Eur.Phys .J. A22

(2004) 261.

[29] G. Roepke Seminar TAMU (2007).

[30] L -W Chen et al., Int .J.Mod.Phys. E15

(2006) 1385.

[31] S. Albergo et al., Nuovo Cimento A 89,

(1985) 1.

[32] J. Lukasik and Z. Majka Acta Phys.

Pol. B 24 (1993) 1959.

209

SUPERHEAVY AND GIANT NUCLEAR SYSTEMS

Walter Greiner1, Valery Zagrebaev2

1Frankfurt Institute for Advanced Studies,

J.W. Goethe-Universitat 60438 Frankfurt am Main, Germany,2Flerov Laboratory of Nuclear Reaction, JINR,

Dubna, 141980, Moscow region, Russia

DEDICATION

I dedicate this talk to my friend Profes-sor Renato Ricci on occasion of his 80thbirthday. I know him for nearly 40 years.Our first encounter was here at Varenna atthe International School on Nuclear Physics,which Renato organized and which wasguided by Victor Weisskopf. I had just com-pleted my PhD and was a student at thattime. For very many years we met at theisland Hvar in Croatia. Nicola Cindro wasthe third important member of the triplet(Cindro, Ricci and myself). Very impor-tant and joyfull were our meetings with D.Allan Bromley at Yale. We spend pleas-ant evenings and dinners together with Mrs.Ricci, Mrs. Bromley and also with my wifeBarbara. With the subject of my talk Iwould like to remind Renato that extremelyimportant physics on time-delay can also bedone (for lighter systems) at Legnaro. I urgeRenato to stimulate and pave the way forthis work there. Dear Renato, stay healthyand be happy for another 20 years. Godbless you!

INTRODUCTION

Superheavy (SH) nuclei obtained in“cold” fusion reactions with Pb or Bi target[1] are along the proton drip line and veryneutron-deficient with a short half-life. Infusion of actinides with 48Ca more neutron-

rich SH nuclei are produced [2] with muchlonger half-life. But they are still far fromthe center of the predicted “island of sta-bility” formed by the neutron shell aroundN=184 (see the nuclear map in Fig. 1).Unfortunately a small gap between the su-perheavy nuclei produced in 48Ca-inducedfusion reactions and those which were ob-tained in the ‘cold” fusion reactions is stillremain which should be filled to get a uni-fied nuclear map.

In the “cold” fusion, the cross sections ofSH nuclei formation decrease very fast withincreasing charge of the projectile and be-come less than 1 pb for Z>112 (see Fig. 1).Heaviest transactinide, Cf, which can beused as a target in the second method, leadsto the SH nucleus with Z=118 being fusedwith 48Ca. Using the next nearest elementsinstead of 48Ca (e.g., 50Ti, 54Cr, etc.) in fu-sion reactions with actinides is expected lessencouraging, though experiments of suchkind are planned to be performed. In thisconnection other ways to the production ofSH elements in the region of the “island ofstability” should be searched for.

In principle, superheavy nuclei may beproduced in explosion of supernova [4]. Ifthe half-life of these nuclei is comparablewith the age of the Earth they could besearched for in nature. However, it is theheightened stability of these nuclei (rare de-cay) which may hinder from their discovery.To identify these more or less stable super-heavy elements supersensitive mass separa-tors should be used. Chemical methods of

Conference Proceedings Vol. 96“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”F. Gramegna, M. Cinausero, D. Fabris (Eds.)SIF, Bologna 2008

211

FIG. 1: Superheavy nuclei produced in “cold” and “hot” fusion reactions. Predicted island ofstability are shown around Z=114, 120 and N=184 (right panel). Experimental and predictedevaporation residue cross sections for production of superheavy elements produced in “cold” (1n)and “hot” (3n) fusion reactions [3] (left panel).

E

mc-

2

+mc 2

Dirac see

po

sitro

nyie

ld1s2p

200

10

20

30

40

400 600 800 1000 1200

t

delay

e+E(e+ ), KeVe-

Z1

U + Cm

Z Z1+ 2Z2

FIG. 2: Schematic figure of spontaneous decay of the vacuum and spectrum of the positrons formedin supercritical electric field (Z1 + Z2 > 173).

separation also could be useful here.

About twenty years ago transfer reactionsof heavy ions with 248Cm target have beenevaluated for their usefulness in producingunknown neutron-rich actinide nuclides [5–7]. The cross sections were found to decreasevery rapidly with increasing atomic numberof surviving target-like fragments. However,Fm and Md neutron-rich isotopes have beenproduced at the level of 0.1 µb. Theoret-ical estimations for production of primarysuperheavy fragments in the damped U+Ucollision have been also performed at thistime within the semiphenomenological dif-fusion model [8]. In spite of obtained high

probabilities for the yields of superheavyprimary fragments (more than 10−2 mb forZ=120), the cross sections for productionof heavy nuclei with low excitation energieswere estimated to be rather small: σCN (Z =114, E∗ = 30 MeV) ∼ 10−6 mb for U+Cmcollision at 7.5 Mev/nucleon beam energy.The authors concluded, however, that “fluc-tuations and shell effects not taken into ac-count may conciderably increase the forma-tion probabilities”. Such is indeed the case(see below).

Recently a new model has been proposed[9] for simultaneous description of all thesestrongly coupled processes: deep inelastic

212

(DI) scattering, quasi-fission (QF), fusion,and regular fission. In this paper we ap-ply this model for analysis of low-energydynamics of heavy nuclear systems formedin nucleus-nucleus collisions at the energiesaround the Coulomb barrier. Among oth-ers there is the purpose to find an influ-ence of the shell structure of the driving po-tential (in particular, deep valley caused bythe double shell closure Z=82 and N=126)on formation of compound nucleus (CN) inmass asymmetric collisions and on nucleonrearrangement between primary fragmentsin more symmetric collisions of actinide nu-clei. In the first case, discharge of the sys-tem into the lead valley (normal or sym-metrizing quasi-fission) is the main reactionchannel, which decreases significantly theprobability of CN formation. In collisions ofheavy transactinide nuclei (U+Cm, etc.), weexpect that the existence of this valley maynoticeably increase the yield of survivingneutron-rich superheavy nuclei complemen-tary to the projectile-like fragments (PLF)around lead (“inverse” or anti-symmetrizingquasi-fission reaction mechanism).

Direct time analysis of the collision pro-cess allows us to estimate also the life-time of the composite system consisting oftwo touching heavy nuclei with total chargeZ>180. Such “long-living” configurations(if they exist) may lead to spontaneouspositron emission from super-strong electricfields of giant quasi-atoms by a static QEDprocess (transition from neutral to chargedQED vacuum) [10, 11], see schematic Fig. 2.

NUCLEAR SHELLS

Quantum effects leading to the shellstructure of heavy nuclei play a crucial roleboth in stability of these nuclei and in pro-duction of them in fusion reactions. The fis-

sion barriers of superheavy nuclei (protect-ing them from spontaneous fission and, thus,providing their existence) are determinedcompletely by the shell structure. Studiesof the shell structure of superheavy nucleiin the framework of the meson field the-ory and the Skyrme-Hartree-Fock approachshow that the magic shells in the superheavyregion are very isotopic dependent [12] (seeFig. 3). According to these investigationsZ=120 being a magic proton number seemsto be as probable as Z=114. Estimatedfission barriers for nuclei with Z=120 arerather high though depend strongly on achosen set of the forces [13].

Interaction dynamics of two heavy nu-clei at low (near-barrier) energies is definedmainly by the adiabatic potential energy,which can be calculated, for example, withinthe two-center shell model [14]. An exam-ple of such calculation is shown in Fig. 4 forthe nuclear system consisting of 108 protonsand 156 neutrons. Formation of such heavynuclear systems in fusion reactions as well asfission and quasi-fission of these systems areregulated by the deep valleys on the poten-tial energy surface (see Fig. 4) also causedby the shell effects.

ADIABATIC DYNAMICS OF HEAVY

NUCLEAR SYSTEM

At incident energies around the Coulombbarrier in the entrance channel the fusionprobability is about 10−3 for mass asym-metric reactions induced by 48Ca and muchless for more symmetric combinations usedin the “cold synthesis”. DI scattering andQF are the main reaction channels here,whereas the fusion probability [formationCN] is extremely small. To estimate such asmall quantity for CN formation probability,first of all, one needs to be able to describe

213

FIG. 3: Proton (left column) and neutron (right column) gaps in the N − Z plane calculatedwithin the self-consistent Hartree-Fock approach with the forces as indicated [12]. The forces withparameter set SkI4 predict both Z=114 and Z=120 as a magic numbers while the other sets predictonly Z=120.

well the main reaction channels, namely DIand QF. Moreover, the quasi-fission pro-cesses are very often indistinguishable fromthe deep-inelastic scattering and from regu-lar fission, which is the main decay channelof excited heavy compound nucleus.

To describe properly and simultaneouslythe strongly coupled DI, QF and fusion-fission processes of low-energy heavy-ion col-lisions we have to choose, first, the unifiedset of degrees of freedom playing the prin-cipal role both at approaching stage andat the stage of separation of reaction frag-ments. Second, we have to determine theunified potential energy surface (dependingon all the degrees of freedom) which reg-

ulates all the processes. Finally, the cor-responding equations of motion should beformulated to perform numerical analysis ofthe studied reactions. In contrast with othermodels, we take into consideration all thedegrees of freedom necessary for descriptionof all the reaction stages. Thus, we need notto split artificially the whole reaction intoseveral stages. Moreover, in that case unam-biguously defined initial conditions are eas-ily formulated at large distance, where onlythe Coulomb interaction and zero-vibrationsof the nuclei determine the motion. The dis-tance between the nuclear centers R (cor-responding to the elongation of a mono-nucleus), dynamic spheroidal-type surface

214

FIG. 4: Adiabatic energy levels and potential energy surface for the nuclear system 264108.

FIG. 5: Driving potential for the nuclear system formed in 136Xe+209Bi collision at fixed defor-mations (left) and at contact configuration (right). The solid lines with arrows show schematically(without fluctuations) most probable trajectories.

deformations β1 and β2, mutual in-plane ori-entations of deformed nuclei ϕ1 and ϕ2, andmass asymmetry η = A1−A2

A1+A2

are probablythe relevant degrees of freedom in fusion-fission dynamics.

The two-center shell model [14] seems tobe most appropriate for calculation of theadiabatic potential energy surface. A choiceof dynamic equations for the considered de-grees of freedom is not so evident. Themain problem here is a proper description

of nucleon transfer and change of the massasymmetry which is a discrete variable by itsnature. The corresponding inertia parame-ter µη, being calculated within the Werner-Wheeler approach, becomes infinite at con-tact (scission) point and for separated nu-clei. In Ref. [9] the inertialess Langevintype equation for the mass asymmetry hasbeen derived from the corresponding mas-ter equation for the distribution function.Finally we use a set of 13 coupled Langevin

215

FIG. 6: Angular (a), energy-loss (b) and charge (c) distributions of the Xe-like fragments obtainedin the 136Xe+209Bi reaction at Ec.m.

= 568 MeV. Experimental data are taken from Ref. [16]. Forother notations see the text.

type equations for 7 degrees of freedom (rel-ative distance, rotation and dynamic defor-mations of the nuclei and mass asymmetry)which are solved numerically.

The cross sections for all the processesare calculated in a simple and natural way.A large number of events (trajectories) aretested for a given impact parameter. Thoseevents, in which the nuclear system over-came the fission barrier from the outsideand entered the region of small deforma-tions and elongations, are treated as fusion(CN formation). The other events corre-spond to quasi-elastic, DI and QF processes.Subsequent decay of the excited CN (C →

B + xn + Nγ) is described then within thestatistical model using an explicit expres-sion for survival probability, which directlytakes into account the Maxwell-Boltzmannenergy distribution of evaporated neutrons[15]. The double differential cross-sectionsare calculated as follows

d2ση

dΩdE(E, θ) =

∫∞

0

bdb∆Nη(b, E, θ)

Ntot(b)

1

sin(θ)∆θ∆E.

(1)Here ∆Nη(b, E, θ) is the number of eventsat a given impact parameter b in which thesystem enters into the channel η (definitemass asymmetry value) with kinetic energyin the region (E, E + ∆E) and center-of-

mass outgoing angle in the region (θ, θ+∆θ),Ntot(b) is the total number of simulatedevents for a given value of impact parameter.In collisions of deformed nuclei an averagingover initial orientations is performed. Ex-pression (1) describes the mass, energy andangular distributions of the primary frag-ments formed in the binary reaction (bothin DI and in QF processes). Subsequentde-excitation cascades of these fragmentsvia emission of light particles and gamma-rays in competition with fission were takeninto account explicitly for each event withinthe statistical model leading to the final

mass and energy distributions of the reac-tion fragments. The model allows us to per-form also a time analysis of the studied reac-tions. Each tested event is characterized bythe reaction time τint, which is calculated asa difference between re-separation (scission)and contact times.

DEEP INELASTIC SCATTERING OF

HEAVY NUCLEI

At first we applied the model to de-scribe available experimental data on low-energy damped collision of very heavy nu-clei, 136Xe+209Bi [16], where the DI pro-cess should dominate due to expected preva-

216

lence of the Coulomb repulsion over nuclearattraction. The adiabatic potential energysurface of this nuclear system is shown onthe left panel of Fig. 5 in the space of elon-gation and mass asymmetry at zero dynamicdeformations. The colliding nuclei are verycompact with almost closed shells and thepotential energy has only one deep valley(just in the entrance channel, η ∼ 0.21) giv-ing rather simple mass distribution of the re-action fragments. In that case the reactionmechanism depend mainly on the nucleus-nucleus potential at contact distance, on thefriction forces at this region (which deter-mine the energy loss) and on nucleon trans-fer rate at contact. Note, that there is awell pronounced plateau at contact configu-ration in the region of zero mass asymmetry(see Fig. 5, right panel). It becomes evenlower with increasing the deformations andcorresponds to formation of the nuclear sys-tem consisting of strongly deformed touch-ing fragments 172Er+173Tm (see Fig. 5),which means that a significant mass rear-rangement may occur here leading to addi-tional time delay of the reaction.

On the right panel of Fig. 5 the landscapeof the potential energy is shown at contactconfiguration depending on mass asymme-try and deformation of the fragments. Ascan be seen, after contact and before re-separation the nuclei aim to become moredeformed. Moreover, beside a regular diffu-sion (caused by the fluctuations), the finalmass distribution is determined also by thetwo well marked driving paths leading thesystem to more and to less symmetric con-figurations. They are not identical and thisleads to the asymmetric mass distributionof the primary fragments, see Fig. 6(c).

In Fig. 6 the angular, energy and chargedistributions of the Xe-like fragments areshown comparing with our calculations (his-tograms). In accordance with experimen-

FIG. 7: Time distribution of all the sim-ulated events for 86Kr+166Er collisions atEc.m.

= 464 MeV, in which the energy loss wasfound higher than 35 MeV (totally 105 events).Conditionally fast (< 2 · 10−21 s), intermediateand slow (> 2 ·10−20 s) collisions are marked bythe different colors (white, light gray and darkgray, respectively). The black area correspondsto CN formation (estimated cross section is 120mb), and the arrow shows the interaction time,after which the neutron evaporation may occur.

tal conditions only the events with the to-tal kinetic energy in the region of 260 ≤

E ≤ 546 MeV and with the scattering an-gles in the region of 40o ≤ θc.m. ≤ 100o

were accumulated. The total cross sec-tion corresponding to all these events isabout 2200 mb (experimental estimation is2100 mb [16]). Due to the rather high ex-citation energy sequential fission of the pri-mary heavy fragments may occur in this re-action (mainly those heavier than Bi). Inthe experiment the yield of the heavy frag-ments was found to be about 30% less com-paring with Xe-like fragments. Our calcu-lation gives 354 mb for the cross section ofsequential-fission, which is quite comparablewith experimental data. Mass distributionof the fission fragments is shown in Fig. 6(c)by the dotted histogram. Note that it is acontamination with sequential fission prod-ucts of heavy primary fragments leading to

217

FIG. 8: (a) TKE-charge distribution of the 86Kr+166Er reaction products at Ec.m.

= 464 MeV[17]. (b) Calculated TKE-mass distribution of the primary fragments. Open, gray and black circlescorrespond to the fast (< 2 ·10−21 s), intermediate and long (> 2 ·10−20 s) events (overlapping eachother on the plot).

FIG. 9: Angular (a), energy (b) and charge (c) distributions of the 86Kr+166Er reaction productsat Ec.m.

= 464 MeV. Experimental data (points) are from [17]. Overlapping white, light and darkgray areas in (b) show the contributions of the fast, intermediate and slow events, respectively [seeFig. 7 and Fig. 8(b)].

the bump around Z=40 in the experimentalcharge distribution.

