ANU-P/726 February 1979

ELECTRIC MOMENTS OF THE FIRST EXCITED STATE OF ^ 0

M.P. Fewell and A.M. Baxter Physics Department,

and

D.C. Kean, R.H. Spear and T.H. Zabel Department of Nuclear Physics,

Australian National University, Canberra, 2600, Australia

Cv

ANU-P/726 February 1979

Accepted for publication in NUCLEAR PHYSICS

ELECTRIC MOMENTS OF THE FIRST EXCITED STATE OF 1 8 0

M.P. Fewell and A.M. Baxter

Physics Department, Australian National University, Canberra, 2600, Australia

and

D.C. Kean, R.H. Spear and T.H. Zabel

Department of Nuclear Physics, Australian National University, Canberra, 2600, Australia

Abstract :

The static cjuadrupole moment Q-+ and the B(E2;0 -*2 ) value of the

first excited state of i 3 0 at E = 1.982 MeV have been determined

using the reorientation effect in Coulomb excitation. Surface

barrier detecrors at laboratory angles of 90° and 174° were used to

detect 1 3 0 ion» elastically and inelastically scattered from 2 0 8 P b .

At both angies, we determined experimentally the maximum bombarding

energies at which nuclear interference effects were negligible. It

is found that Q 2 + = -0.O23 ± 0.021 e.b (-0.052 ± 0.021 e.b) for

destructive (constructive) interference from higher states. This

result is in good agreement with theoretical expectation. For the

transition moment we find B(E2;0*->- 2 +) » 0.00390 ± 0.00018 e 2.b 2

(0.00371 i 0.00018 e 2.b 2) for destructive (constructive) interference.

NUCLEAR REACTIONS 2<> 8Pb( 1 8O, 1 8O*) 2 0 8Pb, E 1 8 * 57-86 MeV, e j a b - 90°, 174';

measured Coulomb excitation probability of 1 8 0 first 2 state, deduced

Q 2* and B(E2;0*-*2+). Enriched target,

2 -

1. INTRODUCTION

There has been considerable controversy over the past few years con­

cerning the static quadrupole moment, Q.+, of the first excited state of 1 8 0 (E = 1.982 MeV, J** 2*). Measurement of this quantity via the usual

reorientation-effect technique is notoriously difficult because the state

concerned is but weakly excited in Coulomb excitation. The controversy was

triggered in 197S when Kleinfeld et al. ' reported a measurement of Q_+

using Si surface-barrier detectors to study projectile excitation of 1 8 0 by ? 0 9 B i . They found Q-+ " -0.16±0.02 e.b, assuming destructive interference

from higher states, or Q~*» -0.19± 0.02 e.b, assuming constructive interfer-21

enre. Engeland and Ellis quickly pointed out ' that this large negative value

was in serious disagreement with the predictions of current models of the

structure of 1 8 0 ; their own shell model calculations, which allowed an admixture

of (sd) 2 and (sd)1* p" 2 configurations, gave Q_+ = -0.034 e.b, although they

were in good agreement with other known properties of the low-lying levels of 1 8 0 , in particular the magnetic dipole moment of the 1.982-MeV state.

This conflict was reinforced by subsequent theoretical work. Lawson et

al. ' analysed a large body of data on the low-lying positive-parity states

of 1 8 0 , and deduced save functions using a model space which included collec­

tive components from core excitations and all basis states formed fiom a

closed 1 6 0 core plus two d,,-» 't/2 neutrons and up to one d_ / 2 neutron. They

found that the data constrained the wave functions within rather narrow limits,

and that their overall fit favoured Q-* • -0.05 e.b, although a value as large 41

as -0.07 e.b could be "tolerated". Erikson and Brown •* considered the co­existence of spherical and deformed states to produce the spectrum of low-lying levels in i 8 0 . Taking, as they propose, an effective charge of 0.5 e for each of the extra-core neutrons, one obtains from this work the values Q 2 + » -0.062 e.b and Q2* e-0.055 e.b for their type II and type III calcu­lations respectively. Klingenbeck ', using a two-p- tide model space and an effective charge of 0.54 e, derived a lower limit for Q^* of -0.0503 e.b.

