Electric quadrupole moments of high-spin isomers in 209Po and 210Po

Nuclear Physics A394 (1983) 245-256 North-Holland Publishing Company

ELECTRIC QUADRUPOLE MOMENTS OF H I G H - S P I N

I N 2°9p0

ISOMERS

AND 21°po* E. DAFNI

Physics Department, SUNY, Stony Brook, NY 11794, USA and Department of Nuclear Physics, Weizrnann Institute of Science, Rehovot 76100, Israel and M. H. RAFAILOVICH, T. MARSHALL, G. SCHATZ* and G. D. SPROUSE

Physics Department, SUNY, Stony Brook, NY 11794, USA Received 22 March 1982 (Revised 17 August 1982)

Abstract: High-spin 209, 2t0po isomers were recoil-implanted into tetragonal tin and the electric quadrupole coupling constants have been measured with the TDPAC technique. Using a calculated value for the quadrupole moment of Q[21°Po(8+)] = - 5 7 fm2 as standard for the electric field gradient calibration, the following other values are derived: Q[2°9po(~Z- )] = - 39(8) fm 2, Q[2 tOpo (11 - )] = -82(19) fm 2 and Q[2i°Po(13-)= -62(11) fm 2. These values are in agreement with the known structure of the isomers. The existence of more than one isomer in each isotope requires a data analysis procedure which takes into account feeding through all levels perturbed by the quadrupole interaction. A two-level formalism was developed and employed. /

E/

I

NUCLEAR REACTIONS 2o7 2OSpbi xn, E = 24 35 MeV measured

t, 2O9po

levels deduced quadrupole moment. Isomer recoil implantation in Sn.

I F

1. Introduction In r e c e n t y e a r s m u c h e x p e r i m e n t a l effort has b e e n d e d i c a t e d to m a g n e t i c m o m e n t m e a s u r e m e n t s of h i g h - s p i n states n e a r c l o s e d shells. M u c h less i n f o r m a t i o n is a v a i l able, as yet, c o n c e r n i n g the electric q u a d r u p o l e m o m e n t s : W h i l e t h e g - f a c t o r s a r e a s i g n a t u r e of the p r e d o m i n a n t f e w - p a r t i c l e s t r u c t u r e s often p r e s e n t at h i g h spins, t h e q u a d r u p o l e m o m e n t s are sensitive to a d d i t i o n a l c o n t r i b u t i o n s a r i s i n g f r o m c o r e d e f o r m a t i o n effects. A s y s t e m a t i c s t u d y of q u a d r u p o l e m o m e n t s o f 12 + i s o m e r s in

* Supported in part by the NSF. * Present address: University of Konstanz, 7750 Konstanz, Germany. 245

246

E. Da/ni et al. ,' Electric quadrupole moments 13-

4372

1~324

93ns

/ J 1475

II

1523 ,

2849 20ns 1292

~b 17/'2

1473 i/~418 88ns

13/2-~ 9/gL2"

~__ 1327

24ns

8+

1557 r~1473 96ns

£/-- , 2*

42ns

--'~11427 I.Sns ,245 1181

?82 5/2-

1181

545

545

I/2209po

o* 21Opo

Fig. 1. Partial level schemes of the 2°9p0 and 21°P0 isotopes.

Pb isotopes 1) has indeed demonstrated that the valence neutrons' effective charge increases as more particle pairs are removed from the closed 2°Spb core. The present work is part of a program to measure the electric quadrupole moments of isomeric states in the 2°Spb region. Results for the 8 +, 11- and 13 isomers in 21°po and the ~ - isomer 2°9po [refs. z 6)] are presented. Partial level schemes of 2°9po and 21°po are shown in fig. 1. Quadrupole coupling constants were measured for the isomers by the timedifferential perturbed angular distribution (TDPAD) technique in the presence ot quadrupole interactions from the internal electric field gradient (EFG) in tetragonal Sn. The :1°P0(8 +) state, whose quadrupole moment was calculated using the known wave function v), has served us as a reference level to determine the absolute values of the other isomeric moments. These quadrupole moments have also been calculated within the shell model from effective single-particle moments and a comparison to the experimental results is made. Data analysis has presented a challenge since there is more than one isomer in each isotope. Low-energy 7-rays depopulating isomers of interest are highly converted, so it is necessary to observe 7-rays of sufficient energy which are, in most cases, low in the cascade (fig. 1). The measured angular distributions reflect the complex quadrupole perturbations from all isomers depopulated by the observed 7-rays. A formalism of quadrupole perturbation of successive isomers was employed for data fitting.