At the second step we analyzed the re-action 86Kr+166Er at Ec.m. = 464 MeV[17], in which the nuclear attractive forcesmay lead, in principle, to the formation ofa mono-nucleus and of CN. The adiabaticpotential energy surface, QF and fusion-fission (FF) processes should in this caseplay a more important role. For the anal-ysis of this reaction we used the same valueof the nucleon transfer rate and the samefriction forces as in the previous case. Forthe nuclear viscosity we choose the value

µ0 = 2 · 10−22 Mev s fm−3 because of inter-mediate values of excitation energies avail-able here as compared with the two previousreactions.

The interaction time is one of the mostimportant characteristics of nuclear reac-tions, though it cannot be measured di-rectly. It depends strongly on the reactionchannel. The time distribution of all the86Kr+166Er collisions at Ec.m. = 464 MeV,in which the kinetic energy loss is higherthan 35 MeV, is shown in Fig. 7. The in-teraction time was calculated starting fromt = 0 at R = Rmax = 40 fm up to

218

FIG. 10: Potential energy at contact “nose-to-nose” configuration and mass distribution of pri-mary fragments for the two nuclear systems formed in 48Ca+248Cm (left) and 232Th+250Cf (right)collisions.

the moment of scission into two fragments(R > Rscission, pR > 0) or up to CN for-mation. The approaching time (path fromRmax to Rcontact) in the entrance channel isvery short (4÷ 5 · 10−22 s depending on theimpact parameter) and may be ignored here.All the events are divided relatively onto thethree groups: fast (τint < 20 · 10−22 s), in-termediate, and slow (τint > 200 · 10−22 s).

A two-dimensional plot of the energy-mass distribution of the primary frag-ments formed in the 86Kr+166Er reaction atEc.m. = 464 MeV is shown in Fig. 8. In-clusive angular, charge and energy distribu-tions of these fragments (with energy lossesmore than 35 MeV) are shown in Fig. 9.Rather good agreement with experimentaldata of all the calculated DI reaction prop-erties can be seen, which was never obtainedbefore in dynamic calculations. Underes-timation of the yield of low-Z fragments[Fig. 9(c)] could again be due to the contri-bution of sequential fission of highly excitedreaction participants not accounted in themodel at the moment.

In most of the damped collisions(Eloss > 35 MeV) the interaction timeis rather short (several units of 10−21 s).These fast events correspond to grazingcollisions with intermediate impact param-eters. They are shown by the white areas in

Figs. 7 and 9(b) and by the open circles intwo-dimensional TKE-mass plot [Fig. 8(b)].Note that a large amount of kinetic energyis dissipated here very fast at relatively lowmass transfer (more than 200 MeV duringseveral units of 10−21 s).

The other events correspond to muchslower collisions with large overlap of nu-clear surfaces and significant mass rear-rangement. In the TKE-mass plot theseevents spread over a wide region of massfragments (including symmetric splitting)with kinetic energies very close to kineticenergy of fission fragments. The solid linein Fig. 8(b) correspond to potential energyat scission point V (r = Rscission, β, α) +Qgg(α) minimized over β. Scission pointis calculated here as Rscission(α, β) =(1.4/r0)[R1(A1, β1) + R2(A2, β2)] + 1 fm,Qgg(α) = B(A1) + B(A2) − B(86Kr) −

B(166Er) and B(A) is the binding energyof a nucleus A. Some gap between the twogroups in the time and energy distributionscan also be seen in Fig. 7 and Fig. 9(b). Allthese make the second group of slow eventsquite distinguished from the first one. Theseevents are more similar to fission than todeep-inelastic processes. Formally, they alsocan be marked as quasi-fission.

219

LOW-ENERGY COLLISIONS OF

TRANSACTINIDE NUCLEI

Reasonable agreement of our calculationswith experimental data on low-energy DIand QF reactions induced by heavy ionsstimulated us to study the reaction dynam-ics of very heavy transactinide nuclei. Thepurpose was to find an influence of the shellstructure of the driving potential (in par-ticular, deep valley caused by the doubleshell closure Z=82 and N=126) on nucleonrearrangement between primary fragments.In Fig. 10 the potential energies are showndepending on mass rearrangement at con-tact configuration of the nuclear systemsformed in 48Ca+248Cm and 232Th+250Cfcollisions. The lead valley evidently revealsitself in both cases (for 48Ca+248Cm sys-tem there is also a tin valley). In the firstcase (48Ca+248Cm), discharge of the sys-tem into the lead valley (normal or sym-metrizing quasi-fission) is the main reac-tion channel, which decreases significantlythe probability of CN formation. In col-lisions of heavy nuclei (Th+Cf, U+Cmand so on) we expect that the existenceof this valley may noticeably increase theyield of surviving neutron-rich superheavynuclei complementary to the projectile-likefragments around 208Pb (“inverse” or anti-symmetrizing quasi-fission process).

Direct time analysis of the reaction dy-namics allows us to estimate also the life-time of the composite system consisting oftwo touching heavy nuclei with total chargeZ>180. Such “long-living” configurationsmay lead to spontaneous positron emis-sion from super-strong electric field of giantquasi-atoms by a static QED process (tran-sition from neutral to charged QED vac-uum) [10]. About twenty years ago an ex-tended search for this fundamental processwas carried out and narrow line structures

in the positron spectra were first reportedat GSI. Unfortunately these results werenot confirmed later, neither at ANL, norin the last experiments performed at GSI.These negative finding, however, were con-tradicted by Jack Greenberg (private com-munication and supervised thesis at WrightNuclear Structure Laboratory, Yale univer-sity). Thus the situation remains unclear,while the experimental efforts in this fieldhave ended. We hope that new experimentsand new analysis, performed according tothe results of our dynamical model, mayshed additional light on this problem andalso answer the principal question: are theresome reaction features (triggers) testifyinga long reaction delays? If they are, new ex-periments should be planned to detect thespontaneous positrons in the specific reac-tion channels.

Using the same parameters of nuclear vis-cosity and nucleon transfer rate as for thesystem Xe+Bi we calculated the yield of pri-mary and surviving fragments formed in the232Th+250Cf collision at 800 MeV center-of mass energy. Low fission barriers of thecolliding nuclei and of most of the reactionproducts jointly with rather high excitationenergies of them in the exit channel willlead to very low yield of surviving heavyfragments. Indeed, sequential fission ofthe projectile-like and target-like fragmentsdominate in these collisions, see Fig. 11. Atfirst sight, there is no chances to get sur-viving superheavy nuclei in such reactions.However, as mentioned above, the yield ofthe primary fragments will increase due tothe QF effect (lead valley) as compared tothe gradual monotonic decrease typical fordamped mass transfer reactions. Secondly,with increasing neutron number the fissionbarriers increase on average (also there is theclosed sub-shell at N=162). Thus we mayexpect a non-negligible yield (at the level of

220

FIG. 11: Mass distributions of primary (solid histogram), surviving and sequential fission fragments(hatched areas) in the 232Th+250Cf collision at 800 MeV center-of-mass energy. On the right theresult of longer calculation is shown.

FIG. 12: (Left panel) Experimental and calculated yields of the elements 98÷101 in the reactions238U+238U (crosses) [5] and 238U+248Cm (circles and squares) [6]. (Right panel) Predicted yieldsof superheavy nuclei in collisions of 238U+238U (dashed), 238U+248Cm (dotted) and 232Th+250Cf(solid lines) at 800 MeV center-of-mass energy. Solid curves in upper part show isotopic distributionsof primary fragments in the Th+Cf reaction.

1 pb) of surviving superheavy neutron richnuclei produced in these reactions [18].

Result of much longer calculations isshown on the right panel of Fig. 11. Thepronounced shoulder can be seen in the massdistribution of the primary fragments nearthe mass number A=208 (274). It is ex-plained by the existence of a valley in the

potential energy surface [see Fig. 10(b)],which corresponds to the formation of dou-bly magic nucleus 208Pb (η = 0.137). Theemerging of the nuclear system into this val-ley resembles the well-known quasi-fissionprocess and may be called “inverse (or anti-symmetrizing) quasi-fission” (the final massasymmetry is larger than the initial one).

221

For η > 0.137 (one fragment becomes lighterthan lead) the potential energy sharply in-creases and the mass distribution of the pri-mary fragments decreases rapidly at A<208(A>274).

In Fig. 12 the available experimental dataon the yield of SH nuclei in collisions of238U+238U [5] and 238U+248Cm [6] are com-pared with our calculations. The estimatedisotopic yields of survived SH nuclei in the232Th+250Cf, 238U+238U and 238U+248Cmcollisions at 800 MeV center-of-mass energyare shown on the right panel of Fig. 12.Thus, as we can see, there is a real chance forproduction of the long-lived neutron-rich SHnuclei in such reactions. As the first step,chemical identification and study of the nu-clei up to 274

107Bh produced in the reaction232Th+250Cf may be performed.

The time analysis of the reactions studiedshows that in spite of absence of an attrac-tive potential pocket the system consistingof two very heavy nuclei may hold in con-tact rather long in some cases. During thistime the giant nuclear system moves overthe multidimensional potential energy sur-face with almost zero kinetic energy (resultof large nuclear viscosity). The total reac-

tion time distribution, dσdlog(τ)

(τ denotes

the time after the contact of two nuclei),is shown in Fig. 13 for the 238U+248Cmcollision. The dynamic deformations aremainly responsible here for the time delay ofthe nucleus-nucleus collision. Ignoring thedynamic deformations in the equations ofmotion significantly decreases the reactiontime, see Fig. 13(a). With increase of theenergy loss and mass transfer the reactiontime becomes longer and its distribution be-comes more narrow.

As mentioned earlier, the lifetime of a gi-ant composite system more than 10−20 sis quite enough to expect positron linestructure emerging on top of the dynami-

cal positron spectrum due to spontaneouse+e− production from the supercritical elec-tric fields as a fundamental QED process(“decay of the vacuum”) [10]. The abso-lute cross section for long events is foundto be maximal just at the beam energy en-suring the two nuclei to be in contact, seeFig. 13(c). The same energy is also optimalfor the production of the most neutron-richSH nuclei. Of course, there are some uncer-tainties in the used parameters, mostly inthe value of nuclear viscosity. However wefound only a linear dependence of the reac-tion time on the strength of nuclear viscos-ity, which means that the obtained reactiontime distribution is rather reliable, see log-arithmic scale on both axes in Fig. 13(a).

Formation of the background positrons inthese reactions forces one to find some ad-ditional trigger for the longest events. Suchlong events correspond to the most dampedcollisions with formation of mostly excitedprimary fragments decaying by fission, seeFigs. 14(a). However there is also a chancefor production of the primary fragments inthe region of doubly magic nucleus 208Pb,which could survive against fission due tonucleon evaporation. The number of thelongest events depends weakly on impactparameter up to some critical value. On theother hand, in the angular distribution ofall the excited primary fragments (stronglypeaked at the center-of-mass angle slightlylarger than 900) there is the rapidly decreas-ing tail at small angles, see Fig. 14(b). Timedistribution for the most damped events(Eloss > 150 MeV), in which a large masstransfer occurs and primary fragments scat-ter in forward angles (θc.m. < 70o), is rathernarrow and really shifted to longer time de-lay, see hatched areas in Fig. 13. For theconsidered case of 238U+248Cm collision at800 MeV center-of-mass energy, the detec-tion of the surviving nuclei in the lead re-

222

FIG. 13: Reaction time distributions for the 238U+248Cm collision at 800 MeV center-of-massenergy. Thick solid histograms correspond to all events with energy loss more than 30 MeV. (a)Thin solid histogram shows the effect of switching-off dynamic deformations. (b) Thin solid, dashedand dotted histograms show reaction time distributions in the channels with formation of primaryfragments with Eloss > 200 MeV, Eloss > 200 MeV and θc.m.

< 70o and A ≤ 210, correspondingly.Hatched areas show time distributions of events with formation of the primary fragments withA ≤ 220 (light gray), A ≤ 210 (gray), A ≤ 204 (dark) having Eloss > 200 MeV and θc.m.

< 70o. (c)Cross section for events with interaction time longer than 10−20 s.

FIG. 14: Energy-time (a) and angular-time (b) distributions of primary fragments in the238U+248Cm collision at 800 MeV (Eloss > 15 MeV).

gion at the laboratory angles of about 25o

and at the low-energy border of their spec-trum (around 1000 MeV for Pb) could be areal trigger for longest reaction time.

CONCLUSION

For near-barrier collisions of heavy ionsit is very important to perform a combined(unified) analysis of all strongly coupled

channels: deep-inelastic scattering, quasi-fission, fusion and regular fission. This am-bitious goal has now become possible. Aunified set of dynamic Langevin type equa-tions is proposed for the simultaneous de-scription of DI and fusion-fission processes.For the first time, the whole evolution of theheavy nuclear system can be traced start-ing from the approaching stage and end-ing in DI, QF, and/or fusion-fission chan-nels. Good agreement of our calculations

223

with experimental data gives us hope toobtain rather accurate predictions of theprobabilities for superheavy element forma-tion and clarify much better than beforethe mechanisms of quasi-fission and fusion-fission processes. The determination of suchfundamental characteristics of nuclear dy-namics as the nuclear viscosity and the nu-cleon transfer rate is now possible. The pro-duction of long-lived neutron-rich SH nu-clei in the region of the “island of sta-bility” in collisions of transuranium ionsseems to be quite possible due to a largemass rearrangement in the inverse (anti-symmetrized) quasi-fission process causedby the Z=82 and N=126 nuclear shells. Asearch for spontaneous positron emissionfrom a supercritical electric field of long-living giant quasi-atoms formed in these re-actions is also quite promising.

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224

Conference Proceedings Vol. 96

“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”

F. Gramegna, M. Cinausero, D. Fabris (Eds.)

SIF, Bologna 2008

PROBING THE NUCLEAR EOS WITH REACTION MECHANISMS AT

FERMI ENERGIES

M. Colonna1,2

, V.Baran3, M. Di Toro

1,2

1 LNS-INFN, I-95123, Catania, Italy,

2 Physics and Astronomy Dept. University of Catania, Italy,

3 NIPNE-HH and Bucharest University, Romania

INTRODUCTION

In the last few years the increased accuracy of the experimental techniques has renewed interest in nuclear reactions at Fermi energies. In particular, recent experimental and theoretical analyses were devoted to the study of the properties and effects of the symmetry term of the EOS (iso-EOS) away from saturation conditions [1,2]. In particular, heavy ion reactions with exotic nuclei at Fermi energies can be used to study the properties of the symmetry term at densities below and around the normal value. In central collisions at 30-50 MeV/A, where the full disassembly of the system into many fragments is observed, one can study specifically properties of liquid-gas phase transitions occurring in asymmetric matter [2,3,4,5]. For instance, in neutron-rich matter, phase co-existence leads to a different asymmetry in the liquid and gaseous phase: fragments (liquid) appear more symmetric with respect to the initial matter, while light particles (gas) are more neutron-rich [2-5]. Hence the analysis of the isotopic content of all reaction products, from pre-equilibrium emission to fragments, allows to get information on low-density properties of the isovector part of the nuclear interaction.

In recent years, the properties of fragments and light clusters emitted in systems with different initial asymmetries have been widely investigated [6,7,8,9,10,11] looking in particular at the production yields of various isotopes, as obtained in reactions between proton-rich and neutron-rich systems.

More recently, the study of the isotopic content of pre-equilibrium emission has revealed a good sensitivity to the iso-EOS, considering the emitted neutron to proton ratio as a function of the kinetic energy [12].

Here we extend this type of investigation to fragments. Correlations between fragment

charges and velocities have been recently observed, providing information on the interplay between thermal and entrance channel (collective) effects in the fragmentation mechanism [13,14]. Following this line, one can also investigate correlations between fragment isotopic content and kinematical properties, trying to get a deeper insight into the reaction path and to improve the understanding of the underlying mechanisms. In this way one can also study more in detail the effects of different EOS’s and, in particular, of the symmetry energy on fragment properties. Information on the low densiy behaviour of the symmetry energy can be obtained also from lower energy reactions, where one can study the competition between reaction mechanisms, such as incomplete fusion, deep-inelastic or fragmentation. In particular, in mid-peripheral collisions a large variety of phenomena is observed, ranging from highly dissipative binary evens to neck break-up and non-statistical light fragment emission. As we will discuss in the following, the study of neutron-rich systems reveals new interesting features, opening the possibility to access independent information on the symmetry energy.

THE MODEL

Theoretically, the evolution of complex systems under the influence of fluctuations can be described by a transport equation with a stochastic fluctuating term, the so-called Boltzmann-Langevin equation (BLE):

[ ] [ ]fIfIHft

f

dt

dfcoll δ+=+

∂∂

= , (1)

225

where ( )tprf ,,rr

is the one-body distribution function, ( )tprH ,,

rris the one-body Halmitonian

and ][ fIδ represents the stochastic part of the two-body collision integral [15,16].