J> -

Recently Morrison et al. have reported calculations within a model space

involving two valence nucléons plus a four particle-two hole deformed state

with a basis of the full p and sei shells; they find Q 2 + - -0.0S e.b.

The predictions of the five theoretical papers discussed above are

summarised in table 1. It is evident that in every case the authors are

unable to reproduce the large magnitude for Q,+ reported by Kleinfeld et 21 al. As pointed out by Engeland and Ellis , confirmation of this large

magnitude for Q-* would require drastic revision of current ideas on

nuclear structure.

Prompted by the worî; of Kleinfeld et al. and of Engeland and Ellis, we

commenced some time ago a projectile-excitation measurement of Q.+ using 2 0 8 P b S targets and ?' surface-barrier detectors at 174° (arnular) snd ± 90".

Initial results obtained at 174° only hive been published (Fewell et al. ' ) .

In order to obtain Q, + from data taken at one angle only, it is necessary to

assume a value for B(E2;0 -* 2 ). On the basis of data available at that time,

Fewell et al. used B(E2;0 +-»2 +) = 0.0044 ± 0.0004 e 2.b 2; this gave Q,+ *

-0.076 ± 0.030 e.b for destructive interference from higher states, or Q- + *

-0.100 t 0.030 e.b for constructive interference. This result substantially

reduced the discrepancy between theory and experiment.

Since then, two further measurements of Q-+ have been published. Void

et al. , using 1 9 6 P t and 2 0 8 P b targets and a particle-gamma coincidence

technique, obtained Q 2* 3 *0.020 ± 0.013 e.b (destructive interference), or

Q-+ = -0.010 i 0.013 e.b (constructive interference). Flaum et al. ' used a

gold target and a QDDD magnetic spectrometer; they obtained Q 2+ • -0.045 ±

0.027 e.b (destructive interference), er Q-+ » -0.073 ± 0.027 e.b (constructive

interference).

The four experimental results discussed above are summarised in table 2.

Also shown are two other results of which we are aware, but of which experimental

details have not been published. The first is t.ie pioneering measurement of

the Chalk River group, listed by Christy and Hausser in theii compilation

and attributed to a private communication from Disdicr et al. The value given

- 4 -

is Q_* = -0.11 ± 0.05 e.b, obtained using a 2 0 8 P b target and Si surface-barrier

detectors; it is not clear whether the analysis assumes constructive or des­

tructive interference from higher states. The second is from the Minnesota

group ; using a 2 0 8 P b target and a split-pole magnetic spectrograph, they

obtained Q 2+ = -0.076 ± 0.020 e.b (destructive interference) or Q_*= -0.107 ±

0.020 e.b (constructive interference).

It is evident that if the result of Kleinfeld et al. is ignored the

discrepancy between theory and experiment becomes less serious. Nevertheless

we cons: der, for the reasons listed below, that we should publish the results

of our complete experiment, which iwolves data obtained at 90° as well as

174° and hence is not dependent on a value of B(E2;0 •* 2 ) deduced from other

work :

1. There is still no convincing explanation of the discordant

result reported by Kleinfeld et al. It is therefore desirable

th3t Q, A should be re-determined using an essentially similar

technique, i.e. one based upon the use of Si surface-barrier

detectors, if onlv to check whether, as suggested in ref. ,

t' Is particular technique may be subject to serious systematic

errors.

2. Even if the result of Kleinfeld et al. is ignored, there remains

scatter in the values of Q,+ which is outside quoted errors.

The values of B(E2;0 •*- 2 ) from the various experiments are also

erratic.

3. It appears that Void et al. measured Q 2+ using i 9 6Pt and 2 0 8 P b

targets, and then corrected their result for the effects of

nuclear interference using for guidance the 174° "safe-energy"

curve obtained by Fewelletal.™ for a 2 0 8 P b target. The basis

for the correction procedure as describee by Void et al. is rather

- 5 -

obscure, and, in addition, their assumption that Coulomb-

nuclear interference behaviour observed for one projectile-

target combination is valid for other projectile-target 121

combinations has been shown to be unjustified. Further­more, LeVine has argued that the procedure used to correlate date obtained at various angles is invalid and leads to over-correction; indeed, results to be presented later in this paper demonstrate that some of the data to which Void et al. applied a substantial correction to allow for nuclear interference were in fact subject to negligible nuclear interference.