E. Dafni et al. / Electric quadrupole moments

247

2. Experimental procedure and data analysis The Po isomers were populated via (~, xn) reactions using isotopically enriched lead targets. Pulsed alpha beams of 24 and 35 MeV were generated by the Stony Brook FN and the Brookhaven MP tandems. The small momentum brought in by the a-projectiles did not allow the recoil out of a thick lead layer. Multilayer targets, consisting of 112(72) layers, each with 40 #g/cm 2 2°spb(z°VPb) and 75 /~g/cm 2 natural Sn were employed. The targets were prepared by successive evaporation of Pb and Sn, the thickness of each layer being determined by a crystal monitor. The target ambient temperature was maintained during the runs by keeping the beam current low (typically 1 particle nA) and by attaching the targets to a thick Ta backing. Time spectra were collected for 7-rays of interest and for background radiation using two Ge(Li) spectrometers at 0 ° and at 90 ° with respect to the beam direction. More details about the experimental arrangement may be found in ref. 7). To reduce the systematic error due to the specific time response of each detector, the detectors were interchanged in the middle of each run. Typical time spectra are shown in fig. 2. For each measurement, a ratio function was formed where

Y(1, 0 °; t) + Y(2, 0 °; t ) - Y(1,90 °; t ) - Y(2, 90 °; t)

R(t) = y(1,OO; t ) + Y(2,0°; t ) + Y(1,90°; t ) + Y(2,90°; t)'

(1)

Y(i,O;t) being the normalized yield of detector i at angle 0 after background subtraction. The measurements are listed in table 1, and some of the ratio functions are shown in fig. 3. I

I

'

I

I

25 2tOp0 S n , 1181 keY

0

E(2 = 3 5 Mev

20

OO

o

9¢m

~5 I0 E

5

07

O.5 -

03 t [ffsec]

0 I

L

Fig. 2. Time spectra of the 1181 keV v-ray in 21°po at an ~-beam energy of 35 MeV. Background time spectra were subtracted and the spectra at 0° and at 90 ° were normalized to yield the same amplitude at long times. The shape of the curves at short times reflect the complex feeding pattern including four isomeric lifetimes. The difference between the 0 ° and 90 ° data is due to the quadrupole interaction in the tin host.

E. Da/hi et al. ,' Electric quadrupole moment,v

248

T,'kBLE 1 Measurements and analysis of PoSn data

Isotope

),-ray energy

eZqQ

11,

I~

1

a2

(keV) z°'~Po "1 2°9Po 21°pob) 21°Po 21Opo c) ") b) ~) d)

17 2 1[ 8+ 13 13

545 + 781 545+781 1181 1292 1475+ 1523

13z 13 6+ 11

0.94 0.75 0.58 0.45

0.12 0.14 0.16 0.37 0.23

! U[,

tl

(MHz)

(MHz)

~;6~41 33(4) 50(8) 60(9) 50(5)

d)

I

a) ,l) 72(11

Using 2°TPb/Sn target. All other measurements were with 2°*Pb/Sn target. With 24 MeV 2-beam. All other measurements were with 35 MeV ~-beam. Fit to eq. (2). All other data were fitted to eq. (7b). Fixed as 0.2Q(ll). See text.

015

]

[

I

I

(3

209p0 Sn, 545÷782 keY

T

.~ o05 rr

-005 I

@

I

L

I

I

I

'

I

b

015 t

2r°po

~

I

,

I

I I

Sn,llSI keV

005~-

-00~ I I

I I

0251-

c

~

e~°po Sn,

I 1

~

I I

~ ~

I I

,

1292 key

015 v rr"

005

-005 O5

04

03

02

0 I

Fig. 3. Ratio functions of the PoS.n system. The solid lines are from least-squares fits as discussed m the text. See table 1.

E. Dafni et al. / Electric quadrupole moments

249

The 1475 and 1523 keV y-rays in 21°po depopulate only one isomer, namely the 13- (fig. 1). These two lines display the same time dependence on the angular distribution and their time spectra were added. The ratio function for these lines was fitted to the expression: 3azG22(t) R(t) = 4+aaG22(t)

,

(2)

with tlmax

G22(t ) = ~" s2, cos (no)ot).