Here we will follow the approximate treatment to the BLE presented in Ref.[17], the so-called Stochastic Mean Field (SMF) model, that consists in the implementation of spatial density fluctuations [17]. Calculations have been performed using a BNV code (TWINGO), where the test particle method is used to solve Eq.(1) [18] . We use a soft EOS, with compressibility modulus K=200 MeV and, for the density (ȡ) dependence of the symmetry energy, we consider two representative parameterizations,

( ) AZNIICAIE symsym /)(,)(/, 2 −≡≡ ρρ one showing a rapidly increasing behaviour with density, roughly proportional to ȡ2

(asystiff) and one with a kind of saturation above normal density (asysoft, SKM

*) (see Ref.[2,19] for more

detail). The two parameterizations obviously cross at normal density. The symmetry energy at densities below the normal value is larger in the asysoft case, while above normal density it is higher in the asystiff case. Hence in the low-density regime, that is the region of interest for the analysis of central dissipactive reactions, isospin effects are expected to be more important in the asysoft case.

FRAGMENT ISOTOPIC PROPERTIES

AND CORRELATIONS

We will first focus on central collisions, b= 2 fm, considering symmetric reactions between systems having three different (N/Z)in initial asymmetry:

112Sn +

112Sn,

124Sn +

124Sn,

132Sn +

132Sn, with (N/Z)in = 1.24, 1.48, 1.64,

respectively. The considered beam energy is 50 MeV/A. 1200 events have been run for each reaction and for each of the two symmetry energies adopted. The first two reactions

112Sn +

112Sn and

124Sn +

124Sn, have been widely

investigated both from the experimental and theoretical point of view [6,7,20]. In central collisions, after the initial collisional shock, the system expands and breaks up into many pieces, due to the development of volume (spinodal) and surface instabilities. The formation of a bubble-like configuration is observed, where the initial fragments are located. The average fragment multiplicity is approximately equal to 6 for the reactions considered here [19]. Along the reaction path, several nucleons are emitted at the early stage (pre-equilibrium emission) and/or are

evaporated while fragments are formed. Primary fragments are identified by applying a coalescence procedure to the matter with density larger than ȡcut = 1/5 ȡ0 (liquid phase). The remaining particles are considered as belonging to the gas phase. First, let us briefly recall some general features concerning the isotopic content of fragments and emitted nucleons, as obtained with the two iso-EOS considered. In the following we will restrict our analysis to fragments with charge in the range between 3 and 10 (that we call intermediate mass fragments (IMF's) ). The average N/Z of emitted nucleons (gas phase) and IMF's is presented in Fig.1 as a function of the initial (N/Z)in of the three colliding systems.

Fig. 1: The N/Z of the liquid (squares,left) and of the gas (circles,right) phase is displayed as a function of the system initial N/Z. Full lines and symbols refer to the asystiff parameterization. Dashed lines and open symbols are for asysoft.

One observes that, generally, the gas phase is more neutron-rich in the asysoft case, while IMF's are more symmetric. This is due to the larger value of the symmetry energy at low density for the asysoft parameterization [19]. It is interesting to note that, in the asystiff case, due to the low value of the symmetry energy, Coulomb effects dominate and the N/Z of the gas phase becomes lower than that for IMF's, because protons are preferentially emitted.

Now we move to investigate in more detail correlations between fragment isotopic content and kinematical properties. The idea in this investigation is that fragmentation originates from the break-up of a composite source that expands with a given velocity field. Since neutrons and protons experience different forces, one may expect a different radial flow for the two species. In this case, the N/Z composition of

226

the source would not be uniform, but would depend on the radial distance from the center or mass or, equivalently, on the local velocity. This trend should then be reflected in the fragment asymmetries. As a measure of the isotopic composition of the IMF's, we will consider the sum of neutrons, N = Ȉi Ni, and protons, Z = Ȉi Zi, of all IMF's in a given kinetic energy range, in each event. Then we take the ratio N/Z and we consider the average over the ensemble of events. This observable is plotted in Fig.2 for the three reactions.

Fig. 2: The fragment N/Z (see text) as a function of the kinetic energy. Left panel:asystiff; Rigth panel: asysoft.

The behaviour observed is rather sensitive to the iso-EOS. For the proton-rich system, the N/Z decreases with the fragment kinetic energy, expecially in the asystiff case, where the symmetry energy is relatively low at low density [19]. In this case, the Coulomb repulsion pushes the protons towards the surface of the system. Hence, more symmetric fragments acquire larger velocity. The same effects are responsible for the proton-rich pre-equilibrium emission observed in this case (see Fig.1). The decreasing trend is less pronounced in the asysoft case (right panel) because Coulomb effects are counterbalanced by the larger value of the symmetry energy. In systems with larger initial asymmetry, the decreasing trend is inversed, due to the larger neutron repulsion in neutron-rich systems. Larger slopes are always observed in the asysoft case.

In conclusion, this analysis reveals the existence of significant, EOS-dependent correlations between the N/Z and the kinetic energy of IMF's. This correlation is linked to the different forces experienced by neutrons and protons along the fragmentation path, that in turn

depend on the detail of the isovector part of the nuclear interaction. This study can be considered as complementary to the pre-equilibrium emission studies [12]. A parallel investigation of pre-equilibrium and fragment emissions would be very important for a cross-check of model predictions against experimental observables sensitive to different phases of the reaction.

NECK EMISSION

Dissipative mid-peripheral collisions, including binary and three-body breakings, offer a unique opportunity to study phenomena occurring in nuclear matter under extreme conditions with respect to shape, intrinsic excitation energy, spin, N/Z ratio, etc., together with the possibility to control these conditions by choosing appropriate entrance and exit channels. Thus, it is possible to probe the mechanisms of nuclear excitation, how intrinsic degrees of freedom are converted into collective modes, how these modes decay and how relaxation processes occur within a small quantal system that is initially far from equilibrium. The velocity and the angular distribution of the reaction products furnish natural clocks from which it is possible to determine the equilibration times of the various degrees of freedom (e.g. N/Z ratio, mass, excitation energy) and discuss whether non-equilibrium features in light particle and IMF emissions are present [21].

Neck emission at Fermi energies has been widely investigated, revealing the presence of features that characterize it as an independent IMF source, clearly distinguishable from the statistical emission of projectile-like (PLF) and target-like (TLF) fragments [21]. In particular, the IMF’s coming from the neck source have a velocity that deviates from the Viola systematics and are aligned, i.e. emitted with a scall angle ĭ with respect to the direction connecting PLF and TLF velocities. It is interesting to study correlations between the fragment N/Z and the alignment. This is presented in Fig.3, for the reaction

124Sn +

64Ni at 35 MeV/u, b = 6 fm. As

already seen for the central reactions, a pronounced decreasing trend of the N/Z is observed in the asystiff case. In this case (semi-peripheral reactions) this can be attributed to the migration of the neutron-richness of the system towards the low-density neck region, influencing especially the properties of IMF’s that interact with the system for a longer time (small ĭ angles).

227

Fig. 3: The N/Z of IMF’s emitted from the neck region as a function of the alignment. Circles: asystiff. Squares: asysoft.

COMPETITION BETWEEN REACTION

MECHANISMS

For dissipative collisions at low energy,

interaction times are quite long and therefore a large coupling among various mean-field modes is expected. In some cases, due to a combined Coulomb and angular momentum (deformation) effect, some instabilities can show up, like in fission decays [22]. This can lead to three-body breakings, where a light cluster is emitted from the neck region, similarly to what is observed at larger beam energy.

For instance, a significant probability for preferential alpha-particle emission perpendicular to the symmetry axis of a fissioning heavy-ion system was reported in Ref.[23] for the system

165Ho +

56Fe at 465 MeV

(see also [24]). In the same energy range, TDHF calculations show a rich variety of dynamical behavior, including deep-inelastic scattering, fusion and three-body break-up (see for instance Ref.[25], where the reaction

86Kr +

139La at 505,

610, 710 MeV is analyzed). Three-body processes, in heavy-ion reactions with exotic systems, can certainly provide a new access to the dynamics of nuclear scission in new conditions, allowing to investigate the role of the isovector part of the nuclear interaction. In particular, one can investigate whether the

development of surface (neck-like) instabilities, that would help ternary breaking, is sensitive to the structure of the symmetry term.

This study has been undertaken in the case of the reaction

132Sn+

64Ni at 10 MeV/n. Semi-

peripheral reactions, corresponding to impact parameters b=6, 7, 8 fm have been considered, for which one observes mostly binary exit channels.

It appears that the neck dynamics is rather different when one considers the asysoft or the asystiff parameterization.

Fig. 4: Density contour plots on the reaction plane obtained in several runs of the reaction 132Sn+64Ni at 10 MeV/n, b = 7 fm, at t = 500 fm/c. Asystiff interaction.

Fig. 5: Density contour plots on the reaction plane obtained in several runs of the reaction 132Sn+64Ni at 10 MeV/n, b = 7 fm, at t = 500 fm/c. Asysoft interaction.

This can be qualitatively seen on Figs. 4-5, where density contour plots of events obtained

228

with the two iso-EOS are represented. Large deformations, strongly suggesting a final

three-body outcome, are observed in the majority of the events in the asystiff case. In fact, in this case, due to the lower value of the symmetry energy, the neutron-rich neck connecting the two systems survives a longer time, leading to deformed primary products, from which eventually small clusters can be dynamically emitted.

To perform a quantitative analysis, one can evaluate the quadrupole or octupole moment of PLF and/or TLF, that are related to the degree of deformation of the di-nuclear system and, hence, to the probability to get a ternary break-up. The distribution of the octupole moment over an ensemble of events is shown in Fig. 6 for the two iso-EOS (the dashed hysto corresponds to asystiff and the full hysto to asysoft) and three impact parameters. In conclusion an asystiff symmetry term leads to more dissipative events, due to lower value of the symmetry energy.

Fig. 6: Distribution of the octupole moment of primary fragments obtained in the reaction 32Sn + 64Ni at 10 MeV/u at b = 6 fm (left), 7 fm (middle), 8 fm (right). Full line: asysoft; dashed line: asystiff.

CONCLUSIONS AND PERSPECTIVES

We have discussed properties of the fragmentation path, in collisions of charge-asymmetric systems at Fermi energies, that can be related to the behavior of the symmetry energy below normal density, thus allowing to extract important information on fundamental quantities of the nuclear interaction.

We focus on the analysis of correlations between fragment isotopic content and kinematical properties, performing simulations based on SMF approaches. This study also allows one to get a deeper insight into the fragmentation mechanism. In fact, the analysis of correlations between fragment composition and

velocity can be used as a clock of fragment formation and as an indicator of the underlying dynamics.

This kind of investigation is extended also to mid-peripheral collisions at energies around 10 MeV/u. Also at these relatively low energies, ternary (neck) break-up is observed in neutron-rich systems, as a manifestation of the degree of dissipation reached, with a good sensitivity to the iso-EOS adopted.

We expect to see effects of the different interaction times and dissipation degree also on the charge equilibration mechanism, probed starting from entrance channels with large N/Z asymmetries, like

132Sn (N/Z=1.64) +

58Ni

(N/Z=1.07). Moreover, the equilibration mechanism is also directly linked to the strength of the symmetry term. For more central collisions this can be studied via the direct measurement of the prompt Dynamical Dipole emission, nucleus-nucleus collective bremsstrahlung radiation during the charge equilibration path, see Refs.[26,27]. Nice experimental features of such dipole radiation are the angular anisotropy, with maximum emission orthogonal to the beam axis, and the gamma spectrum, with centroid at energies well below the expected GDR emission from the residues. The energy range around 10 MeV/u seems to optimize the effect, see the recent data of Ref.[28] with stable beams. From this class of phenomena one can access new independent information on the low-density behavior of the symmetry energy.

[1] Isospin Physics in Heavy-ion Collisions at Intermediate Energies, Eds. Bao-An Li and W. Udo Schroeder, Nova Science Publishers (2001, New York). [2] V. Baran, M.Colonna, V.Greco, M.Di Toro, Phys. Rep. 410 (2005) 335. [3] H.Mueller and B.D.Serot, Phys.Rev. C52 (1995) 2072 [4] Bao-An Li and C.M.Ko, Nucl.Phys. A618 (1997) 498 [5] Ph. Chomaz, M. Colonna, J. Randrup, Phys. Rep. 389, (2004) 263 [6] H.S.Xu et al., Phys. Rev. Lett. 85 (2000) 716. [7] M.B. Tsang, W.A. Friedman, C.K. Gelbke et al., Phys. Rev. Lett. 86 (2001) 5023 [8] A.S. Botvina, O.V. Lozhkin and W. Trautmann, Phys. Rev. C65 (2002) 044610. [9] E. Geraci et al., Nucl. Phys. A732 (2004) 173 [10] D.V.Shetty, S.J.Yennello, G.A.Souliotis, Phys Rev. C75 (2007) 034602; S.Kowalski et al.,

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Phys Rev. C75 (2007) 014601 [11] M.Colonna and M.B.Tsang, Eur. Phys. J. A30 (2006) 165 [12] M.Famiano er al., Phys. Rev. Lett. 97 (2006) 052701 [13] G.Tabacaru et al., Nucl. Phys. A764 (2006) 371 [14] J.D. Frankland et al., Nucl. Phys. A689 (2001) 940; J.Colin et al., Phys. Rev. C67 (2003) 064603 [15] S.Ayik, C.Gregoire, Phys. Lett. B212 (1998) 269 and refs. therein. [16] J.Randrup and B.Remaud, Nucl. Phys. A514 (1990) 339 [17] M. Colonna et al, Nucl. Phys. A642 (1998) 449 [18] A.Guarnera, M.Colonna, Ph.Chomaz, Phys. Lett. B373 (1996) 297. [19] V. Baran et al., Nucl. Phys. A703 (2002) 603 [20] B-A Li, C.Ko, and Z. Ren, Phys. Rev. Lett. 78

(1997) 1644; T.X.Liu et al., Phys. Rev. C69

(2004) 014603 [21] V. Baran, M. Colonna, M. Di Toro, Nucl. Phys. A730 (2004) 329; E. De Filippo et al., Phys. Rev. C71 (2005) 044602 [22] M.Colonna, M.Di Toro, A.Guarnera, Nucl .Phys. A589 (1995) 160 [23] W.W.Wilcke et al., Phys. Rev. Lett. 51 (1983) [24] U.Brosa et al., Phys. Rep. 197(1990)167 [25] K.T.R.Davies et al., Phys. Rev. C20 (1979) 1372 [26] C.Simenel, Ph. Chomaz, G.de France, Phys. Rev. Lett. 86 (2000) 2971 [27] V.Baran, D.M.Brink, M.Colonna, M.Di Toro, Phys. Rev. Lett. 87 (2001) 182501 [28] D.Pierroutsakou et al., Phys. Rev. C71 (2005) 054605

230

PROPERTIES OF HEAVY ION COLLISIONS AT FERMI

ENERGIES

S.Piantelli1 for the FIASCO Collaboration1,2

1 INFN Sezione di Firenze, 2 Dipartimento di Fisica Universita di Firenze

INTRODUCTION

Heavy ion collisions with beam energybetween 10 and 50AMeV are usually in-dicated as reactions at Fermi energies be-cause the Fermi energy for nucleons insidenuclei is of the same order of magnitude(around 30MeV). In this energy domain pe-ripheral and semi-peripheral collisions showbinary character, with two heavy remnants(the Quasi-Projectile QP and the Quasi-Target QT) in the exit channel. The bestway to put into evidence this behaviouris to present the experimental yields ofthe emitted Light Charged Particles (LCPs,Z = 1, 2) and Intermediate Mass Fragments(IMFs, 3 ≤ Z ≤ 7) as a function of the par-allel and perpendicular components of theircenter of mass velocity with respect to QP-QT separation axis; an example of such rep-resentation is presented in Fig.1 (from [1])for the symmetric reaction 93Nb +93 Nb at38AMeV. The figure shows clearly two in-tensified circular regions located around thevelocity of QP and QT for protons (top) andα particles (middle), corresponding to theso-called Coulomb rings. The events withtwo heavy remnants in the exit channel con-stitute more than 50% of the total reactioncross section.