91 4. The experiment of Flaum et al. ' was performed using a Au

target at 60 MeV bombarding energy. No attempt was made to

check experimentally whether this energy is "safe"; it has 121 been shown ' that such experimental verification is highly

desirable. In addition, although Flaum et al. used a QDDD

magnetic spectrometer as particle detector, the peak-to-valley

ratios in their published spectra are no better than 5 to 1,

and it is our experience that reliable analysis of such spectra

can be difficult.

In what follows we describe our complete experiment to determine Q-+

and B(E2;0*+ 2*). The results presented supersede those reported by Fewell

et al. 7^.

- 6 -

2. EXPERIMENTAL PROCEDURE

The underlying principles of the projectile excitation technique are

similar to those discussed in connection with target excitation by Esat et

al. . In order to determine both Q-+ and B(E2;0*-*- 2*), two independent

measurements of the excitation probability ?n*+2+ a r e required. In the

present experiment this is achieved by taking data at two different scattering

angles, 174° and 90°.

An annular Si surface-barrier detector was mounted at a distance of 65 mm

from the target, corresponding to a mean laboratory scattering angle of 174°.

The advantages of the axial geometry provided by an annular detector have been

discussed at length in réf.* ' .

The sensitivity of excitation probability to scattering angle becomes

more important at forward angles, i.e. (3P/38)/P increases with decreasing

6. At 6= 90°, the rate of change is 2% per degree. Therefore, in order to

determine P to an accuracy of 1%, it is necessary to know 6 to an accuracy of

0.5*. To achieve this level of precision, two Ortec T-series detectors were

mounted on a single rigid supporting bar on either side of the target, and

each at a distance of 180 mm from the target, so as to detect ions scattered

through ± 90°. By averaging results obtained with these two detectors, the

effect of uncertainties in scattering angle due to uncertainties in the

trajectory of the incident beam was rendered negligible. In addition, the

target orientation was alternated between i 45* relative to the beam direction,

thus removing the uncertainty in the scattering angle caused by the uncertainty

in the lateral position of the beam spot. The remaining uncertainty in the

scattering angle for 90° scattering is then due to the uncertainty in the

collinearity of the beam spot and the two detector-defining slits. The centres

of these defining slits were optically aligned with the centre of the target

mount to within ± 0.1 mm. The target foil was mounted on a 9 mm diameter

- 7 -

hole and, allowing for reasonable movement of the foil under bombardment,

the uncertainty in the position of the beam spot relative to the mount is

taken, at the one standard deviation level, as ± 1 mm normal to the target

plane. This corresponds to ± 0.3° uncertainty in 8 and ± 0.6% uncertainty

i n V-2*-Energy spectra were obtained at 1 8 0 bombarding energies ranging from

57 to 86 MeV. Beams of 1 8 0 ions were obtained from the ANU 14UD pelletron

accelerator. The beam energy had been previously calibrated ' to better

than 0.1\. The target consisted of 2 0 8PbS evaporated onto a thin carbon

foil. The isotopic enrichment of 2 0 8 P b was 99.14%, and the partial thickness

of 2 0 8 P b was approximately 8 yg/cm2. A thin layer of carbon (approximately

1 Ug/cm ) was evaporated onto the target to reduce target deterioration

under bombardment.

3. SPECTRUM ANALYSIS

The experirr.snt was performed in two stages. Firstly, spectra were

obtained at 174° with the plane of the target perpendicular to the beam

direction. This configuration minimizes the effects of target roughness

on spectrum quality. These spectra formed the basis for the initial results

reported by Fewell et al. in réf. . Typical spectra for both 1 8 0 and 1 6 0

projectiles are shown in fig. 1 of that paper. The 0 spectra are useful in

providing lineshapes for the analysis of 0 spectra, and they also provide

checks on the possible presence of peaks due to elastic scattering from con­

taminants in the target.