(3)

n=O

Here, a k = AtkPk are the angular distribution coefficients, A k and PR being the statistical tensors of the radiation field and the nuclear ensemble respectively. Terms with the a4 coefficients are neglected since they are known to be smaller than 0.02 for the transitions of interest, based on the measured a 2 coefficients and the formalism of ref. s). The Sk, coefficients are tabulated for high spins in ref. 9). The basic quadrupole frequency coo is given by ~oo = 3 e E q Q / 4 I ( 2 I - 1 ) h for integer spins, (co o = 6 e 2 q Q / 4 I ( 2 I - 1)h for half-integer spins), where eq is the E F G in the host and Q is the nuclear quadrupole moment. Underlying this analysis procedure is the assumption that the Po isomers are subject to quadrupole interaction from a unique E F G in the tetragonal Sn host. Some of the Po nuclei might not have been recoiled out of the lead layers into tin. The effects of EFG's from radiation damage on Po nuclei in the Pb host were seen in experiments with an external magnetic field 7). However, under the present experimental conditions, no modulation of the time spectra at the time region of interest were observed for the PoPb system lo). Therefore, those Po nuclei which stopped in Pb resulted only in a reduction of the observed a 2 values. A distribution of the EFG's strength in the Sn host is possible due to radiation damage or to lattice sites different from the substitutional site. Our experiments are not sensitive to such a distribution since we observed only the initial fall-off of the alignment and since we measured the relative interaction strength for different isomers under the same conditions. In all measurements, other than with the 1475+1523 keV lines, the observed radiation depopulated two isomers or more. These y-rays displayed a complex angular distribution and a derivation of an expression for data fitting was required. We consider the case of m isomeric levels in a cascade (fig. 4a). A level 11 is populated at t = 0 and then decays by a cascade of y-rays where Yl depopulates the level Ii with the lifetime ~. Ym is observed at a time t. Only isomeric levels with a lifetime long enough to allow an extranuclear perturbation to the angular distribution are considered. Short-lived intermediate levels may effect the angular

250

E. D a l h i et al. ,' Electric quadrupoh, m o m e n t s

/

IOO%

I I ,T,

i2 ,v2

Irn ,Tin ~mobserved

I

/(I-f)

12 ,T2 observed

Fig. 4. Successiveisomers in a cascade. (a) The general case of m isomers. (b) Two isomers with side feeding. correlation coefficients % but not the time dependence of the angular distribution. An axial symmetric quadrupole interaction is applied to the levels I~..... Ira, with the basic frequencies ~o~..... ~o~'. At the time of the population, the ensemble is described by the statistical tensors P kqoo ( I i , t = 0) which are known from the population mechanism 8, 11). These statistical tensors develop in time due to the transitions in the cascade and to the quadrupole interaction into p~?,(I m, t). We define the generalized perturbation factors c:.~mqott~ V k m k o \ ~ ! by pq~(l,,,t)

=

V' Gqmqotl oo kmko~ 1. . . . , ,", , , t )Pko(ll, t = 0).

(4)

koqo

They are calculated as follows: (i) The effect of the transitions from one isomer to the next is : p'~(Ii, t) = Uk(Ti)P~,(li

1, t).

(5)

The U k coefficeints are defined and tabulated in ref. 8). The time development within the lifetimes of each isomer is: p~(I,t)

= ~ Gkk,(I, q¢ q' t - - t ' )pk,(l, t').

(6)

k'q'

The G~I being the usual one-level perturbation factors for quadrupole interaction in a single crystal 12).

E. Dafni et al. / Electric quadrupole moments

251

(ii) Weighted time integrals over the lifetimes of unobserved transitions are performed. (iii) Since our targets were polycrystalline foils, an averaging over the orientation of the E F G symmetry axis in the many microcrystals must be carried out. To simplify the computations we have adopted an approximation in which we use the polycrystalline perturbation factors in eq. (6), rather than the single crystal ones. The physical meaning of this approximation is that averaging over the EFG orientation is done for each transition and not only once for the whole cascade. The approximation is probably inappropriate for a cascade with many isomers. In our case, however, we limit actual fitting to cases with at most two isomers. Furthermore, in the one-level case, the initial fall-off of the anisotropy is rather independent of the single crystal orientation or to the target being a polycrystal. Our experiments are sensitive mostly to this time regime. Using the above guidelines we get: m-1

Gkk(I1,.. Ira, t) =

i=1 e -r~t i=1~

(Fj-- F i

,}

x

......

n= = -n=

li=l jq:i

~2~

....

...n, .....

Sk'~'l; j~=l fi (~_t_ Fj , j

(7a)

1=1 lq:j

where Fj = Fj-injcO~o (Fj = 1/zfl. It is convenient to write the perturbation factors using the complex frequencies, Fj. They are, however, real. We have limited the analysis to cases with two isomers in the cascade (m = 2). In these cases eq. (7a) reads as :

Gkk(I1, 12, t) =

Uk(,~l)(F2 - F1) e-Flt_e-F2t

F ,1 =0 .... 1_. 1 ~.