Another characteristic property of theFermi energy domain is the large amountof IMFs and LCPs emitted with velocity in-termediate between those of QP and QT,the so called “midvelocity” emission [1–11].Their presence clearly emerges if we com-pare the experimental (v‖, v⊥) plots to those

020406080

TKEL=200MeV TKEL=500MeV TKEL=800MeV

020406080

020406080

-50 0 50

V⊥ (

mm

/ns)

-50 0 50-50 0 50

E/A=38MeV

FIG. 1: Efficiency corrected experimental yieldsin the plane (v‖, v⊥) with respect to the QP-QTseparation axis with the origin in the center ofmass reference frame; data refer to the symmet-ric system 93Nb +93 Nb at 38AMeV and theyhave been collected by the FIASCO setup. Rowscorrespond, respectively, from top to bottom, toprotons, α particles and IMFs with 3 ≤ Z ≤ 7.Each column corresponds to a different central-ity of the collision. From [1].

obtained for a pure evaporative simulationmainly based on the GEMINI code [12] (apure evaporative code based on the statis-tical model), as shown in Fig.2 (from [8]).Especially the fourth row, corresponding tothe IMFs case, shows that while the simu-lation (right column) predicts an emissiononly located around the Coulomb rings, theexperimental emission pattern (left column)is mainly concentrated in the central re-gion between the velocity of the QP andof the QT. An emission in the midvelocityregion, superimposed to the emission alongthe Coulomb rings, is present also for the

Conference Proceedings Vol. 96“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”F. Gramegna, M. Cinausero, D. Fabris (Eds.)SIF, Bologna 2008

231

LCPs. The origin of this phenomenon is stilldebated, but the usual interpretation at-tributes it to the rupture (in the first phaseof the reaction) of the neck of nuclear mat-ter which is formed between QP and QT inthe interaction phase.

0

50

100Experiment (corr.)

p

Statistical simulation

p

0

50d

v perp

(m

m/n

s) d

0

50Z=2 Z=2

0

50

-50 0 50

Z=3-7

-50 0 50

Z=3-7

vpar (mm/ns)

FIG. 2: Left column: efficiency corrected exper-imental yields in the plane (v‖, v⊥) with respectto the QP-QT separation axis with the origin inthe center of mass reference frame; data referto the system 116Sn +93 Nb at 29.5AMeV andthey have been collected by the FIASCO setup.Right column: same kind of data for a purelyevaporative simulation. From [8].

This work concerns the presentation ofthe physical analysis developed by the FI-ASCO experiment [13] in the past eightyears; the discussed data concern the sym-metric systems 93Nb +93 Nb at 17, 23, 30and 38AMeV and 116Sn +116 Sn at 23,30, and 38AMeV; the asymmetric reaction116Sn +93 Nb at 29.5AMeV is included too.The experiments were performed at Labo-

ratori Nazionali del Sud of INFN in Cata-nia. The goals of our data analysis con-cern: i) the separation of the midvelocitycomponent from the evaporation from theexcited QP and QT; ii) the characterizationof both kinds of emission (evaporative andmidvelocity) from the point of view of par-ticle multiplicities and isotopic composition(for Z=1 only) as a function of the impactparameter; iii) the comparison among dif-ferent beam energies; iv) the average energyand mass balance for the whole reaction; v)the estimate of the time scale associated tothe midvelocity process.

THE EXPERIMENTAL SETUP

As it has been already pointed out, thesetup we used for our data collection iscalled FIASCO (Florentine Initiative Af-ter Superconducting Cyclotron Opening);this setup is described in a detailed wayin [13]; here only its main characteristicsare reminded. FIASCO was specially de-signed for the investigation of peripheraland semi-peripheral heavy ion collisions; infact, for such purposes, it includes 24 posi-tion sensitive Parallel Plate Avalanche De-tectors (PPADs), covering about 70% ofthe forward hemisphere (see Fig.3, wherethe frames of the PPADs are displayed inpolar representation), which measure thevelocity vector of heavy fragments (Z >10) with very low detection thresholds (<0.1AMeV ); as a consequence, they can de-tect the low energy QT also in peripheraland semi-peripheral collisions. In this wayit is possible to obtain a natural clean se-lection of two-body events, which, for ouranalysis, are defined as events with only twofragments with Z > 10 in the exit chan-nel. The setup includes also 96 Silicon tele-scopes (∆E = 200µm, Eres = 500µm),located behind the six most forward gas

232

detectors, which measure charge, energyand mass (this last point was obtained byadding the information concerning the timeof flight given by the coincident PPAD)for the QP. Concerning LCPs and IMFs,FIASCO is equipped with 182 three-layerphoswich telescopes (covering about 30% ofthe forward hemisphere) which identify pro-tons, deuterons, tritons and particles withcharge from 2 up to 15-20 and they measuredirectly their time of flight; in this way theparticle velocities can be obtained withoutenergy calibration of the phoswiches whichis always difficult (and requires dedicatedbeams). The three scintillator layers con-sist of a thin (∼ 180µm thick) fast plas-tic scintillator (Bicron BC404, decay con-stant τ = 1.8ns), a 5mm-thick slower plas-tic scintillator (Bicron BC444, τ = 180ns)and a CsI(Tl) (τ = 600 − 3500ns; thick-ness: 3 − 5cm); in the first measurementcampaign performed by FIASCO some ofthe phoswiches were without the slow plas-tic scintillator (two-layer phoswiches). Fi-nally, the setup includes also the hodoscopeHODO-CT [14], whose data were not usedfor the presented analysis.

-50

0

50

-50 0 50

13

1415

1617

18

19

2021

22

23

24

θ sin φ

θ c

os φ

θ=900

-10

0

10

-10 0 10

1

23

4

5

6

7

8

9

10

11

12

θ sin φ

∗

FIG. 3: Frame of the gas detectors of the FI-ASCO setup in polar representation. From [13].

The flight path of the most forwardPPADs is very long, about 3.5m, as it is ev-ident from Fig.4, where the side view of thesetup is presented; in this way it is possible

to obtain the time of flight of the forwardflying QP in an accurate way. Fig.5 and

-100

-50

0

50

100

-50 0 50 100 150 200 250 300 350 400Beam-axis Z (cm)

X (

cm)

BEAM

side view

FIG. 4: Side view of the FIASCO setup. From[13].

Fig.6 show two photographs of FIASCO asit was mounted inside the Ciclope scatteringchamber at LNS in Catania. In particular,Fig.5 shows the most forward ring (that at3.5m) and Fig.6 presents the target region,with some PPADs in foreground.

An example of the experimental two-bodyevents detected by the PPADs for the sys-tem 116Sn +93 Nb at 29.5AMeV is pre-sented in polar representation in Fig.7. Theforward-backward enhancement due to elas-tic and quasi-elastic collisions is clearly ev-ident. The empty circular zone on the leftside of the figure is due to the shadow ofthe target holder, which was tilted at about45 in order to reduce the material encoun-tered by the very slow QTs flying at about90 in the laboratory frame and to allowthem to reach the detectors escaping the tar-get. The target itself was very thin, about200µg/cm2.

The efficiency of the PPADs for the dif-ferent ions was obtained from the coinci-dences with the phoswich telescopes locatedbehind them; an example of the obtainedresults is presented in Fig.8 as a functionof the velocity in the laboratory frame. Itis evident that while for the Ne (Z = 10)and Mg (Z = 12) the efficiency falls down

233

FIG. 5: Photograph of FIASCO as it wasmounted inside the Ciclope scattering chamberat LNS in Catania. View from the most forwardring. From [13].

very quickly when the ion velocity increases,for the Si (Z = 14) the efficiency is around100% in almost the whole velocity range. Inany case it is worthwhile to note that QPand QT reach such small values of charge(they start from Z = 50 or Z = 41) onlyfor the most dissipative collisions, which areexcluded from the presented analysis.

Concerning the phoswich telescopes, anexample of the obtained particle identifica-tion is presented in Fig.9 for LCPs and inFig.10 for IMFs. The left side of each figurerefers to the identification obtained for thetwo-layer configuration, while the right sideconcerns a three-layer phoswich. The verygood charge resolution up to Z = 25 − 30for the three-layer configuration is evidentfrom Fig.10; the performances are some-what worse for the two-layer case. Con-cerning the LCPs, the isotopic resolution isvery good for the Hydrogen, while it is quite

FIG. 6: Photograph of FIASCO as it wasmounted inside the Ciclope scattering chamberat LNS in Catania. The target region. From[13].

-50 0 50θ sin ϕ

-50

0

50

θ cos ϕ

-5 0 5θ sin ϕ

-5

0

5θ cos ϕ

1

10000

FIG. 7: Experimental two-body events detectedby the PPADs of FIASCO for the system116Sn +93 Nb at 29.5AMeV in polar represen-tation. From [13].

marginal for the Helium and this fact is truefor both kinds of configurations. The iden-tification thresholds are due to the punchthrough of the first layer of scintillator; forthe LCPs they are about 3AMeV.

As it has been already pointed out, the

234

0

20

40

60

80

100NEON

40 50 60 70 80

Effi

cien

cy (

%)

MAGNESIUM

40 50 60 70 80vlab (mm/ns)

SILICON

40 50 60 70 80

FIG. 8: Detection efficiency for the PPADs ofFIASCO for different ions as a function of theirvelocity in the laboratory frame; the arrow cor-responds to the beam velocity. From [13].

1 1.5 2 2.5 3PI

0

1000

2000

3000

4000

5000

countsDouble phoswich

p

d

t

He−4

Li

PI1 1.5 2 2.5 3

Triple phoswich

He−4

LiHe−3

t

d

p

FIG. 9: LCP identification for a phoswichtelescope (typical case). Left side: two-layerphoswich; right side: three-layer phoswich.From [13].

angular coverage of the phoswich telescopesis only a fraction (about 30%) of the forwardhemisphere, as it can be seen from Fig.11,where the experimental counts acquired bythe phoswiches and by the hodoscope inthe reaction 93Nb +93 Nb at 38AMeV arepresented in polar representation. Countshave been uniformly distributed on the ac-tive area of each detector. Because of thisfinite coverage, all the data discussed in the

0 5 10

HHe

Li

Be

B

C

N

O

FCou

nts

(a.

u.)

0 5 10 15 20 25

H

HeLi

Be

B

CN

OF

NeMg S Ca Fe

Particle Identification

Double Triple Phoswich

FIG. 10: IMF identification for a phoswichtelescope (typical case). Left side: two-layerphoswich; right side: three-layer phoswich.From [13].

following sections concerning LCP and IMFmultiplicities have been corrected for geom-etry and detection thresholds of the setup.

-50 0 50

-50

0

50

-10 -5 0 5 10 15

-10

-5

0

5

10θ =90

ϕθsin ϕθsin

θcosϕθcosϕ

FIG. 11: Experimental counts acquired by thephoswich telescopes and the hodoscope in polarrepresentation. From [13].

As last point, the charge identification forthe QP, obtained from the Silicon telescopeswith the ∆E-Eres technique for the reaction116Sn +93 Nb at 29.5AMeV, is presented inFig.12. An unit charge resolution is appar-ent up to the projectile charge.

235

Z

1

10

102

103

10 20 30 40 50

FIG. 12: Charge identification for the QP asobtained from the Silicon telescopes. From [13].

EXPERIMENTAL RESULTS

The impact parameter estimate

As it has been already pointed out, thefirst problem we have to face is the estimateof the impact parameter; since this quantityis not directly accessible, we need an exper-imental observable which is monotonicallycorrelated to it. We used the observableTKEL = Ec.m.

in − 1

2µv2

rel under the hypoth-esis of two-body kinematics, where Ec.m.

in isthe available energy in the center of mass inthe entrance channel, µ is the reduced massof the primary QP-QT system, obtainedfrom the Kinematic Coincidence Method(KCM) [15] and vrel is the reconstructedprimary relative velocity between QP andQT (given by the KCM). It is well knownthat in the low energy domain the TKELis indeed the Total Kinetic Energy Loss, i.e.the amount of kinetic energy of the entrancechannel which is converted into excitationenergy of QP and QT (and rotational mo-tion); as a consequence, it is strictly corre-lated to the centrality of the reaction. Thsmaller the impact parameter, the more vi-olent the collision, with an higher degree ofdissipation of the translational kinetic en-

ergy (higher TKEL) and, as a consequence,an higher excitation of QP and QT. In theFermi energy domain, where the collision isno more strictly binary, such identificationof the TKEL with the energy dissipated inthe reaction is lost (at least partially, aswe will see later), but we can still use theTKEL as an order parameter to classify thecollisions in order of increasing centrality,as we have verified by means of a simula-tion based on the QMD model CHIMERA[16]. The results of the simulation are pre-sented in the top part of Fig.13 and theyclearly show that the relationship betweenthe TKEL and the impact parameter is ef-fectively monotonic even at Fermi energies.Moreover, the simulation told us that forperipheral and semi-peripheral collisions therelationship between the impact parameterb and the TKEL is independent of the beamenergy for a given system (see for examplethe case of the 93Nb +93 Nb at 23, 30 and38AMeV), while there is a difference whenwe move from one system (93Nb +93 Nb) toan other one (116Sn+116Sn). The differenceis of the order of 1fm.

We have also performed an experimentalestimate of the relationship between b andthe TKEL (bottom part of Fig.13) by inte-grating the experimental cross section start-ing from the elastic scattering, as in [17] and[18]; a detailed description of the adoptedtechnique is presented in [1]. The agreementbetween the results given by the experimen-tal evaluation and those obtained from thesimulation is very satisfactory.

Separation of the QP evaporation from

the midvelocity emission

The second problem to solve is how to sep-arate the midvelocity component from theQP evaporation. In order to achieve this re-sults, we take advantage of the emission pat-

236

0

2

4

6

8

10

12

b (

fm)

QMD

0

2

4

6

8

10

12

0 200 400 600 800 1000 1200 1400 1600

TKEL (MeV)

b (

fm)

↓↓↓

EXP

NbNb38NbNb30NbNb23NbNb17

SnSn38SnSn30

FIG. 13: Relationship between the impact pa-rameter (b, fm) and the TKEL. Top: resultscoming from the QMD simulation CHIMERA[16]. Bottom: experimental results. Arrows in-dicates the Ec.m.

in for each reaction. From [1].

tern of the particles on the plane (v‖, v⊥).On the base of the comparison of the experi-mental pattern with that expected for a pureevaporative emission (see Fig.2) we can as-sume that the most forward emission in theQP reference frame (origin in the QP veloc-ity, black point in the left side of Fig.14) ispurely evaporative. As a consequence, wecan separate the two components if we lookat the angular distribution of the emittedparticles with respect to the QP referenceframe (right side of Fig.14). A spin 0 sourceevaporates particles in an isotropic way; forthis reason the angular distribution in theQP reference frame displays a sine-like be-

haviour, as it is shown by the dashed-dottedcurve on the right side of Fig.14. In presenceof a non-zero spin, the emission tends toconcentrate on the reaction plane and fromthe out-of-plane distribution it is possible toestimate the spin of the source (in our case,it increases up to 30h for less peripheral col-lisions); the corresponding angular distri-bution in the QP reference frame flattensand becomes lower than a sine-like function(dotted curve on the figure), but it remainsforward-backward symmetric. Therefore itis possible to evaluate the QP evaporationstarting from the emission with θem below30 − 45 (where θem is the emission anglein the QP reference frame) and extendingit to the whole angular range following theproper curve according to the estimated spinof the QP. The midvelocity emission is ob-tained as the difference between the wholeexperimental angular distribution and theso estimated QP evaporation. With refer-ence to the right side of Fig.14, the differ-ence between the experimental distributionand the dotted curve clearly indicates thatthe midvelocity distribution extends fromthe backward region with respect to the QP(towards the center of mass) well below 90.

Particle multiplicities

Once the separation of the QP evapora-tion from the midvelocity emission has beenachieved, we can look at the particle mul-tiplicities (i.e. the average number of emit-ted particles per event) as a function of theTKEL and of the beam energy for the twoinvestigated symmetric systems. Concern-ing the QP evaporation, the obtained resultsare summarised in Fig.15. For all the par-ticle species and for all the beam energiesthe multiplicities tend to increase when thecentrality of the collision increases; this fact

237

0

20

40

60

80

-20 0 20 40 60

v⊥(mm/ns)

v// (mm/ns)

vc.m. vPLF

l

θ

a)

0

200

400

600

800

1000

1200

0 50 100 150

Yield(a.u.)

θ (deg)

l=0h-

l=30h-

expb)

FIG. 14: Left side: efficiency corrected experi-mental yields in the plane (v‖, v⊥) with respectto the QP-QT separation axis with the origin inthe center of mass reference frame; data refer tothe symmetric system 93Nb+93 Nb at 38AMeV.Right side: angular distribution of the experi-mental yields of the left side picture with v‖ ≥ 0;the emission angle is calculated with respect tothe QP velocity (black point on the left side).From [9].

is quite obvious since to a more violent colli-sion corresponds a higher excitation energyof the QP and, as a consequence, a higheramount of particle evaporation. If we com-pare the multiplicities of the 116Sn +116 Snsystem to those of the 93Nb +93 Nb sys-tem, we can observe that the emission ofthe 116Sn +116 Sn system is systematicallysmaller than that of the other system. Suchan effect, which is confirmed also by theGEMINI code, may be brought back to thehigher N/Z of the 116Sn +116 Sn system,which tends to favour the neutron evapora-tion with respect to the LCP emission.