In the second stage of the experiment, spectra were obtained simultaneously

at 90° and 174° with the plane of the target at 45° to the beam direction. With

this configuration the spectra arc more subject to the malignant effects of

taTget roughness. Typical 90° spectra for 0 and 0 projectiles are shown in

fig. 1. The structure and broadening of the group corresponding to the

- 8 -

excitation of the 1 8 0 projectiles are due to recoil following gamma decay in

flight. The group corresponding to target excitation of the 3" state at 2.61

MeV in 2 0 8 P b is sufficiently well resolved that it presents no significant

difficulties for the analysis.

The crux of the experiment lies in determining the excitation probability

of the weakly populated 2 state from the ratio of inelastically and elastically

scattered 1 8 0 ions. The experimentally determined Coulomb excitation probability

P of the 2* state is defined as exp

P exp if/ [!C • (CI • The 2 peak sits on a tail extending d^wn in energy from the much larger 0

elastic peak. A useful criterion of spectrum quality is the peak-to-valley

ratio, p/v, defined as the ratio of the height of the inelastic peak to the

minimum in the valley between the elastic and inelastic peaks.

Three possible effects may be considered as contributing substantially

to the low-energy tail of the elastic peak: (i) slit-edge scattering from

defining slits for the beam and in front of the Jstectors; (ii) target non-

uniformity; and (iii) the intrinsic lineshape of the Si surface-barrier

detectors for monoenergetic 1 8 0 ions. Various authors, e.g. Void et al. ,

have suggested that a particularly serious aspect of (iii) is inelastic excita­

tion of the 2* states of 2 8 S i and 1 8 0 in the silicon detectors. To investigate

this phenomenon, we mounted representative Si detectors in the focal plane of

a split-pole magnetic spectrometer and examined the spectra produced by 1 8 0

ions scattered at 8 * 15 s from a lead target. This procedure selects ions

which are monoenergetic to the degree determined by the width of defining slits

in front of the detectors (approximately SO keV). A typical spectrum obtained

in this way is shown in fig.2. There is no indication whatsoever of peaks due

to inelastic excitation of 2 8 S i or 1 8 0 in the detector, and indeed the intrinsic

lincshape has a tail whose strength is < 10" 5 times that of the elastic peak

in the region relevant to the present experiment, i.e. about 2 MeV below

- 9 -

the elastic peak. We therefore conclude th t the intrinsic lineshape of the silicon detectors provides negligible contribution to spectrum tailing. It is also apparent that for the data of fig. 2 the level of slit-edge scattering is < 10" 5 times the height of the elastic peak. Effects of target non-uniformity are certainly important. For example, it is found that rotation of the target angle from 90° to 45° usually produces an approximately two-fold increase in p/v in backscattering spectra.

Procedures used in analysing the spectra were similar to those described previously ' ' . An analytic function was fitted to the elastic group, and this fit used to determine the magnitude of the elastic tail under the in­elastic group. Additionally, lineshapes extracted from 1 5 0 data were used to generate an elastic tail for some of the 1 8 0 spectra. In all cases values of f determined by the two procedures were cont_üxdaül lu within one standard deviation.

4. DETERMINATION OF MAXIMUM SAFE BOMBARDING ENERGIES

In contrast to previously reported measurements of Q 2 + in 1 8 0 , we present herein the results of a detailed investigation of the maximum bombarding energies at which th ; effects of nuclear interference are negligible. Fig. 3 shows the results, obtained at laboratory scattering angles of 90° and 174°. The ratio of P to P ,, the excitation probability calculated assuming a pure Coulomb exp coul <* r

interaction, is plotted as a function of laboratory bombarding energy, E. . , and of the distance of closest approach of the nuclear surfaces, s, as given by

s< ecm> = " I 0.72 ZjZ 2

lab e

1 + coseel-j^

1.25 [A]'3 + A^ 3] fm (2)

where Z , A and Z , A are the atomic ni.mbers and masses of projectile and target, respectively, 6 is the scattering angle in the centrc-of-mass system,

