Tariq Al-Abdullah

Hashemite University, Jordan

Cairo 2009

Problems and Issues in Nuclear Astrophysics

Why nuclear physics in astrophysics?

Why indirect measurements of cross sections

in nuclear astrophysics?

The indirect teqhniques and their applicatoins!

Perspectives of the method: RIB and (part,g) reaction

Nuclear Physics Research and Education!

SUMMARY

Nucleosynthesis

1945: Gamow’s Hypothesis

“ all of today elements were made during the early BIG BANG of the Universe “

Questions:

When did it start ??

What elements are produced and can we understand the

isotopic composition ??

Do parameters of the Early Universe have an influence ??

wrong!

Big Bang Nucleosynthesis

Wrong for 3 simple reasons

oBinding energy of deuteron (2.22 MeV) is too small !!

oBinding energy of 4He is too large (28.3 MeV) !!

oThere are no stable isotopes with A=5 and A=8 !!

Deuterons are being dissociated until the Universe Has cooled down to 80 keV !!!

for further fusion the train has Long left the station !!

Universe composition:~76% H and ~23% 4He

Stellar life cycle

energy productionenergy production stability against collapsestability against collapse synthesis of “metalssynthesis of “metals””

thermonuclear thermonuclear reactionsreactions

BIRTHBIRTHgravitational contractiongravitational contraction

explosion DEATH

mixing of mixing of interstellinterstell

ar gasar gas

Interstellar gas Stars

abundance distribution

The goals of experimental Nuclear Astrophysics are:- study of the origin of the elements or

nucleosynthesis- study of the energy generation processes in stars.

Courtesy: M. Arnould

Experimental nuclear astrophysicsExperimental nuclear astrophysics

M. Smith & E. Rehm

Average Reaction rate per particle pair:

In stellar plasma the velocity of particles varies over a wide range

Assume (v) is the velocity distribution

Thermonuclear reactions in stars: general features

Reaction rate: r = N1 N2 v (v) (# reactions Volume-1 Time-

1)

R v σ(v) (v) dv

0

Thermonuclear reactions in stars: general features

<v> is a KEY quantity

Total reaction rate R12 = (1+12)-1 N1N2 <v>12

Energy production rate 12 = R12 Q12

<v> to be determined from experiments / theoretical considerations

as star evolves, T changes evaluate <v> for each temperature

energy production as star evolves - change in abundance of nuclei X

NEED ANAYLITICAL EXPRESSION FOR !

Mean lifetime of nuclei X against destruction by nuclei a

σvN

1(X)

a

a

charged particles Coulomb barrier

tunneleffect

Ekin ~ kT (keV) ECoul ~ Z1Z2 (MeV)

nuclear well

Coulomb potential

V

rr0

T ~ 15x106 K (e.g. our Sun) kT ~ 1

keV

T ~ 1010 K (Big Bang) kT ~ 1 MeV

energy available from thermal motion

exp(-2 = GAMOW factor

reactions occur by TUNNEL

EFFECT

tunneling probability P exp(-

2)

during quiescent burnings: kT << ECoul

Thermonuclear reactions in stars: charged particles

in numerical units: 2 = 31.29 Z1Z2(/E)½ in amu and Ecm in keV)

(E) = (1/E) exp(-2) S(E)

ASTROPHYSICAL FACTOR

Penetration

probability

Thermonuclear reactions in stars:Astrophysical factor

For non-resonant reactions, the cross section behaviour is dominated by the Gamow factor

Cross section can be parameterized as

Sharp drop with

energy!!!!

De Broglie wavelengh

t

S(E) is a sort of linearization of the cross section where all non-nuclear effects have been taken

out

exp 2E

Maxwell-Boltzmann velocity distribution

Quiescent stellar burning scenarios:non-relativistic, non-degenerate gas in thermodynamic equilibrium at temperature T

= reduced massv = relative velocity

Pro

bab

ilit

y (

E)

EnergykT

(E) E

(E) exp(-E/kT)

Thermonuclear reactions in stars: general features

kTE

exp2kTμv

expΦ(v)2

dE E kTE

exp σ(E)(kT)

1πμ8

σv0

3/2

1/2

1212

Reaction rate:

1 2

3 2 1 20

8 1( )exp

E bS E dE

KT EKT

Thermonuclear reactions in stars: Gamow window

E0

Gives the energy dependence

MAXIMUM reaction rate:

Gamow peak

tunnelling throughCoulomb barrier exp(- )

Maxwell-Boltzmanndistribution exp(-E/kT)

rela

tive p

rob

ab

ilit

y

energykT E0

/GE E

( )0

df E

dE

varies smoothly with energy

only small energy range contributes

to reaction rate

OK to set S(E) ~ S(E0) =

const.