Some interesting information on the be-haviour of the midvelocity emission can beinferred from Fig.16, where the ratio amongthe midvelocity multiplicities and the total(midvelocity plus QP evaporated) multiplic-ities is presented as a function of TKEL for

Evaporative Multiplicity

10-1

1Nb+Nb 38Nb+Nb 30Nb+Nb 23Nb+Nb 17

p

10-2

10-1

1

Sn+Sn 38Sn+Sn 30

d

10-2

10-1

t

10-1

1α

10-3

10-2

10-1

1

0 200 400 600 800 1000

IMF

TKEL (MeV)

FIG. 15: QP evaporation: experimental par-ticle multiplicities as a function of the TKELfor two symmetric systems ( 93Nb +93 Nb and116Sn +116 Sn) at different beam energies be-tween 17 and 38AMeV. From [1].

different beam energies and systems. Theratio tends to decrease in a systematic waywhen the centrality of the collision increases;as a consequence, the best environment forthe investigation of the midvelocity processis constituted by peripheral collisions. Inparticular, in such reactions, for the IMFsthe midvelocity contribution constitutes al-most the whole particle emission. The ra-tio is higher for the tritons than for the

238

deuterons and the protons: the midvelocityemission is richer in bounded neutrons withrespect to the standard QP evaporation (asobserved also in other experiments, for ex-ample [3]). At a given TKEL, the ratio in-creases when the beam energy increases andthe growth is less pronounced for more pe-ripheral collisions. The behaviour is similarfor the two investigated systems.

0.5

1 Nb+Nb 38Nb+Nb 30Nb+Nb 23Nb+Nb 17

p

0.5

1 Sn+Sn 38Sn+Sn 30

d

0.5

1

t

0.5

1

α

0.5

1

0 200 400 600 800 1000

IMF

TKEL (MeV)

FIG. 16: Ratio among the particle multiplicitiescoming from the midvelocity emission and thetotal (midvelocity plus QP evaporated) multi-plicities as a function of the TKEL for two sym-metric systems ( 93Nb +93 Nb and 116Sn +116

Sn) at different beam energies between 17 and38AMeV. From [1].

Average energy and mass balance

We have performed an average energy andmass balance for the reaction 93Nb +93 Nbat 38AMeV by disentangling the contribu-tion of the two emission components (theQP evaporation and the midvelocity emis-sion). The adopted technique, whose detailsare presented in [9], takes advantage of theextracted particle multiplicities, of the mea-sured velocities of the emitted particles andQP and of the measured secondary chargeand mass of the QP. The energy and massconservation between the entrance channeland the final one is imposed. The largestuncertainty is due to the neutron sharingbetween the midvelocity and the QP evapo-rated components (on the contrary, the to-tal multiplicities of the neutrons is muchless uncertain, since it is estimated from themass conservation adopting the hypothesisA = 2Z for the IMFs). Since the reaction issymmetric, all the contributions have beenestimated only in the region with v‖ (withrespect to QP-QT separation axis) ≥ 0. Theobtained results are presented in Fig.17 forthe QP (left column) and for the midve-locity source (right column). The first rowconcerns the average mass emitted by thesource, while the second one is relative tothe average excitation energy of the source.The main features emerging from this pic-ture are: i) the relationship between the ex-citation energy of the source and the TKELis about linear even at Fermi energies (theslope parameter is obviously smaller than0.5, since part of the available energy goesin the midvelocity emission); ii) the exci-tation energy of the midvelocity source is ofthe same order than the excitation energy ofthe QP; iii) since the mass of the QP sourceis of the order of the mass of the Nb, theenergy density of the QP is ≤ 2MeV/nucl;iv) on the contrary, since the mass of themidvelocity source, although not clearly de-

239

fined, is considerably smaller than the QPmass, the energy density of the midveloc-ity source is considerably higher: it rangesfrom 7 to 14 MeV/nucl, depending on theadopted hypothesis on the source size (wecan identify it with the emitted mass atmidvelocity (≤ 20amu) or we can includea part of the QP); such high values are wellabove the threshold for the multifragmen-tation process (3 − 5MeV/nucl, [19]). Asa consequence, from one side we can con-clude that a large amount of excitation en-ergy remains localized in the contact regionbetween QP and QT and from the otherwe can see the midvelocity emission as afirst example of multifragmentation limitedto the contact region [20].

0

10

20

30

amu

Aevap Amidv

0

100

200

0 200 400 600 800

TKEL (MeV)

MeV

Eevap

200 400 600 800

TKEL (MeV)

Emidv

FIG. 17: Average mass (top) emitted from thesource and average excitation energy (bottom)of the source for the QP (left column) and forthe midvelocity source (right column) for the re-action 93Nb +93 Nb at 38AMeV.

Comparison with GEMINI

If we compare the experimental QP evap-orated particle multiplicities to the predic-tion of the GEMINI code for a source ofthe proper excitation energy (deduced asdescribed in the previous subsection), wecan obtain a very nice agreement for theabsolute values for all the particle species(see Fig.18). Neutrons are obviously presentonly in the GEMINI data.

10-2

10-1

1

n p d t α IMFn p d t α IMFn p d t α IMFn p d t α IMF

E*=100MeV

n p d t α IMF

Gemini,L=30,A=93

n p d t α IMF

Gemini,L=0,A=93

n p d t α IMF

Gemini,L=30,A=76

n p d t α IMF

expGemini,L=30,A=93

E*=200MeV

FIG. 18: Experimental QP evaporated particlesmultiplicities (full circles) for two TKEL bins(corresponding to the excitation energy of theQP source indicated in each picture) for the sys-tem 93Nb +93 Nb at 38AMeV. Open symbolsrefer to the particle multiplicities predicted byGEMINI for a source of the same excitation en-ergy (and the proper mass). From [1].

If we look at the particle multiplicities asa function of 1/

√E∗ (where E∗ is the exci-

tation energy of the source) for the exper-imental QP evaporation and for the GEM-INI code (Fig.19), we can see that the gen-eral agreement is very good, both from thepoint of view of the general trend (which islinear in a semilogarithmic plot, as expectedfor a system ruled by statistical laws, wherethe emission probability is proportional toexp(−E∗/B); B is the emission barrier) and

240

from the point of view of the absolute valuesof the multiplicities.

10-2

10-1

1

0.06 0.08 0.1 0.12

b)

GeminiL=30 A=93

p

d

t

α

IMF

1/√E*

FIG. 19: Semilogarithmic plot of the particlemultiplicities as a function of 1/

√E∗ (where

E∗ is the excitation energy of the source) forthe experimental QP evaporation for the system93Nb +93 Nb at 38AMeV (left side) and for theGEMINI code. From [1].

These facts allow to conclude that the QPemission is fully compatible with the stan-dard evaporation of an equilibrated sourceat normal density.

A similar analysis can be applied to themidvelocity emission (with the proper ex-citation energy of the source, as estimatedfrom the energy balance); the obtained re-sults are presented in Fig.20. The generaltrend is still linear and this fact suggeststhat also the midvelocity process is ruledby statistical laws; but the particle hierar-chy is completely different with respect to

the QP emission (left side of Fig.19): forexample, there is an inversion between pro-tons and α particles and between tritons andIMFs. Moreover, the whole dynamics is in-cluded within one order of magnitude, to becompared with the three orders of magni-tude observed for the QP evaporation. Thisevidence brings to the conclusion that themidvelocity emission can not be interpretedin terms of a standard evaporation from anequilibrated source at normal density.

10-1

1

0.06 0.08 0.1 0.12 0.14

Nb+Nb 38

pd

t

α

IMF

1/√E*midv

FIG. 20: Semilogarithmic plot of the particlemultiplicities as a function of 1/

√E∗ (where E∗

is the excitation energy of the source) for the ex-perimental midvelocity emission for the system93Nb +93 Nb at 38AMeV. From [1].

A similar conclusion can be drawn if wecompare the N/Z ratio for the Hydrogen iso-topes coming from the QP evaporation tothat obtained for the midvelocity emission(Fig.21). While the ratio for the QP emis-sion (full points) is in substantial agreementwith the prediction of the GEMINI code(non-continuous lines), i.e. with what weexpect for the standard evaporation froma source at normal density, the ratio ob-tained for the midvelocity part is consider-ably higher. This is a further confirmationof the richness in bounded neutrons of themidvelocity emission.

241

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000

N/Z for Z=1Nb+Nb 38AMeV

exp mid-velocity

exp PLF-emission

GeminiL=30,20,0

TKEL (MeV)

N/Z

FIG. 21: N/Z for the Hydrogen isotopes for thesystem 93Nb +93 Nb at 38AMeV: open pointsmidvelocity emission, full points QP evapora-tion; uncontinuous lines refer to different GEM-INI calculations. From [1].

Estimate of the time scale of the

midvelocity process

In order to estimate the time scale asso-ciated to the midvelocity process, we havetried to reproduced the experimental emis-sion pattern of the IMFs for peripheralcollisions (where the IMF emission comes,almost completely, from the midvelocitysource) by means of a three-body Coulombtrajectory calculation including two heavyfragments (QP and QT) and an IMF. Re-sults are presented in Fig.22 as yields on the(v‖, v⊥) plane. In the framework of this sim-ulation, experimental data (d) can be verywell reproduced only if we couple an emis-sion from the middle of QP and QT (a) de-veloping over times of the order of 100fm/c(compatible with the neck rupture mecha-nism in the first phase of the reaction) to alater emission (∼ 200fm/c) from the pos-sibly deformed surface of QP and QT (b).This latter process can be seen as an evolu-tion of the fast oriented fission process [17]for extreme mass asymmetries. More details

on the used simulation can be found in [8].

0

50Mid-vel.

a)

v perp

(m

m/n

s)

Surfaceb)

0

50

-50 0 50

Mid-vel. + Surfacec)

-50 0 50

Expd)

vpar (mm/ns)

10

10 2

10 3

-50 0 50

yiel

d

vpar (mm/ns)

e)

0 25 50 75

f)

vperp (mm/ns)

FIG. 22: a), b) and c): simulations based on athree-body Coulomb trajectory calculation aimedto reproduce the experimental d) emission pat-tern of the IMFs for peripheral collisions for thereaction 116Sn +93 Nb at 29.5AMeV; the pre-sented pictures are yields on the (v‖, v⊥) plane.e) and f): v‖ and v⊥ distributions obtained fromthe pictures a)-d). From [8].

The existence of a midvelocity surfaceemission is furtherly confirmed by the ex-perimental kinetic energy spectra of par-ticles emitted around 90 in the QP ref-erence frame (first raw of Fig.23). It isvery clear the presence of two components,which can be fitted simultaneously with twoMaxwellian-shaped curves with very differ-ent inverse slope parameters. The compo-nent with smaller slope parameter (the sloperanges between 2 and 4MeV and it increaseswith the TKEL) can be easily identified withthe standard QP evaporation, since the ob-tained value of the slope is equal (within theerrors) to that obtained for forward emit-ted particles in the QP reference frame (sec-ond raw of Fig.23), where, as we have seen,

242

only the QP evaporation contribution is ex-pected. The second component shows anslope parameter of the order of 8-10MeV forthe Hydrogen isotopes and a higher value(about 12-13MeV) for α particles; the trendis substantially constant as a function ofTKEL for all the particles. In the frame-work explained in this work, we interpretthis second component as due to an emission(on a faster time scale with respect to thestandard QP evaporation) from the locallyhot and highly excited surface region of theQP which, in the first phase of the collision,was in contact with the QT. This explana-tion is in agreement with the previous ob-servation, coming from the energy balance,that the excitation energy is strongly local-ized in the contact region.

cou

nts

10

210

310 °-95°=85θprotons

TKEL=450-550MeV

°-95°=85θα

TKEL=550-650MeV

(MeV)kinE0 20 40 60 80

cou

nts

10

210

310 °-25°=5θprotons

TKEL=450-550MeV

(MeV)kinE0 20 40 60 80 100 120

°-25°=5θα

TKEL=550-650MeV

FIG. 23: Experimental kinetic energy spec-tra for protons (left column) and α particles(right column) for the system 93Nb +93 Nb at38AMeV. First row refers to particles emittedbetween 85 and 95 in the QP reference frame;second raw refers to particles emitted between5 and 25 in the QP reference frame.

CONCLUSIONS

In this work we have presented a sum-mary of the physical analysis developed bythe FIASCO experiment in the past eightyears, concerning the characterization of pe-ripheral and semi-peripheral heavy ion col-lisions at Fermi energies; in particular, wefocused on the investigation of the LCP andIMF emission.

We separated the two contributions whichcan be identified in the particle emissionpattern, i.e. the QP emission and the mid-velocity contribution. We investigated theirevolution as a function of the centrality ofthe reaction (estimated from the TKEL)and of the beam energy (between 17 and38AMeV ). From the comparison with theprediction of the GEMINI code we have seenthat the QP emission can be very well de-scribed in terms of standard evaporationfrom an equilibrated source at normal den-sity. On the contrary, the midvelocity emis-sion shows a very different behaviour fromthe point of view of particle multiplicities(see, for example, the N/Z ratio for the Hy-drogen isotopes or the general trend as afunction of 1/

√E∗). As a consequence, the

midvelocity emission is not an evaporativeprocess from an equilibrated source at nor-mal density; it may be of statistical nature,after a dynamical phase responsible for thesource formation.

Moreover, the midvelocity emission itselfcan be seen as a two component process: aprompt emission from the central region be-tween QP and QT on very fast time scales(∼ 100fm/c) reminding of the neck rupturemechanism in the first phase of the reac-tions, and a later emission from the possiblydeformed surface of QP and QT, which canbe interpreted as an evolution of the fast ori-ented fission process for extreme mass asym-metries.

An extremely clear evidence for the ex-

243

istence of this surface emission comes fromthe kinetic energy spectra of particles emit-ted around 90 in the QP reference frame:they clearly show the presence of two com-ponents with very different slope parame-ters; the softer one can be identified with thestandard QP evaporation, while the harderone may come from the locally hot surface ofthe QP, whose excitation is due to the con-tact with the QT in the first phase of thecollision.

The energy density is strongly localizedin the contact region between QP and QTand according to the fact that its value forthe midvelocity source is greater than thethreshold for the multifragmentation pro-cess, we can see the midvelocity emission asa first appearance of the multifragmentationphenomenon limited to the contact zone.

As last remark, we must observe thatperipheral collisions are the best environ-ment for the investigation of the midveloc-ity process; in fact from one side we havethe largest midvelocity-to-evaporative ratioin the particle emission and from the otherthe relative velocity between QP and QT ismaximal and therefore the separation of themidvelocity contribution from the QP/QTevaporation is easier.

Many thanks are due to all the per-manent and temporary members of theFIASCO collaboration (A.Mangiarotti,P.R.Maurenzig, A.Olmi, M.Bini, G.Casini,G.Pasquali, G.Poggi, A.A.Stefanini,N.Taccetti, L.Bardelli, A.Bartoli, L.Bidini,C.Coppi, S.Poggi, E.Vanzi); in particular toP.R.Maurenzig, A.Olmi and A.Mangiarottiwho contributed in a significant way to thepresented analysis.

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329.

244

Conference Proceedings Vol. 96

“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”

F. Gramegna, M. Cinausero, D. Fabris (Eds.)

SIF, Bologna 2008

ULTRARELATIVISIC NUCLEUS-NUCLEUS COLLISIONS: STATUS AND

PERSPECTIVES

F. Antinori

Dipartimento di Fisica and INFN Padova, Italy

ABSTRACT

The study of ultrarelativistic heavy-ion collisions has become one of the centre-stage subjects in

nuclear physics. The first round of discoveries at CERN-SPS has been followed by a series of

exciting new results from RHIC-BNL. I give a bird’s-eye overview of the current status of the field

and of the perspectives for the jump to the LHC energy.

INTRODUCTION

Despite its remarkable quantitative successes, the Standard Model (SM) of particle physics still presents us with a few puzzles. Two reside in the strong interaction sector of the SM; they have to do with the phenomenon of confinement and with the generation of the masses of the hadrons: i) one-half of the fundamental fermions of

the SM – the six quarks – are not observable as free particles: they seem to be permanently confined inside hadrons. We think that this behaviour derives from the properties of Quantum Chromo-Dynamics (QCD), but of this there is actually no rigorous proof

ii) most of the mass of the hadrons is unaccounted for in terms of those of their valence quarks. If, for instance, we add together the current masses of the three quarks making up a proton, we account for only 1% or so of the proton’s mass, How about the remaining 99%?

The two puzzles are generally thought to be related – the mechanism that confines the quarks to the interior of hadrons is presumably responsible for the generation of the bulk of the hadrons’ mass as well – and to originate in the non-perturbative behaviour of QCD.

The prime experimental tool for the exploration of this region of the SM is provided by ultrarelativistic nucleus-nucleus collisions. In this presentation, I will try to give a short overview of where we stand today in this relatively young and very lively field of nuclear physics, which had Prof. Ricci as one of its early backers in Italy, and to illustrate some of the

perspectives for the field’s near future.