- 10 -

E. . is in MeV, and the nvclear radius is taken to be 1.2S A ^ fa. lab *

It is apparent from fig. 3 that nuclear interference effects are neglig­

ible for bombarding energies up to and including about 72 MeV and 60 MeV at

90° and 174°, respectively. The fact that the ratio P /P . at 90* remains

essentially constant for 65 t E. . $ 72 MeV shows that over this energy range

sources of systematic error (other than those having the same energy dependence

as Coulomb excitation) are negligible. For the 90* spectra, p/v ranged from

11 to 42 for 65 $ E. . * 72 MeV. Spectra were also obtained at lower bombarding

energies, ranging down to 59 MeV. However the quality of these spectra was

poor, having p/v between 3 and 7, and the resultant data points, shown without

error bars in fig. 3, are evidently subject to systematic errors arising from

difficulties in spectrum analysis. For the sake of consistency, we also show

without error bars two of the 174* data points which were included by Fewell

et al. in their analysis, but which have p/v < 7.

From fig. 3, Coulomb-nuclear interference appears to be negligible for

values of s greater than about 6.1 fm and 6.4 fm at 90° and 174°, respectively.

Given the energy separations between the data points, these minimum safe

values of s are strikingly similar. Thus, the present data are consistent

with the onset of interference for 2 0 8 P b • 1 B 0 , at scattering angles between

90° and ld0°, occurring at a constant value of the classical quantity s(6 )

as given in equation (2). This conclusion is supported, for 2 0 8 P b + 1 8 0 at

scattering angles between 90° and 180°, by the coupled-channel calculations of

LeVine '. This simple result must, of course, have its limitations; e.g. it

obviously cannot be extended to very small scattering angles. Interference

effects are determined by the energy- and angle-dependence of the Coulomb and

nuclear reaction amplitudes, and these may not be as simple as equation (2)

implies. Data from other mass regions, e.g. in the fp shell ', show quite 81 different behaviour. This led Void et al. ' to correct their own and previous

1 8 0 data for Coulomb-nuclear interference by assuming that AQ, the effect of

interference on the value obtained for Q 2+, i 5 independent of scattering angle;

for all Measurements, the correction was treated as a function of s(180°),

given by the 174* data of *ig. 3. The assumption that, for a given value of

s(180°) , AQ is the same at all scattering angles, is consistent with the usual

method of formulating rules for avoiding interference effects; these have

stipulated that, regardless of the angle at which data are taken, the maximum

bombarding energy used should be such that s(180°) > s . , where the recommended m m

181 171 value of s . has increased over the years from 3 fm ''to 7.5 fm ' (for a

m m * *•

nuclear radius parameter of 1.25 fm).

Since a change AP_, in the excitation probability due to interference

induces an error in the extracted Q_+ value given by

uQ = AP^j/lP P(6,C)] (3)

where P(9,5) is the sensitivity of the excitation probability to the quadrupole

14") moment, as defined fcr example in ref. , it follows that AQ is independent of

scattering angle only if APçy/P bas the same angle dependence as P(8,£). This

implies, for example, that for a given value of bombarding energy, AP r«/P at

9 = 90° is about half that at 180°. It is evident from fig. 3 that this is

not the case for ?b + 0 . Large interference effects are observed in the

174° excitation function at bombarding energies where the 90* excitation

function is still consistent with pure Coulomb excitation. Because the

correction applied by Void et al. uses our 174° results at all angles, it

overestimates interference effects at more forward angles; consequently,

significant corrections are applied at bombarding energies which the present

data show to be quite "safe" for 2 0 8 P b • 1 8 0 .