Skn~Skn2

2

~i~ = 0... n2~.

×

~

e-r, '

'(F j- Fi) cos (nioit)+ (nioio + pn~cO~o)sin (nioiot)-l (~TZj_F ~ T 7 ~

~

j.

(7b)

i=1,2 p=-l,1

In an actual two-isomer case we usually have a direct feeding into the lower isomer along with its population through the higher isomer (fig. 4b). A detector's

E. Da/ni et al. ,' Electric quadrupole moments

252

yields of 72 at angle 0 is then: 1--(

y(72,0;t ) = ;

W(l~,12,0;t)(e--t:~,-e

,'_W(lz, O;t)e r,,,~+

"[2

'/~:),

(8)

~1 - - ~ 2

where f is the fraction of nuclei for which the upper isomer is populated. The angular perturbed distribution functions, W(O,t), are calculated with the one- or two-level perturbation factors. For data fitting and calculations we assumed the same a 2 coefficients for the two feeding paths (i.e. a 2 = At2(~'z)p2(Iz, t = 0 ) =

A*2(72)Uz(71)p2(lx, t 0)). Calculated R(t) functions for two isomers in a cascade in the 21°po nucleus are =

shown in fig. 5, using the known lifetimes of the 8 + and 6 + states~). A value of Q(6 + )/Q(8 + ) = 0.2 was used, assuming the predominant structure of 0zh~) and the same effective charges for the two levels. These assumptions are supported by the well-known ,q-factors and B(E2) values. From fig. 5 it is obvious that the 6 + state has an important role and it cannot be neglected in the 8 + analysis. A least-square fit of the experimental ratio functions of the 545+781 keV (in 2°~po), the 1811 keV and the 1292 keV (in 21°po} lines was done to a theoretical ratio function using eq. (8). The feeding factor, .£ must be known in the analysis. We have determined it for each case from total 7-ray intensities and from shapes and amplitudes of the time spectra. The f values are listed in table 1 along with the fitting results. 11 and 12 for each data point are as defined in fig. 4b. The population of the higher spin isomers (11 , 13-) in 21°po was negligible with the 24 MeV s-beam and so was the population of the 2°gPo(3L- ) isomeric state even with the 35 MeV beam. At a beam energy of 35 MeV, the 1181 keV line in 2 1 ° p o had significant

'

'

'

,

04

'

'

'

,

'

d--

.\

.\%

o2 0 C

""

t

.. ............................. /

"'"

a

\-~-

I

~

r

'

.."

\\

-

-0.2 -

'

I 0.1

J

-

~--"'--~

I

I

r

]

t

I-

0.2

t 1277"0980

Fig. 5. C a l c u l a t e d R(t) functions for the 21°pb 1181 keV (2 + - , 0 +) ,/-ray, values of a 2 1, a4 = 0 were used• (a) A s s u m i n g the 6 + state has a v a n i s h i n g lifetime (pure 8 + pattern)• (b) U s i n g lifetimes of 138 a n d 61 ns for the 8 + a n d 6 + isomers, with Q(6+)/(Q8 +) = 0.2 a n d 100% feeding t h r o u g h the 8 + state. (c) Same as (b) with 40o/o direct p o p u l a t i o n of the 6 + isomer. This is the e x p e r i m e n t a l s i t u a t i o n with 24 MeV ~-beam. (d) The pure 6 + pattern. =

E. Dafni et al. / Electric quadrupole moments

253

210po(8*) fitting results for different fixed parameters I

I

8O!7o ~6£

1

I

I

f

~

~ 5c

~0~"t:4(

x-R~O15

3C

o-'e ~0 ZO

201

,-R:ozs

,oi 04

*-R:030 .:

I 05

o[~%o,~-,],o[~,,-,] I 06

I 07

I 08

f

Fig. 6. Quadrupole coupling constants for the 21°po(8 +) isomer in Sn from fitting with fixed values of feeding fractions and quadrupole moments ratios. See text for further details.

contributions from four isomers and this data was not fitted. Since our data are not sensitive enough to allow the simultaneous derivation of many parameters, we have fixed the ratio between the quadrupole moments of the two isomers whenever a reliable estimate could be made. The moment of the 6 + isomer in 2~°Po was fixed as 0.2 of the 8 ÷ moment. The same quadrupole moment ratio was used for the 2°9po 9 - and ~z- isomers. The sensitivity of the fitting results to the feeding fractions and to the quadrupole moment ratios was studied by fitting the data with these parameters fixed at different values (fig. 6). The quoted errors in table 1 reflect the statistical errors along with the uncertainties in these parameters.