THE QCD PHASE DIAGRAM AND AA

COLLISIONS

In QCD, non-perturbative problems are treated by discretization on a space-time lattice. This allows to avoid ultraviolet (i.e. large momentum scale) divergences, and to recover finite results. Lattice QCD predicts that as the temperature and/or the baryon density of a system of hadrons is increased, the confining effects of strong interaction will at some point disappear, as the individual, colourless hadrons dissolve into a Quark-Gluon Plasma (QGP), where coloured quarks and gluons can freely roam. As an example, figure 1 shows the predicted behaviour of the energy density ε of a strongly interacting system with 3 active quark flavours and zero net baryon density as a function of the system’s temperature T [1]. The energy density, divided here by the T

4 factor of the Stefan-Boltzmann

law, is proportional to the number of degrees of freedom in the system. A rapid rise is seen as the temperature crosses a critical value TC, estimated to be around 170 MeV (in units where the Boltzmann constant k is set equal to 1), due to the activation of the partonic degrees of freedom, much more numerous than the hadronic ones. The energy density at T = TC is expected to be of the order of the GeV/fm

3.

In the deconfined phase, the quark masses are expected to go down from the effective, constituent value they take inside hadrons to the current value of the fundamental Lagrangian, thereby restoring, at least partially, the chiral

245

symmetry which is normally broken in the world of hadrons.

Ultrarelativistic collisions of heavy nuclei allow us to reach values of the energy density in that range, over a relatively extended strongly interacting system, thereby opening up a window for the experimental exploration of the phenomenology of confinement and chiral symmetry breaking.

Fig. 1: Energy density (divided by T

4) versus

temperature (in units of critical temperature) from a lattice calculation with 3 active flavours and zero net baryon number.

SPS: THE EARLY EVIDENCE

The first pieces of evidence for the formation of partonic matter where collected at the CERN Super Proton Synchrotron (SPS) accelerator, with collisions of lead nuclei.

After a first round of experiments with relatively light ions (oxygen and sulphur), an upgrade of the CERN SPS accelerator facility allowing the acceleration of heavy ions was approved in 1990. It involved the construction of a new facility upstream of the Proton Synchrotron Booster (PSB) and modifications to the remaining existing accelerator chain, by a collaboration between CERN and external laboratories (figure 2) [2]. In particular, the Low Energy Beam Transport (LEBT) line and the Radio Frequency Quadrupole (RFQ), accelerating ions to 250 keV/u (figure 3) were built by Laboratori Nazionali di Legnaro (with Prof. Ricci very much supporting the whole operation). The CERN Heavy-Ion Facility started operating in 1994. In total, 9 experiments collected data between 1994 and 2003, with a spectrum of

different physics focuses (photons, low mass dileptons, particle spectra, interferometry, strange particles, high mass dileptons, charmonium, …) and experimental techniques (silicon microdetectors, time projection chambers, photon detectors, muon chambers, Cherenkov detectors, to name but a few).

The programme was a success. A harvest of results was reaped on many features of the new, peculiar strongly interacting system formed in Pb-Pb collisions at a centre-of-mass energy per nucleon-nucleon collision NNs = 17.3 GeV. Doing justice to the outcome of such a rich physics programme would be largely beyond the scope of the present paper. I will concentrate on two topics only: the hyperon enhancements and the J/ȥ suppression, two of the oldest, historic proposed signatures of deconfinement.

Fig. 2: Scheme of the complex of the CERN Heavy-Ion Facility. As briefly discussed above, deconfinement into the QGP phase is believed to be accompanied by a partial restoration of chiral symmetry. For the strange quark this implies a reduction of the value of the mass from around 500 MeV to about 150 MeV. This is comparable with the estimated value of the deconfinement temperature: copious production of strange quark-antiquark pairs, enhanced with respect to elementary collisions, is therefore expected in the QGP [3,4]. This enhancement is predicted to be stronger for particles containing multiple strange quarks, which can be built at the hadronization stage by recombining s quarks produced in independent microscopic reactions [5].

In the QGP phase the interaction potential is expected to be screened for distances larger than a certain value (the Debye length λD), analogously to what happens in an electromagnetic plasma. As a consequence, it is

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predicted that charmonium ( cc ) and bottomonium ( bb ) states with a radius larger than λD will not bind, and their production in the plasma will be suppressed [6]. The value of λD, and therefore which quarkonium states will be suppressed, depends on the temperature.

Fig. 3: Layout of the first stages of the CERN Heavy-Ion Facility. Fig. 4: Hyperon enhancements in Pb-Pb collisions relative to p-Be collisions at the SPS, as a function of the collision centrality (number of wounded nucleons).

Enhancements in the production of hyperons [7], increasing with the hyperon’s strange quark content (figure 4), and an anomalous suppression of the production of the J/ȥ charmonium state [8] (figure 5), were both observed at the SPS. Prof. Ricci was involved in the discovery of the hyperon enhancements, as a member of the WA97 experiment. When these and other results from the SPS lead ion programme are pieced together, the emerging picture is that of a strongly collective system, with a very large

pressure buildup and signature features – like the hyperons enhancements and charmonium suppression patterns discussed above – predicted to characterize the behaviour of a partonic system. Fig. 5: Observed J/ȥ suppression at the SPS (divided by the amount of suppression expected from nuclear absorption) as a function of the collision’s energy density.

HIGHLIGHTS FROM RHIC

The next jump in the field was the coming online in the year 2000 of the Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Laboratory on Long Island. Built specifically for heavy-ions, RHIC extended by one order of magnitude the centre-of-mass collision energy reach for nucleus-nucleus collisions, to NNs = 200 GeV. Four dedicated experiments were built around the collider’s ring. The programme quickly started pouring out an impressive stream of results. Here, again, I will only mention a few. Perhaps the most spectacular RHIC result was the observation of high-pT suppression. In the absence of medium effects, the production of particles at high transverse momentum (pT) in nucleus-nucleus collisions is expected to scale like the number of binary nucleon-nucleon collisions in the reaction. This can be checked by computing the nuclear modification factor RAA, as the ratio of the particle yields per nucleon-nucleon collision in nucleus-nucleus and proton-proton collisions. As shown in figure 6, approximate scaling of charged particle production at high pT with the number of nucleon-nucleon collisions (RAA ~ 1) is seen for the most peripheral gold-gold collision events (60-80%). For central collisions,

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however, a strong suppression is observed [9]. When looking at two-particle azimuthal correlations using a high-pT “trigger” particle (figure 7), a clear back-to-back jet correlation peak is visible at 180 degrees in pp and deuteron-gold collisions. In central Au-Au collisions, however, the peak has disappeared [10]. These effects can be explained in terms of energy loss of the partons as they attempt to traverse the strongly interacting medium formed in the collision. It looks as though particles created close to the medium boundary manage to escape, while the rest are strongly absorbed in the medium (“jet quenching”). Fig. 6: Nuclear modification factor RAA for the production of charged particles at RHIC, as a function of transverse momentum. Fig. 7: Two-particle correlations at RHIC: distribution of the distance in azimuth from a “trigger” particle – selected with 4 < pT < 6 GeV/c – of associated particles with pT > 2 GeV/c.

One of the early puzzles emerging from RHIC data had to do with the production of baryons at medium pT. Figure 8, for instance, shows the proton, kaon and pion pT spectra in Au-Au collisions at NNs = 200 GeV. Fig. 8: RHIC transverse momentum spectra for pions, kaons, protons and antiprotons, for central (top) and peripheral (bottom) collisions. For central collisions, as many protons as ʌ+

and as many antiprotons as ʌ− are found to be produced at high pT [11]. When looking at the nuclear modification factor Rcp (figure 9; Rcp is calculated in a similar way as RAA, but relative to peripheral Au-Au instead than to pp collisions), it looks like high transverse momentum proton production is not suppressed [12], contrary to what is observed for pions. Fig. 9: Nuclear modification factors Rcp for protons and neutral pions at RHIC. How could this be if the suppression was due to parton energy loss? How would the partons

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“know” if they would end up generating pions or protons? An important clue came with the measurement of the Rcp factors for 0

SK and ȁ [13], which extended the comparison of baryon and meson production to higher transverse momenta (figure 10) than was initially possible for pions and protons. Lambdas, too, were found to be eventually suppressed; only it looked like the effect for them was shifted to a higher pT with respect to kaons.

Fig. 10: Nuclear modification factors Rcp for neutral kaons and lambdas at RHIC. Two different peripheral centrality classes are used in the Rcp definition ( top and bottom plots). Such a behaviour finds a natural explanation within valence quark recombination/coalescence models [14]: if hadrons are formed by recombining quarks from the partonic phase, one expects features of the parton spectrum, such as a suppression at high pT, to end up at different places in the transverse momentum spectrum of mesons and baryons, with momentum scaling factors of 2 and 3 for mesons and baryons respectively, as determined by their respective number of valence quarks/antiquarks. This is in good agreement with the pattern observed in the data. Strong support for the recombination picture came also from the study of the azimuthal dependence of particle production. Due to strong collective expansion effects, for non-central events the distribution of the produced particles retains a memory of the initial azimuthal asymmetry of the nucleus-nucleus collision. This is quantified by measuring the second coefficient

(v2) in the Fourier transform of the azimuthal distribution of particle production. The behaviour of v2 as a function of pT appears – again – to be different for baryons and mesons (figure 11), but the two sets of measurements can be reconciled if both the v2 and the transverse momentum are divided by the number of valence quarks in the hadron (figure 12) [13, 15], as expected, again, if hadron formation in this pT region is dominated by recombination effects.

Fig. 11: Azimuthal asymmetry parameter v2 for strange particles at RHIC.

Fig. 12: v2/n as a function of pT/n for mesons and baryons at RHIC. n being the number of valence quarks/antiquarks.

After the first pieces of evidence for deconfinement where collected at the SPS (incidentally, very similar results on both hyperon enhancements and J/ȥ suppression were later found also at RHIC), RHIC provided us with new evidence for partonic behaviour with the discovery of the valence quark recombination

STAR

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counting rules, and opened up the way to the study of the medium properties with high energy probes with the discovery of high pT suppression.

THE FUTURE: LHC

The Large Hadron Collider (LHC), planned to come online at CERN next year, while designed primarily for the study of proton-proton collisions at s = 14 TeV, will also allow to collide heavy ions. The centre-of-mass energy per nucleon-nucleon collision for the lead-lead system is NNs = 5.5 TeV. With the LHC, a new quantum jump is anticipated, into a region where new, hard probes, such as heavy flavours and fully developed jets will become accessible with high statistics. Here, again, I will limit myself to a few examples, to give a flavour of the physics potential expected at the next machine.

Jet quenching is predicted to be different for heavy and light partons. In the BDMPS framework [16], parton energy loss is calculated in QCD, and found to be mainly due to gluon radiation by bremsstrahlung. The average energy loss for a parton propagating in a QCD medium is computed to be proportional to the parton’s Casimir factor, which measures its colour charge (4/3 for quarks and 3 for gluons), leading to a larger suppression for light hadrons, originating predominantly from gluon jets, than for heavy flavoured hadrons, produced in quark jets. Within the quark sector, then, heavy quarks are predicted to lose less energy than light quarks, due to the so-called dead cone effect, whereby a massive parton cannot lose energy by radiating gluons below a minimum angle, determined by the parton’s mass/energy ratio [17, 18]. Heavy-flavoured particles are therefore expected to be overall less “quenched” than the light-flavoured ones.

The study of the production of heavy flavour in nucleus-nucleus collisions is already being undertaken at RHIC, mainly relying on the extraction of “non-photonic electron” spectra, i.e. electron spectra where the contribution from photon conversions and light hadron decays has been subtracted. When the nuclear modification factor RAA is calculated for such electrons, their suppression seem to be as strong as that of light hadrons (figure 13) [19] contrary to the theoretical expectations discussed above. Attempts at reconciling data and theory are being made, for instance by considering the possibility of a reduced contribution from beauty production, although beauty decays would in

principle be expected to dominate non-photonic electron spectra above a few GeV of pT. Since, due to their lower mass, c quarks are thought to lose more energy than their b counterparts because of the dead-cone effect discussed above, if the production of non-photonic electrons at RHIC were dominated by charm decays across the accessible pT range, it would indeed still be possible to recover some agreement with the theory [20].

Fig. 13: RAA for non-photonic electrons at RHIC as a function of pT. The high pT suppression for charged hadrons (hashed band) and the predictions from various quenching models assuming only c or both c and b contributions are shown for comparison.

Experimentally, this is a rather complicated matter, since the RHIC experiments are not currently equipped with microvertex detectors, which – besides providing an experimental cross-check as to the heavy flavour origin of the non-photonic electron spectra – would allow a separate measurement of their b and c components.

Heavy flavours will be abundantly produced at the LHC, with over a hundred cc pairs and a few

bb pairs per central Pb-Pb collision predicted [21]. ALICE, the LHC experiment dedicated to the study of heavy-ion collisions, is equipped with a silicon pixel microvertex detector (see [22] at this workshop). Good performance for heavy flavour measurements in general and in particular for the b/c separation is anticipated, making it possible to explore the properties of the system with well calibrated probes (see [23] at this workshop).

High energy jets will also be abundantly produced at the LHC [21]. On average, about one 20 GeV jet per central Pb-Pb event is foreseen; even for jet energies as large as 200 GeV, the

non phot.

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estimated statistics is still good: about 100,000 per months at nominal luminosity. Such jets should be well visible even among the large background of low momentum particles of central Pb-Pb collisions at the LHC. The jet fragmentation function, which quantifies the fraction z of the parton’s original momentum ending up in the produced hadrons, is expected to be modified relative to the vacuum case by the parton’s propagation through the medium [24], as shown, for instance, in figure 14 [25] (where the variable ξ = ln(1/z) is used). This is a crucial measurement, for which, again, good performance is expected in ALICE (see figure 14), providing us with yet another tool for exploring the properties of deconfined matter.

Fig. 14: Expected ALICE performance (triangles) for the measurement of the ratio of the fragmentation functions for central (modified) and peripheral (taken to be unmodified) collisions for jets with a mean energy around 125 GeV, as a function of ξ = ln (1/z). The ideal case of perfect jet reconstruction is shown as a histogram. The modification of the fragmentation function was calculated using quenching weights [26] with a medium transport coefficient q = 50 GeV2/fm. R is the jet cone radius. Figure from [25].

CONCLUSION

As was originally hoped, after over a decade of experiments at the SPS and RHIC, good evidence has been collected for the creation of an extended partonic system in the collision of ultrarelativistic heavy ions. As the field matures and prepares for the jump to yet a higher energy regime, the focus is now moving to the study of the properties of this new state of matter, thought to have been that of our Universe a few

microseconds after the Big Bang. The ALICE experiment at the LHC is well equipped to carry on such an ambitious physics programme. Sure enough Professor Ricci, a long-time member of the ALICE Collaboration, is still involved.

[1] U. Heinz, Nucl.Phys. A 685 (2001) 414 [2] N. Angert et al., CERN 93-01 (1993) [3] J. Rafelski, Phys. Rep. 88 (1982) 331 [4] J. Rafelski and B. Müller, Phys. Rev. Lett. 48 (1982) 1066 [5] P. Koch et al., Phys. Rep. 142 (1986) 167 [6] T. Matsui and H. Satz, Phys. Lett. B 178 (1986) 416 [7] E. Andersen et al., Phys. Lett. B 449 (1999) 401 [8] M.C. Abreu et al., Phys. Lett. B 410 (1997) 337 [9] J. Adams et al., Phys. Rev. Lett. 91 (2003) 172302 [10] C. Adler et al., Phys. Rev. Lett 90 (2003) 082302 [11] S.S. Adler et al., Phys. Rev. C 69 (2004) 034909 [12] S.S. Adler et al., Phys. Rev. Lett. 91 (2003) 172301 [13] J. Adams et al., Phys. Rev. Lett. 92 (2004) 052302 [14] See e.g.: R.J. Fries, J. Phys. G 30 (2004) S853 and refererences therein [15] J. Castillo et al., J. Phys. G 30 (2004) S1207 [16] R. Baier et al., Nucl. Phys. B483 (1997) 291 [17] Yu L. Dokshitzer and D.E. Kharzeev, Phys. Lett. B 519 (2001) 199 [18] N. Armesto et al., Phys. Rev. D 69 (2004) 114003 [19] B.I. Abelev et al., Phys. Rev. Lett 98 (2007) 192301 [20] N. Armesto et al., Phys. Lett. B 637 (2006) 362 [21] ALICE Collaboration: Physics Performance Report, Vol. II, J. Phys. G 32 (2006) 1295 [22] S. Moretto, this workshop [23] A. Dainese, this workshop [24] N. Borghini and U.A. Wiedemann, arXiv: hep-ph/0506218 [25] F. Antinori et al., J. Phys. G 34 (2007) S511 [26] C.A. Salgado and U.A. Wiedemann, Phys. Rev. D 68 (2003) 014008

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Conference Proceedings Vol. 96

“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”

F. Gramegna, M. Cinausero, D. Fabris (Eds.)

SIF, Bologna 2008

PHYSICS PROGRAM OF THE ALICE EXPERIMENT AT THE LHC

A. Dainese, for the ALICE Collaboration

INFN, Laboratori Nazionali di Legnaro, viale dell’Università 2, 35020 Legnaro (Padova), Italy

1. INTRODUCTION

ALICE [1,2] is a general-purpose heavy-ion experiment designed to study the physics of high-density strongly interacting matter in nucleus–nucleus collisions at the CERN Large Hadron Collider (LHC) at a centre-of-mass energy of 5.5=NNs TeV per nucleon–nucleon collision, for the Pb-Pb system. In these collisions, a system with an energy density hundreds of times larger than that of ordinary atomic nuclei is expected to be produced. Under these conditions, the formation of a thermally-equilibrated medium characterized by partonic, rather than hadronic, degrees of freedom (the so called Quark-Gluon Plasma, QGP) is predicted by the theory of strong interactions (Quantum Chromodynamics, QCD). A discussion on the evidences for QGP formation collected in past and present heavy-ion experiments at CERN-SPS and BNL-RHIC, as well as a description of the most relevant observables for the characterization of the state of strongly-interacting matter formed in high-energy nucleus-nucleus collisions, can be found in Ref. [3].