5. RESULTS

191 The de Boer-Winthei multiple Coulomb excitation code ' was used to

derive Q 2* and B(E2;0+ -* 2*) following procedures similar to those described

in detail by Esat et al. . Higher states included in the analysis were

those at 3.555, 3.635 and 3.921 McV (J* = 4*, 0* and 2*, respectively); other

12 -

states were found to have negligible effects. Matrix elements for E2 and Ml 20) transitions were obtained fro» the recent compilation by Ajzenberg-Selove

Corrections have been applied for the effects of target thickness, electron

screening ', vacuum polarization "\ the use of the semi-classical approxima­

tion ', nuclear polarization ', mutual excitation } and Ml reorientation ' ;

the net effect of these corrections is to reduce |Q2+| by 0.001 e.b, and to

increase B(E2;0*-»-2*) by 0.00011 e 2.b 2. The E4 matrix element for the

transition between the ground state and the 3.555 MeV state is not known;

however, even if the strength of the transition were 50 Weisskopf units,

it would change |Q_ +| by only 0.001 e.b. The effect of the 2 0 7 P b in the

target (0.69%) is negligible.

Allowance has also been made for the effect of virtual excitation of

states in the giant dipole resonance (G0R). The magnitude of this effect can

be expressed in terms of the parameter k, which is the ratio of a_ 2, the

observed minus-two moment of the total photo-absorption cross section, to the

hydrodynamic model estimate of this quantity , i.e. k = o_2/3.5 A 3. Since

the writing of ref. , new evidence has emerged concerning the value of k for 1 8 0 . Berman et al. ' have measured 1 80(Y,p) and 1 80(Y,n) cross sections

291 from threshold to E = 30 MeV, and Kneissl et al. ' have reported total

photoneutron cross sections for 1 8 0 from 9 to 33 MeV. These data indicate

that k s 1, although it may be as large as 1.5, depending on the behaviour of

the total photoneutron cross section above 33 MeV, the maximum photon energy

used by Kneissl et al. We have assumed k » 1. In fact the value obtained

for Q-+ when data are obtained at 174° and 90° is not very sensitive to the

GDR correction; in the present work its effect is to reduce | Q 2 + | by 0.011

e.b, which is about half the statistical uncertainty in the result. It

increases the value of B(E2;0*-> 2 +) by 0.00027 e 2.b 2.

In determining Q 2 + and B(E2;0* +2 * ) , we have used 90" data obtained at

the eight bombarding energies between 65 and 72 MeV, inclusive. As discussed

in section 4, spectra obtained at lower energies are of inferior quality and

difficulties of lineshape analysis become more severe. The 90° spectra used

- 13 -

all have p/v > 7. For the sake of consistency, we have rejected in the present

analysis two of the 174° spectra, which were included by Fcwell et dl. , but

which had p/v < 7. These are the data at 57 and 59 MeV. The 174° data in­

cluded in the analysis are those at 58 and 60 MeV. Results obtained using this

selection of data are presented in table 3. The quoted errors do not include

the uncertainty in the GDR correction, which is difficult to estimate and may

be cor.uaiible to the size of the correction itself. If the 57 and 59 MeV

points at 174° are included, the magnitude of Q 2 + is increased by 0.002 e.b

and the value of B(E2;0*-»-2+) by 0.00001 e 2.b 2, i.e. the changes are negligible

Even if we include all data obtained in the present work below the maximum

safe bombarding energies, the results are changed by only -0.017 e.b for Q~+

and +0.00019 e 2.b 2 for B(E2;0+ •> 2 + ) . Data used to estimate these changes

include 90° spectra with small values of p/v, and 174° spectra obtained

with a target angle of 45°, again with a small value of p/v. The smaliness

of the changes indicates the relative insensitivity of our result to possible

systematic errors in spectrum analysis.

Target contaminants in the mass range A = 183 to 188 and A = 169 to 179

would place pea'.s under the 1 8 0 inelastic peak in the 174° and 90° spectra

respectively. The level of such impurities was determined by scattering 40-MeV 1 8 0 ions from the same targets that were used to collect the higher energy data.

At the level of two standard deviations of the background, upper limits of 1.3%

and 0.8% could be placed on contributions from impurities to the measured ex­

citation probabilities at 174° and 90'', respectively. Examination of various 1 6 C spectra gave limits consistent with these.