221 eZZ

2b

E0 < E0

T ~ 106 – 108 K E0 ~ 100 keV << Ecoul tunnel effect

10-20 barn < < 10-9 barn

average interaction time ~ <v>-1 ~ 109 y

unstable species DO NOT play a significant role

Scenario of quiescent burning stages of stellar evolution

FEATURES

PROBLEMS

10-20 b < < 10-9 b poor signal-to-noise ratio major experimental challenge extrapolation procedure required

REQUIREMENTS

poor signal-to-noise ratio long measurements ultra pure targets high beam intensities high detection efficiency

Experimental approach: generalities

measure measure (E)(E) over a wide range of energies, over a wide range of energies,

EXTREXTRAPOLATEAPOLATE down to Gamow energy region down to Gamow energy region

around Earound E00

Experimental procedureExperimental procedure

LOGSCALE

E0EEcoulcoul

Coulomb barrier

(E)(E)

non-resonant

resonance

direct measurements

extrapolation needed !

many orders of magnitude

C.M. Energy

Experimental approach: extrapolation

DANGER IN EXTRAPOLATION: large uncertainties!

Even using the S(E)-factor, extrapolation is not a piece of cake!!!

Experimental approach: extrapolation II

Er

non resonant process

interaction energy E

direct measurement

0

S(E)

(LINEARSCALE)

-Er

sub-threshold resonance

low-energy tail of broad resonance

Extr

apol

atio

n

EEXPERIMENTAL SOLUTIONXPERIMENTAL SOLUTION

IMPROVEMENTS TO INCREASE THE NUMBER OF DETECTED PARTICLES

New accelerator with high beam intensity

Gas target

4 detectors

IMPROVEMENTS TO REDUCE THE BACKGROUND

Use of laboratory with natural shield reduce (cosmic) background

example: LUNA facility in Italy

Experimental approach: avoiding extrapolation

IDEA: To avoid extrapolation it is necessary to measure

Cros sections in the Gamow region

The ELECTRON SCREENING

A NEW PROBLEM ARISE

BUT…

at astrophysical energies

Experimental approach: new problem

WHY IS THIS A PROBLEM?

It is a problem because electron screening in STARS

and in LABORATORIES is not the same!

To avoid extrapolation experimental techniques were improved

to perform measurement at very low energiesAfter improving measurements at very low energies,

electron screening effects

were discovered

To extract the To extract the

bare astrophysical Sbare astrophysical Sbb(E)(E) –factor–factor

from from direct (shielded) measurementsdirect (shielded) measurements

extrapolation were performed at higher energextrapolation were performed at higher energiesies

EXTRAPOLATION IS BACK AGAIN

Is there any way out ?

INDIRECT METHODS

Asymptotic Normalisation Coefficients (ANC) method (radiative capture reactions).

Trojan Horse Method (thermonuclear reactions induced by light particles)

Coulomb Dissociation method (radiative capture reactions).

In order to solve some of the problem cited above (low cross sections, electron screening) some indirect approaches were proposed such as:

Direct Capture Reactions for charges particles:

The binding energy of the captured particle is low. The capture occurs through the tail of the overlap function. The Amplitude of the tail is given by the ANCs.