The ALICE detector has been designed to cope with the highest particle multiplicities among those anticipated for Pb–Pb collisions (dNch/dy up to 8000) and it will be operational at the start-up of the LHC, now expected in summer 2008 with proton–proton (pp) collisions at 14=s TeV. In addition to heavy-ion systems, the ALICE Collaboration will study collisions of lower-mass ions, which are a means of varying the energy density of the system formed in the collision, and protons (both pp and proton–nucleus), which primarily provide reference data for the nucleus–nucleus collisions. In addition, the pp data will allow for a number of genuine pp physics studies.

We briefly summarize the ALICE Physics list in section 2. In section 3 we describe the ALICE experimental setup, and in section 4 we outline

the strategy for event reconstruction, giving some of expected performance figures. In the following sections, we go through the main points of the ALICE Physics program.

2. ALICE PHYSICS LIST AND

OBSERVABLES IN A NUTSHELL

• Energy density of the hot and dense system produced in the collision å measurement of the charged-particle multiplicity and charged-particle rapidity density.

• Temperature and baryon density of the system at the chemical freeze-out and temperature at the kinetic freeze-out å measurement of identified-particle yields (probe chemical freeze-out) and momentum spectra (probe kinetic freeze-out).

• Hadronization mechanism of the system: interplay between quark recombination from a partonic medium and parton fragmentation outside the medium å measurement of the baryon-to-meson ratios as a function of momentum and rapidity.

• Size of the hot particle-emitting source å HBT interferometry with identical bosons (Bose-Einstein correlations).

• Pressure-driven expansion of the system, to be compared to hydrodynamical models å measurement of radial flow and elliptic flow (azimuthal particle production anisotropy in non-central collisions).

• Fluctuations induced by the QCD phase transition å measurement of event-by-event

particle spectra • Effect of parton energy loss via medium-

induced gluon-radiation on heavy quarks (charm and beauty): dependence of energy loss on the parton colour charge (c quarks vs.

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gluons) and on the parton mass (b quarks vs. c quarks) å measurement of transverse momentum spectra of D and B mesons.

• Quarkonium (charmonium and bottomonium) suppression by dissociation due to colour screening in a deconfined medium vs. charmonium enhancement by parton recombination in a charm-rich medium å measurement of charmonium and bottomonium yields.

• Initial temperature of the QGP via thermal photons from the medium å measurement of the transverse momentum spectrum of single photons.

• Effect of parton energy loss on jet structure and jet fragmentation function å measurement of reconstructed jets and photon-tagged jets (provide initial jet energy calibration).

3. ALICE DETECTOR LAYOUT

The detector (see Fig. 1) consists of a central barrel, which measures hadrons, electrons and photons, and of a forward spectrometer to measure muons. The central barrel, which covers polar angles from 45

o to 135

o over the full

azimuth, is embedded in the large L3 solenoidal magnet providing a magnetic field of up to 0.5 T.

Fig. 1: Layout of the ALICE experimental setup.

It consists of: an Inner Tracking System (ITS)

with six cylindrical layers of high-resolution silicon detectors, among which two layers of Silicon Pixel Detectors (SPD) [4]; a cylindrical Time-Projection Chamber (TPC); a single-arm electromagnetic calorimeter (PHOS); and three particle identification arrays of: Time-Of-Flight (TOF) detector, Transition Radiation Detector (TRD), and a single-arm ring imaging Cherenkov (HMPID). The forward muon arm (covering polar angles 171

o–178

o) consists of a

complex arrangement of absorbers, a large dipole magnet, and fourteen planes of tracking and triggering chambers. Several smaller detectors (ZDC, PMD, FMD, T0, V0) for global event characterization and triggering are located at forward angles. An electro-magnetic calorimeter (EMCAL) for jet measurements and jet triggering, covering one third of the central barrel azimuthal acceptance and its full polar acceptance, will be added in 2009-2010.

4. TRACK RECONSTRUCTION AND

PARTICLE IDENTIFICATION

The primary vertex of the collisions is found using the clusters reconstructed in the two innermost ITS layers, made of the Silicon Pixel Detector (SPD) [3]. In central Pb–Pb collisions, the vertex position is reconstructed with a precision of about 5 たm in the beam direction and about 25 たm in the transverse plane. For pp collisions, the precision on the vertex position is about one order of magnitude worse. However, due to the very low track multiplicity in pp events, this deterioration of the vertex precision does not have a significant impact on the reconstruction of physics signals, such as charm and beauty particle decays.

The track finding in the central detectors starts in the TPC. For tracks with a sufficient number of hits and transverse momentum pt above 0.2 GeV/c, the TPC track-finding efficiency is almost 100%, even for the charged-particle densities of central Pb–Pb collisions. The effective TPC track-finding efficiency is lower, around 85% (and around 90% for tracks with pt above 1 GeV/c), because of particle decays and the dead zones between the TPC sectors. The momentum resolution of tracks reconstructed in the TPC is about 0.7% (at pt = 1 GeV/c and the magnetic field 0.5 T), and the specific energy loss (dE/dx) resolution is about 6%. These resolutions depend only slightly on event multiplicity.

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The tracks reconstructed in the TPC are then prolonged to the ITS. Using the ITS measurements, the track impact-parameter (distance of closest approach to the primary vertex) resolution is improved to 60 たm for 1 GeV/c tracks in central Pb–Pb collisions (see Fig. 2). As we will show in section 10, such resolution, mainly provided by the two layers of Silicon Pixel Detectors at r = 4 and 7 cm, allows a good performance for the reconstruction of charm and beauty decay vertices, displaced by a few hundred μm from the primary vertex.

Fig. 2: Track impact parameter resolution in the directions transverse (rφ) and parallel (z) to the beamline, for different particle species, as a function of the transverse momentum pt [2].

Including the ITS measurements and, to a lesser extent, also the TRD data in the track reconstruction significantly improves the momentum resolution at high pt; at pt = 100 GeV/c the momentum resolution is around 3.5% in magnetic field B = 0.5 T. However, in this case the effective tracking efficiency is reduced to about 60%, because of particle absorption in the TRD and in the support structure.

In the last step, the reconstruction algorithm searches for secondary vertices from strange particle decays (V0’s: K

0S→π+π−,

Λ0→pπ−; cascades: Ξ-→Λ0π−, Ω-→Λ0Κ−) and

kinks (i.e. charged pion or kaon decays on the flight, like K

+→μ+νμ). The V0 and cascade decays are reconstructed within the fiducial volume between 1 cm from the primary vertex and the TPC inner radius (85 cm). Typical reconstruction efficiencies are 60% for K

0S’s,

40% for Λ’s, and 5% for Ξ’s. The kinks are

reconstructed inside the TPC in the fiducial volume 120 < r < 220 cm. The kink reconstruction efficiency for charged kaon decays is about 70% in pp collisions and about 40% in central Pb–Pb collisions for kaons with pt up to 20 GeV/c.

The identification of charged hadrons is done by combining the PID information provided by the ITS, TPC, TDR, TOF, and HMPID detectors. The efficiency of the PID algorithm is above 95% up to p = 6 GeV/c for pions, above 60% up to p = 3 GeV/c for kaons, and above 70% up to p = 5 GeV/c for protons, in all cases the contamination with wrongly-identified particles is below 30%. The overall effective PID efficiency is limited by particle decays and absorption in the material. It is about 50% for pions and protons, and about 40% for kaons, integrated over momentum. Electrons with momentum above 1 GeV/c are identified by the TRD with the efficiency above 90% and with the pion-rejection factor of about 100.

The PHOS spectrometer detects and identifies photons with high energy and position resolutions. In the low-momentum range, below 20 GeV/c, the direct-photon spectrum is obtained by subtracting, from the overall identified-photon spectrum, the contribution from decay photons, mainly from the light neutral mesons. The yields of these mesons are measured by an invariant-mass analysis. In the high-momentum range, above 20 GeV/c and up to 100 GeV/c, direct photons are identified on an event-by-event basis, by the shower-shape and the isolation-cut discrimination techniques. The identification efficiency for photons (0.5 GeV < E < 40 GeV) in pp collisions is above 90%. In central Pb–Pb collisions this efficiency is above 50%. The contamination from misidentified particles (electrons, charged hadrons, long-lived neutral mesons, neutrons and antineutrons) remains below 3%. For even higher-energy photons (40 GeV < E < 120 GeV) the detection efficiency decreases to about 40%, however, the contamination from non-resolved π0→γγ is smaller than 10%.

The Photon Multiplicity Detector (PMD) counts photons in the forward pseudorapidity region 2.3 < η < 3.5. The photon-reconstruction efficiency is a function of the pseudorapidity with a maximum of 70% at η = 2.6. The purity of the sample of reconstructed photons is above 60% in the whole pseudorapidity range.

The reconstruction quality in the muon arm depends on the level of the background. However, even for the worst background

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scenario (using the pile-up of two highest multiplicity events), the muon-arm track-finding efficiency is about 95% and the resolution in the reconstructed ϒ (bottomonium) mass is better than 100 MeV/c

2, thus allowing the separation of

the three states ϒ, ϒ’ and ϒ’’.

5. COLLISION CHARACTERIZATION

The initial geometry of the collisions is determined by measuring the global event properties. This measurement allows also to study how the available centre-of-mass energy is redistributed in phase space.

The collision geometry can be estimated using several observables. One way is to use the information from the Zero-Degree Calorimeters (ZDCs). The number Npart of participant nucleons in the collision (Npart

≈ 400 in central Pb–Pb) is determined with the resolution σNpart = 15, roughly independent of centrality.

The charged-particle multiplicity and the charged-particle pseudo-rapidity distribution, which is related to the energy density of the system formed in the collision, can be measured over almost 8 units in pseudorapidity, by means of the Forward Multiplicity Detector (FMD), and of the innermost layers of the ITS (SPD). A simplified tracking algorithm will be used in the ITS to measure multiplicity in a robust way, defining ‘tracklets’ by associating clusters of hits in the two SPD planes. In Pb–Pb collisions, the charged-particle multiplicity is measured with very good accuracy for all centralities. In the mid-rapidity region, even for very peripheral events, the resolution on multiplicity is better than 10%, and it becomes progressively smaller for more central collisions.

6. PARTICLE PRODUCTION

The comprehensive measurements of particle ratios and momentum spectra are an important part of the ALICE physics program. They are important both in the low-pt region, where a thermal and chemical analysis of the system freeze-out conditions is the main aim, and at intermediate and high pt, where the role of radial flow, quark recombination, and, eventually, hard processes, becomes apparent.

Figure 3 illustrates the expected coverages in pt for the different identified particles, for one month of data taking at nominal LHC luminosity

with Pb-Pb. By combining the information from different

PID detectors, stable charged hadrons (pions, kaons, and protons) can be identified and measured from very low momentum (hundreds of MeV) up to at least 50 GeV. Secondary vertices are used to identify charged and neutral kaons as well as hyperons up to, and beyond 10 GeV. Baryon production will be measured in the central region (p, Λ0

, Ξ-, Ω-

, and their anti-particles) to study the baryon number transfer in rapidity both in Pb–Pb and pp collisions.

Resonances bring additional information about the final stages of the collision. Three resonances have been investigated so far, the ρ0

, the K0*,

and the φ. In addition to production spectra, ALICE will be able to measure to some extent variations in the resonance parameters (mass, width, line shape), which may arise from the restoration of chiral symmetry.

Fig. 3: Expected pt ranges for identified particles (one month Pb-Pb at nominal luminosity) [2].

7. TWO-PARTICLE INTERFEROMETRY

(HBT)

The space–time geometry of the particle-emitting source created in ultra-relativistic heavy-ion collisions can be studied by the analysis of two-particle intensity interferometry (HBT).

ALICE will contribute to the existing results of HBT analysis in heavy-ion collisions as well as open the possibility for new analysis, such as direct-photon interferometry or event-by-event HBT analysis. Data from the LHC may help to clarify the ‘RHIC HBT puzzle’ (the expected increase with collision energy of the size of the particles source is not seen in the experimental data) by extending the excitation function to

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much higher energy and particle multiplicities, and by making precise measurements of the shape and the anisotropy of the particle-emitting source as given by azimuthally-sensitive HBT analysis. It will also extend the existing investigations to a larger number of different hadron species, which will help to better understand the particle emission, and therefore the geometry and evolution of the system.

8. FLOW

High-accuracy measurements of anisotropic flow are very important for understanding the dynamics of the heavy-ion collisions at the LHC.

The determination of the reaction plane, a prerequisite for the measurement of anisotropic flow, will benefit from the possibility to be done independently by the different subsystems of the ALICE detector, and by different analysis methods. At mid-rapidity, making use of the elliptic flow signal (v2), we will be able to determine the reaction plane for a very wide range of particle multiplicities and magnitudes of the elliptic flow. At beam-rapidity, using the directed flow signal (v1), we will get an independent determination of the reaction plane from the ZDCs.

The expected precision of the reaction-plane determination will allow for anisotropic flow measurements with unprecedented accuracy for both charged and identified particles in a momentum range from a few hundred MeV/c up to well above 10 GeV/c. These measurements are expected to provide constraints on the equation of state (low pt, below 2 GeV/c), collective motion of the constituent quarks (intermediate pt, 2-7 GeV/c), and path-length dependence of the in-medium parton energy loss (high pt, above 7 GeV/c).

9. EVENT-BY-EVENT FLUCTUATIONS

Fluctuations of thermodynamic quantities are fundamental to the study of the QGP phase transition.

The ALICE experiment is well suited to precise event-by-event measurements of various observables: temperature fluctuations, multiplicity and strangeness fluctuations, fluctuations of conserved quantities including net-charge fluctuation, balance functions, fluctuation in azimuthal anisotropy, fluctuation

in space–time parameters from correlation measurements.

Fluctuations in these observables can be studied in order to understand the physics of bulk properties of matter as well as high-pt particles and jets. Recent lattice QCD calculations have shown that interesting fluctuation patterns might be present also at the small chemical potential, which will prevail at LHC energies.

10. CHARM AND BEAUTY

LHC is the first machine where heavy quarks will be produced abundantly in heavy-ion collisions. The study of heavy-flavour production in both pp and nucleus–nucleus collisions down to almost zero transverse momentum will allow a sensitive comparison with QCD predictions and a study of the in-medium energy loss of heavy quarks compared to massless partons (light quarks and gluons).

Fig. 4: Sketch of the D0→K−π+ decay (top) and example of K−π+ invariant-mass distribution after applying the selection cuts, in central Pb–Pb events, after the subtraction of the combinatorial background in the insert (bottom) [2].

The benchmark decay channel D0→K

−π+ has

π

pointing angle θpointing

secondary vertexprimary vertex

D reconstructed momentum 0

D flight line0

d

d

0

0

K

K

π

impact parameters ~100 mµ

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been studied in detail. Figure 4 shows a sketch of the decay topology and an example K

−π+

invariant-mass distribution in central Pb–Pb collisions, as expected after applying the secondary-vertex selection cuts. In one LHC year at nominal luminosity, we expect to cover, in |η| < 0.9, the transverse-momentum range 1 GeV/c < pt < 18 GeV/c in central Pb–Pb collisions and 0.5 GeV/c < pt < 18 GeV/c in pp and pPb collisions, with statistical errors smaller than 15–20% at high pt in all cases.