The possibility of transfer reactions contributing peaks under the 1 8 0

inelastic peak was investigated. Single-neutron transfer reactions were

prominent in both 174° and 90° spectra at high bombarding energies. However,

they arc kinematically unable to contribute to the spectrum in the region of

the 1 8 0 inelastic group. Furthermore, they become undetectable at bombarding

energies below 76 MeV (90°) and 66 MeV (174"). No evidence for any other

reactions was seen at any bombarding energies. Tho only single-nucleon

transfer reaction wliich could contribute to the spectrum in the region of

- 14 -

the 1 8 0 inelastic peak is the 2 0 8 P b ( 1 8 O , I 9 F ) 2 0 7 T t reaction. The *ork of

Buttle and Goldfarb ' suggests that this reaction has a much lower cross,

section than the single neutron transfer reactions. Ev?n assuming it to

have the same cross section, it is possible from examinâtion of the spectra

to set upper limits, at the level of two standard deviations of the back­

ground, of 4% (90°) and 2% (174*) of the inelastic peak area for the con­

tributions of transfer reactions at the bombarding energies used in the

analysis.

We have made no allowance for effects due to the hexadecapole moment,

H.+, of the 1.982-MeV state, since there are no available data on this

quantity, however, the largest value known for H.+ in the s-d shell is

0.0016 e.b 2 for 2 0Ne(ref. 3 1O and, for 1 8 0 , it would have to be as large as

0.0046 e.b 2 to change the value of Q 2 + by 0.001 e.b.

6. DISCISSION OF RESULTS

In table 4 the present result for B(E2;0 ->2 ) is compared with previous

determinations, which include reorientation-effect experiments, lifetime

measurements using the recoil-distance method, and Doppler-shift attenuation

measurements. The errors shown are those given by the authors themselves. 13) LeVine ' has made a careful evaluation of the errors involved in various

recoil distance measurements, and has deduced a weighted-mean value for

B(E2;0*->2*) of 0.00413 ± 0.00015 e 2.b 2 from the work of r e f s . 3 2 ~ 3 5 ) ; his

weighted-mean value for the re-orientation effect experiments of refs. ' ' "

is 0.00412 t 0.00014 e 2.b 2. The present result (0.00390 ± 0.00018 e 2.b 2

for destructive interference) is consistent with these values.

Comparison of tables 1 and 3 shows that the present result for Q 2 +

is in very good agreement with theoretical expectations. It should be

noted that sone theoretical works ' ' ' specifically predict thit the

interference from higher states should be destructive. Ample comment on

•

1

15 -

the significance of other experimental work has been made in section 1 above. 81 While the result of Void et al. can be understood in terms of unnecessary

corrections for Coulomb-nuclear interference, the problem of the large value

for IQ-*! obtained by Kleinfeld et al. persists. It seems likely that the

difficulties of that work are associated with the forward-angle data, where

excitation probabilities are relatively small, and (3P/36)/P is relatively

large, so that the results are particularly sensitive to contributions from

target contaminants, errors in angle determination, and errors in spectrum

analysis. It is noteworthy that if forward-angle spectra are ignored, the

data of Kleinfeld et al. give Q-+ = -0.04 e.b for destructive interference 171 (deduced from fig. 15 of ref. ), in agreement with the present work.

- 16 -

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- 17 -

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1

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- 19 -

TABLE 1

Theoretical predictions of the static quadrupole moment, Q~+, of

the first excited state of 1 8 0 . The dual values from the work

of Erikson and Brown correspond to two different assumptions

made in their calculations (cases II and III).

Authors Q 2 + (e.b) (calculated)

21 Engeland and Ellis

Lawson et al. 4) Erikson and Brown '

Klingenbeck '

Morrison et al. '

-0.034

-0.05

-0.062 or -0.055

>, -0.0503 -0.05

TABLE 2 Previous einoerimental determinations of the static quadrupole moment, Q-+, of the first excited state of 16r The column headed "GDR correction?" indicates whether or not allowance has been made for the effects of interference from the giant dipole resonance.

Reference Q2* (e.b) GDR Correction

Detectors Target Energies used in analysis (MeV)

Angles Reference Dest. int. Const, int.