For a Transfer reaction (X+A→Y+B):• The DWBA amplitude:

• The Asymptotic behavior of the radial overlap function:

• The Asymptotic normalization of the bound-state wave function:

• For r > RN, the radial dependences are the same

0 2 4 6 8 10 12 140.0

0.2

0.4

0.6

0.8

1.0

rh ,

r (

fm-1

/2)

r (fm)

12C+n-->13C

E0

p

A

Y

B (A+p)

X (Y+P)( ) ( )

, , , ,( ) ( ) ( )B Xf A p A p Y p Y p iM E I r V I r

, 1 2( ), ,

2( )

NB

r Rl BB sp B

A p A p

W rI r C

r

, 1 2, , ,

2( )

NB

B B B B B

r Rl B

n l j l j

W rr b

r

, ,( ) ( )BA p A pI r S r 2 2C = Sb

Asymptotic Normalization Coefficients (ANCS)

Peripheral Transfer Reaction (X+A→Y+B):

The reaction cross section:

In terms of the ANCs:

Procedure to extract the ANCs:

B B X X B B X X

B B X X

DWBAAal j yal j l j l j

l j l j

dS S

d

2 2

2 2B B X X

B B X X

DWBAB XAal j Yal j

Aal j Yal j

dC C

d b b

A

Y

B(A+a)

X (Y+a)

a

C2(B)

C2(X)

Elastic Scattering

ExperimentalAngular Distribution

Double FoldingWood-Saxon

OMPs

Transfer Reaction

DWBAcalculation

Comparison

Spectroscopic factors

ExperimentalAngular Distribution

ANCs

Elastic Scattering

ExperimentalAngular Distribution

Double FoldingWood-Saxon

OMPs

Transfer Reaction

DWBAcalculation

Comparison

Spectroscopic factors

ExperimentalAngular Distribution

ANCs

Extracting the ANCS

Ne-Na cycle

12C 13C

13N 15N

15O

14N

17O

17F

16O

19F18F

18O14O

19Ne18Ne

13O

11C

12N

8B

7Be

9C 10C

10B

11N

11B9B

8Be

20Ne 22Ne21Ne

9Be

23Na

17Ne

16F15F

22Na21Na20Na

24Al23Al 25Al

24Mg23Mg22Mg21Mg20Mg

19Na

(p,γ)(p,α)(β+ ν)

= studied at TAMU

CNO, HCNO

25Si24Si 26Si

June 2008

Comp with direct meas: 16O(3He,d)17F vs. 16O(p,)17F

Gagliardi e.a. PRC 1999 vs. Morlock e.a. PRL 1997

7Be(p,)8B (solar neutrinos probl.):

p-transfer: S17(0)=18.2±1.7 eVbBreakup: S17(0)=18.7±1.9 eVbDirect meas: S17(0)=20.8±1.4

eVb

Experiments using the ANCS

ANC’s measured by stable beams

• 9Be + p 10B [9Be(3He,d)10B;9Be(10B,9Be)10B]• 7Li + n 8Li [12C(7Li,8Li)13C]• 13C + p 14N [13C(3He,d)14N;13C(14N,13C)14N]• 14N + p 15O [14N(3He,d)15O]• 16O + p 17F [16O(3He,d)17F]• 20Ne + p 21Na [20Ne(3He,d)21Na]

beams 10 MeV/u

ANC’s measured by radioactive (rare isotope) beams

• 7Be + p 8B [10B(7Be,8B)9Be] [14N(7Be,8B)13C]

• 11C + p 12N [14N(11C,12N)13C] • 13N + p 14O [14N(13N,14O)13C] • 17F + p 18Ne [14N(17F,18Ne)13C]

beams 10 - 12 MeV/u

ANC’s measured by stable beams (mirror symmetry)

7Be + p 8B [13C(7Li,8Li)12C]

22Mg + p 23Al [13C(22Ne,23Ne)12C]**

17F + p 18Ne [13C(17O,18O)12C]**

** T. Al-Abdullah, PhD Thesis

Rare Isotope Accelerators

Why RIA ??

How are the heavy elements created?

How do nuclear properties influence the stars?

What is the structure of atomic nuclei?

How do complex systems get properties from their

constituents?

How can complex many-body systems display

regularities?

Which new symmetries characterize exotic nuclei?

What are the fundamental symmetries of nature?

Radioactive Nuclei in Supernovae

International Prespectives

The international effort to study the science of rare

isotopes is highly complementary.

RIA will be the first and only facility that will have the

capability to meet the challenge of understanding the origin

of the elements.

RIA will attract the brightest minds, new generations of

the highest-caliber students and the future nuclear

scientists.

RIA will provide many new isotopes that can be used to

specific diagnostic and therapeutic applications. RIA: Connecting Nuclei with the Universe

Research and Education

Well organized Institute

People Quality Instruments Funding Support

Thank you