Beauty production in central Pb–Pb collisions can be measured via semi-leptonic decays. Identified electron tracks displaced from the primary vertex provide a measurement of the b-hadron cross section above a given pt

min . As

shown in Fig. 5, ALICE can cover the range 2 GeV/c <pt

min < 30 GeV/c (in |η| < 0.9) with

statistical errors of order 10% or less. Single muons and opposite-sign dimuon pairs allow a measurement of open-beauty production with high statistics in the forward pseudorapidity region −4 < η < −2.5 in the transverse-momentum range 2 GeV/c < pt

min < 22 GeV/c.

Fig. 5: Expected performance for the reconstruction of the B-meson production cross section as a function of pt

min, using the semi-electronic decay channel, in one month of Pb–Pb data taking. The statistical errors (inner bars) and combined statistical and systematic errors (outer bars) are shown. The predicted B-meson suppression due to b-quark energy loss in the hot and dense medium is also shown [2].

Additional channels are currently under investigation, such as D

+ reconstruction,

electron–muon and multi-muon correlations,

beauty production via displaced J/ψ’s from B decays and the perspectives for the measurement of W-boson-decay muons (which will be useful as a medium-blind reference to study the in-medium energy loss of heavy flavour).

11. QUARKONIA

At LHC, the complete spectrum of heavy quarkonia states (J/ψ, ψ’, ϒ, ϒ’, and ϒ’’) is accessible and will allow a very detailed study of both suppression phenomena (due to deconfinement, which should affect members of both the charm and beauty family) and possible enhancement (due to recombination, significant only for the charmonium states).

Quarkonia are detected in ALICE at mid-rapidity (−0.9 < η < 0.9) in the di-electron channel, and at backward rapidity (−4.0 < η < −2.5) in the di-muon channel.

Fig. 6: Di-electron (e+e-) invariant-mass spectrum for central Pb-Pb collisions, as expected to measured in the central rapidity region (|η|<0.9) in one month of Pb–Pb data-taking. The uncorrelated (combinatorial background) is not subtracted in the figure [2].

The expected performance is illustrated by the

di-lepton invariant-mass spectra shown in Figs. 6 (di-electrons) and 7 (di-muons).

In the central-rapidity region, the J/ψ production cross section will be measured down to pt = 0 GeV/c in the minimum-bias data sample. The data triggered with high-pt electrons have the pt threshold for J/ψ acceptance of about 5 GeV/c. The production of ϒ states is measured over the full transverse-momentum range in both minimum-bias and triggered data samples.

[GeV/c]mintB p

0 5 10 15 20 25 30

) [m

b]m

int

> p

t/d

y (p

B NN

σd

-610

-510

-410

-310

-210

= 5.5 TeVNNsPb-Pb, 0-5%, e+X→B

/fm2 = 25--100 GeVq

= 0bm

= 4.8 GeVbm

258

Fig. 7: Di-muon (μ+μ-) invariant-mass spectrum for central Pb–Pb collisions, as expected to measured in the backward rapidity region (-4<η<-2.5) in one month of Pb–Pb data-taking. The uncorrelated (combinatorial background), evaluated from like-sign combinations, has been subtracted in the figure [2].

The mass resolutions are σm = 30 MeV/c2 for

the J/ψ and σm = 80 MeV/c2 for the ϒ. About

105 J/ψ and 10

3 ϒ will be measured in central Pb–Pb collisions during one year of data taking.

Quarkonia measured at forward rapidity allow measurement of parton distributions at x values as small as 10

−5. The modest transverse-

momentum cut on single muons applied at the trigger level extends quarkonia detection down to zero transverse momentum. The number of detected J/ψ is about 7×10

5 per year, allowing

for a detailed study of J/ψ production as a function of centrality and transverse momentum. Similar studies can be carried out for the ϒ, but with significant statistical errors, since the expected yearly statistics is of about 10

4 ϒ’s.

12. PHOTONS

Direct prompt photons at high pt allow the study of hard processes in the dense medium without any final-state modification. In the low-pt domain, thermal photons trace the thermal evolution of the system and, in particular, of the hot and early phase of the reaction.

The photon spectrum will be measured in ALICE with the PHOS spectrometer. Hard photons will be identified on an event-by-event basis using shower-shape and isolation-cut analyses. In this energy domain, the systematic errors due to misidentified neutral mesons will be of the order of a few per cent. Statistics will limit the measurement in the high-energy part of the spectrum to about 100 GeV both in pp and in Pb–Pb collisions. Prompt photons will be used to tag charged jets emitted in the opposite direction in order to study jet-fragmentation functions

(Fig. 8). In-medium modification of the fragmentation function will be measured with an accuracy of the order of a few per cent (Fig. 9).

Various correlations, such as photon–hadron and photon–photon correlations will provide additional information on the medium modified di-jet structure.

In the low-energy domain direct photons will be identified as an excess of identified photons (with shower-shape analysis) when compared with the spectrum of decay photons

Fig. 8: Photon-tagged jet measurement. The photon provides a measurement of the energy of the parton that originates the jet, thus allowing to study the in-medium modification of the jet energy.

The systematic error on the measurement of the excess will be about 8%. This excess has several origins, including thermal photons from the QGP and hadron gas, photons generated by fast partons traversing the medium, and prompt photons. Various correlations, such as photon–hadron and photon–photon correlations will provide additional information on the medium modified di-jet structure. In the low-energy domain direct photons will be identified as an excess of identified photons (with shower-shape analysis) when compared with the spectrum of decay photons. The systematic error on the measurement of the excess will be about 8%. This excess has several origins, including thermal photons from the QGP and hadron gas, photons generated by fast partons traversing the medium, and prompt photons

259

Fig. 9: Expected performance of the measurement of the nuclear modification, in Pb–Pb (medium) with respect to pp (no medium) collisions, of the fragmentation function of photon-tagged jets. The expected error bars are reported on the curve (RFF = 1) expected if jets are not affect by the medium. The curve below shows the expected modification induced by energy loss (quenching) in the medium: RFF > 1 for z close to 0, RFF << 1 for z close to 1.

13. JET PHYSICS

The properties of the hot and dense medium produced in nucleus–nucleus collisions can be studied via the energy loss experienced by fast partons in the medium (jet quenching). The highest sensitivity to the medium properties is expected when measuring the longitudinal and transverse fragmentation functions of jets both at large and at small relative momentum fraction z.

In central Pb–Pb collisions at LHC, jet rates within the ALICE acceptance are sufficient to map out the energy dependence of jet fragmentation over a very wide kinematic range, up to Et = 200 GeV. However, jet reconstruction in nuclear collisions has to cope with the large background from the underlying event, therefore, jet reconstruction has to be limited to small cone sizes ( 22 ηφ Δ+Δ=cR ) in the range 0.3 < Rc < 0.5. In addition, a transverse momentum cut in the range 1 GeV/c < pt < 2 GeV/c has to be applied to reduce the background. As a consequence, even for perfect calorimetry, the energy resolution is limited to ΔEt/Et = 20%.

To study the ALICE performance, jets with energies in the range from 20 GeV to 200 GeV have been embedded into simulated Pb–Pb events and passed through the full detector

simulation and reconstruction chain. The energy spectrum and jet-structure observables are reconstructed and compared to unmodified jets as measured in pp collisions. Only for cone energies below 50 GeV, fake jets do influence the quality of the reconstruction, as shown in Fig. 10.

In its initial design, ALICE can measure only the charged particles within the jets, limiting the jet-energy resolution to 40–50%. Nevertheless, at high Et, charged-jet reconstruction is shown to be much superior to studying high-pt parton fragmentation using leading particles only, because the bias in the fragmentation function is significantly reduced. Fig. 10: Jet energy spectrum reconstructed with charged tracks only (no calorimetry) in one month of Pb–Pb data taking. The upper curves represents the input spectrum, the lower curve the spectrum reconstructed in a simulation without the Pb–Pb background, the markers represent the spectrum reconstructed in a simulation with the full Pb–Pb background, that causes the reconstruction of fake jets below 50 GeV.

Whereas the high-pt and high-jt (momentum

transverse to the jet axis) regions of the leading parton remnants are essentially background free and will be measured very well in ALICE, the spectra of particles originating from radiated gluons have to be extracted mostly from kinematic regions, where background dominates the signal (S/B = 10

−1-10

−2). In such domain the

low-pt tracking capabilities of ALICE are essential and unique, and allow a study of this region (including PID information) on a statistical basis.

In the low-Et-jet region, jet-structure modifications will be studied with inclusive

260

spectra of identified particles and particle correlations, as shown by the RHIC experiments. These studies require excellent low-pt and PID capabilities and ALICE will extend them to heavy-ion collisions at the LHC.

The planned electromagnetic calorimeter (EMCAL) for ALICE (2009-2010) will improve the jet-energy resolution, increase the selection efficiency and further reduce the bias on the jet fragmentation. Furthermore, it will add a jet trigger which is needed to increase the statistics at high Et. The low- and high-transverse-momentum tracking capabilities combined with electromagnetic calorimetry represent an ideal tool for jet-structure modification studies at the LHC over a wide kinematic region of jet and associated-particle momenta.

14. CONCLUSIONS

In summary, the ALICE detector will allow us to study the properties of strongly-interacting matter in extreme conditions and to enjoy Nuclear Physics at the highest energies.

ACKNOWLEDGEMENTS

The author warmly thanks the organizers of the Workshop for inviting him to give this presentation.

[1] ALICE Collaboration, Physics Performance Report, Volume 1, J. Phys. G30 (2004) 1517. [2] ALICE Collaboration, Physics Performance Report, Volume 2, J. Phys. G32 (2006) 1295 [3] F. Antinori, these proceedings. [4] S. Moretto, these proceedings.

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Conference Proceedings Vol. 96

“The Nuclear Physics from the f7/2 to the Quark - Gluon Plasma”

F. Gramegna, M. Cinausero, D. Fabris (Eds.)

SIF, Bologna 2008

THE SILICON PIXEL DETECTOR FOR ALICE EXPERIMENT

Sandra Moretto

on behalf of ALICE SPD collaboration

Dipartimento di Fisica dell’Universitá and INFN Sezione di Padova, I-35131 Padova, Italy

INTRODUCTION

ALICE (A Large Ion Collider Experiment) is

an experiment under construction at the CERN

Large Hadron Collider (LHC) optimized for the

study of ultra-relativistic nucleus-nucleus

collisions, at a center-of-mass energy of 5.5 TeV

per nucleon. The prime aim of the experiment is

to study in detail the behavior of nuclear matter

at extreme densities and temperatures, in view of

probing deconfinement and chiral symmetry

restoration. For a recent description of the

ALICE experimental apparatus see ref. [1]. The

Inner Tracking System (ITS) [2] will provide

precise tracking information close to the

interaction point. It consists of six concentric

layers of three different types of silicon

detectors, within a radius of about 44 cm: two

innermost layers of Silicon Pixel Detectors

(SPD), two layers of Silicon Drift Detectors

(SDD) and two layers of Silicon Strip Detectors

(SSD). The secondary vertexing capability of the

SPD will allow the detection of charm and

beauty hadrons which are of particular interest to

probe the formation of deconfined matter [3].

An overview of the SPD system and of its

integration inside the ALICE detector is

presented.

THE ALICE SILICON PIXEL DETECTOR

The SPD consists of two barrel layers of hybrid

Silicon Pixel Detectors, mounted on a carbon

fiber support, placed around the beam line at

radii of 3.9 cm and 7.6 cm, respectively. In the

following we describe the main components of

the SPD and how they have been assembled.

The ladder

The heart of the SPD is the ladder, which is an

assembly of a 200 μm thick p+n silicon sensor

flip-chip bonded to five readout chips. In the

following we will use the cylindrical coordinates

as reference system, with the z axis along the

beam direction. The silicon sensor is a matrix

with an active area of 12.8 mm (rφ) x 70.7 mm

(z), arranged in 256 rows (rφ) x 160 columns (z)

of pixels. The size of each pixel is 50 μm (rφ) x

425 μm (z). Each pixel is bump-bonded to a

contact of the ALICE1LHCb read-out chip, a

mixed analogue-digital signal chip developed in

a 0.25 μm CMOS technology, radiation hardened

by design layout [4]. Each chip, 150 μm thick,

contains 8192 readout cells arranged in 256 rows

and 32 columns. Five chips are bump-bonded to

each ladder. A modular test system was

developed based on LabView and VME, which

allows to test individual bare front-end pixel

chips as well as single flip-chip bonded chips and

ladders [5].

Half-Stave

The basic module of the SPD is the Half-Stave

(HS), that is made of two ladders mounted

together, along the beam direction, one

grounding foil, an Al-polyimide 5-layer bus and

a multi-chip-module (MCM). An Al-Kapton foil,

70 μm thick, is glued to the chip side of the

ladder to provide the proper grounding of the

Half-Stave and an electrical shielding with

respect to the mechanical carbon-fiber support.

An Al-polyimide 5-layer bus is glued on the

sensor side of the ladder. The bus incorporates

control and data lines and is connected to the

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front-end read-out chip and to the MCM by

ultrasonic wire-bonding, as shown in figure 1.

The MCM, that carries auxiliary read-out and

control signals, is placed at one end of the Half-

Stave. All signals to and from the counting room

are transmitted via optical fibers. The alignment

constraints and the proper gluing are crucial for

the wire-bonding, consequently the micrometric

alignment of the components with respect to

each other relies on a Mitutoyo coordinate

measuring machine and have been carried out in

a Clean Laboratory.

Fig. 1: The SPD Half-Stave layout and a sketch of

the wire-bonding connections.

The Sector

Two Half-Staves are coupled together to form

a Stave. The Staves are glued on a 200 μm thick

Carbon Fiber Support Sector (CFSS), each sector

carries 6 staves: 4 for the outer layer and 2 for

the inner layer. Ten CFSS are mounted around

the beam line and constitute the mechanical

support of the SPD barrel. Since the front-end

chips may generate a heat load up to 20-25 W

per Stave, to remove the total power dissipated in

the front-end electronics, an evaporative C4F10

based cooling system has been adopted to

maintain the SPD at constant temperature. To

this end the Sectors are equipped with cooling

ducts, made of Phynox, embedded in the CFSS.

Due to the strong requirements on relative

positioning of the components, to the severe

material budget constrains and to fragile nature of

the components, the Sector assembly has

required the development of specific tools and

mounting techniques for the manipulation of all

the components. A dedicated system for the

assembly has been mounted on the working

plane of a JOHANSSON TOPAZ Measuring

Machine, placed in a Clean Laboratory. The

mechanical coupling is obtained by fixing the

Half-Staves directly to the CFSS by means of

UV-curable glue tags and carbon fiber clips for

the outer layers. The thermal coupling between

the Half-Stave and the cooling duct is ensured by

means of thermal grease pads.

Fig. 2: The first Half-Barrel assembled.

Half-Barrel and SPD

Five Sectors have been assembled together to

form an Half-Barrel, as shown in figure 2. Two

Half-Barrels mounted face-to-face around the

beam pipe form the entire SPD, as shown in

figure 3 in which the SPD is mounted on a

specific mechanical support for the final

assembly tests. Due to the severe thermal

stability requirements of the Silicon Drift

Detectors, positioned just outside the SPD barrel,

a thermal shield surrounds and isolates the SPD

volume. The shield is made of two halves, each

consisting of a half-cylinder and a half-cone. It

provides mechanical protection during the

installation procedures and also the structural

support for the final assembly around the beam

pipe.

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Integration

The integration of the SPD around the beam

pipe, inside the ITS, and the installation

procedures have been quite complex. The

presence of the ALICE forward muon arm

complicates the access to the area of the inner

detectors, moreover a minimum distance

between the closest SPD component and the

beam pipe of only 5 mm and the delicate cooling

system connections give additional constrains.

For these reasons the installation procedure is a

sequence of many delicate operations, which

have been first tested with the aid of a 3D CAD

modeling and then performed, in all the details,

in the laboratory before the final installation.

Fig. 3: The entire SPD mounted at CERN.

CONCLUSIONS

The commissioning of the ten Sectors has been

done and the integration of the whole SPD has

been completed. The installation of the SPD in

the ALICE experimental hall and all the cabling

of the detector have been completed. At the

present date the start of the commissioning of the

SPD is scheduled for October 2007.

[1] ALICE Physics Performance Report Vol. I, J.

Phys. G: Nucl. Part. Phys. 30 (2004) 1517.

[2] ITS Technical Design Report, CERN-LHCC 99

12, 1999.

[3] ALICE Physics Performance Report Vol. II, J.

Phys. G: Nucl. Part. Phys. 32 (2006) 1295.

[4] K. Wyllie et al., Front-end pixel chips for tracking

in ALICE and particle identification in LHCb,

Proceeding of PIXEL 2002 Conference, SLAC

Electronic Conference Proceedings, Carmel, USA,

September 2002.

[5] P.Riedler et al., Nucl. Instr. Meth. A568 (2006)

284.

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