GDR Correction

Detectors Target Energies used in analysis (MeV)

Angles

Kleinfeld et al.1* -0.16 ± 0.02 -0.19 ± 0.02 No Si S.B. 209 B i 58-63 45,-175°

Fewell et al. 7 ) -0.076 ± 0,030 -0.100 ± 0.030 Yes Si S.B. 208pb 57-60 174°

Void et al. 8 ) •0.020 ± 0.013 -0.010 ± 0.013 Yes i'article-gamma coinc.

196 p t

208 p b 58-63 65#-140*

Flaum et al.9* -0.045 ± 0.027 -0.073 ± 0.028 Yes QDDD spectro­meter

Au 60 4S•-1S0•

Chalk River10* -0.11 ± 0.05 ? Si S.B. 208 p b 65 65#-177*

Minnesota ' -0.076 ± 0.020 -0.107 t 0.020 No Split pole magnet

208 p b 63 45,-150°

o

t

- 21 -

TABLE 3 Values determined in the present work for Q 2 + and B(E2;0 -*2 ) . considering both destructive and constructive interference fron

higher states

Interference Q 2* (e.b) B(E2;0*-2*) (e2.b2)

Destructive

Constructive

-0.023 ± 0.021

-0.052 ± 0.021

0.00390 ± 0.00018

0.00371 ± 0.00018

- 22 -

TABLE 4

Measurements of B(E2;0**2*) for the 1.982 MeV state of l 8 0 . Techniques used are recoil distance (rec.dist.)» Coulomb excitation (Coulex) and Doppler-shift attenuation

(DSA).

Authors Year Technique BfE2:0*-*2*) (e*.b* x KT1»)

Asher e t a l . 3 2 '

Li Hey . e t a l . 3 3 )

Berant et a l . '

' McDonald e t a l . 3 5 )

!

Flaum et a l . '

! Void e t a l . S )

1976

1976

1974

1974

1977

1977

Rec .d is t .

ii H

» H

II II

Coulex

••

44.2 ± 1.8

42.2 ± 2.8

38 ± 2

40 ± 2

45 .3 t 2 .5

40.2 ± 1.4

Dehnhardct a l . ' i 1977 • f 38 ± 4

Klcinfeld et a l . 1 ' 1975 „ 48 ± 2

Chalk R i v e r 1 0 ) 1972 " 39 ± 4

Litherland et a l . ' 1963 DSA 36 ± 8 371 Olness et a l . ' 1973 II 46 ± 12

Hermans et a l . ' 1975 •i 47.8 t 1.9

Present work 1978 Coulex 39.0 ± 1.8

- 23 -

FIGURE CAPTIONS

Fig. 1. Typical 90° spectra for 1 6 0 and 1 8 0 projectiles. The full

curves are fits obtained as described in the text.

Fig. 2. Spectrum obtained with an annular Si surface barrier detector

for "monoenergetic" **0 ions. The detector was mounted in the

focal plane of a split-pole magnetic spectrometer, and a 42 MeV

beam of 1 8 0 ions was scattered from a lead target into the

spectrometer at 15° to the beam direction. Spectra obtained

in the same way for Ortec F-series detectors showed similar,

low-level, structureless tails.

Fig. 3. The double ratio P /P , is plotted as a function of " exp coul bombarding energy E. . and distance of closest approach

of the nuclear surfaces, s. The 174° data are those shown

previously in ref. '; they do not include data taken with

the target surface at 45* to the beam direction. The

significance of the points without error bars is discussed

in the text.

24

M i l l I | l | I I I I I • | l l l l l |

1 ' • • • '

j Q ÛL

O 10 O)

• • 1 U I L ,1 U l U O - L

O O

siNnoo

Fi* . I

CO

o o

5 10

10

3 10

10 L

10 _

l 8 o 42MeV ANNULAR COUNTER LINESHAPE

3100

2 MeV

iMtovmW^ 3200

CHANNEL

»

I nn" 3300

J.

î £fj

(UJJ)S 01

î i i ' — i — » — 1 — i — i — i — ! — l — i — l — i — i — \ — i — r

>ZI 5 0

i l

1 1 I ' T l

01 09 (A8W) m3

0 1 »T X

o^

so — .06

H il

il««'»!.. • 01

Wg 08 01 09 J I I l ' l t ' I » « i I I I 1 1 1 L

92 -