3. Discussion

In the present experiments the magnitude of the quadrupole coupling constants, the Po isomers in tin have been measured. The determination of the nuclear quadrupole moments requires the knowledge of the E F G for dilute Po impurities in Sn. Such information, usually being obtained via a reference level with a known quadrupole moment, is not available for the PoS_n system. We rely on the fact that the 21°Po(8+) isomer is known to have a very pure (nh~) configuration 6) and the quadrupole moment can be computed from the (8 + ~ 6 +) B(E2) value as Q[2'°Po(8+)] = - 5 7 fm 2 [ref. 7)]. In a shell-model picture the (nh~) configuration results in a quadrupole moment only ~ larger than the (rth~) single particle moment. This is in agreement with the value measured by hyperfine splitting Q[2°9Bi(9+)] = - 3 7 fm 2 [ref. 13)], after

e2qQ/h, for

254

E. DaJhi et al. / Electric quadrupole moments TABLE 2 Q u a d r u p o l e m o m e n t s of Po isomers

Isotope

1"

21°Po

8+ 11 13-

2O9po

L~-

M a i n configuration (nh92/z) (~h9/2i13/2) (zrh92/2)8(vg9/2P~-/21)5 (nh2/z)a(vp~,~)+,.. ~)

IQexpl (fro2)

Qcal (fro2)

82(19) 62(1 1) 39(8)

- 57 105 - 84 - 49

") See detailed wave function in the text.

applying a ~ 15 O//ocorrection to account for the Sternheimer shielding 6). Using the calculated Za°Po(8+) moment and the measured quadrupole coupling constants in tin, other quadrupole moments are deduced and listed in table 2 a s Qexp" The signs of the moments cannot be determined from our experiment but they all are expected to be negative. In addition to the 21°Po(8+) level, the other Po isomers under study are also known to have well-defined predominant configurations, although not as pure as the 8 + one. The experimental Qexp are compared to shell-model calculated quadrupole moments, Qca|, in table 2. These were derived, assuming a single particle moment of 42.7 fm 2 for the (nh 0 orbital, along the following lines: (i) Z l ° P o ( l l - ) : A (nh~i¥) structure is assumed. The square amplitude of the (8 + ® 3-)a 1 component in the wave function, where 8 + refers to the z~°Po(8+) state and 3 is the first excited state of 2°Spb, is known to be about 0.05 [ref. 14)]. This small component which affects the (11- ---, 8 +) E3 transition rate strongly, does not change the 11- quadrupole moment significantly. The radial integral for the i~ proton was calculated as ( r e) = 41.7 fm 2 with the radial wave function of Blomqvist et al. aS). The E2 polarization charge, epo~, (epol = e~ff for neutrons, = eeef - 1 for protons), is not measured experimentally for that orbital. For neutron states in the 2°Spb region the quantity %ol(r2)/(k(r)), with k(r) = - r d f ( r ) / d r , f ( r ) being the radial dependence of the shell-model potential, is found to be independent of the orbital. Assuming that the above holds true also for proton states, the effective charge of the i¥ proton is derived from the nh~ effective charge as eoff = 1.87. This value is obtained assuming for the nh,~ orbital a radial integral of ( r 2) = 34.8 fm 2 from the wave function of ref. 15) and an effective charge of eeff/e = 1.66 in agreement with the 21°Po[B(E2 ; 8 + --. 6 + )] value. The (k(r)) matrix elements were taken from Astner et al. 16). (ii) 21°Po(13-): This state consists of the coupling of the (nh~)8 + level to the 5- second excited state in 2°Spb. The 5- level, whose main configuration is (vg~p~-1), has in addition components with proton particle-hole excitations such as (nh~s~- 1)5 and (nh~d~-a)5_ [ref. 1~)]. These components, however, cannot participate in the construction of a 13- state via coupling to the (nh~) structure. The 13- quadrupole moment was calculated for the (8+@ vg~p~S1)a3- configuration using the radial

E. Dafni et aL / Electric quadrupole moments

255

integral ( r 2} = 44.1 fm 2 and E2 effective charge ecfr/e = 0.84 for the g~ neutron ~6). The p½ neutron hole does not affect the quadrupole moment at first order. (iii) 2 ° 9 p 0 ( ~ - ) : The wave function is calculated by Balbridge et al. ~8) as I~z - ) = 0.95618 + ® p~-~)-0.23918 + ® f ~ ) - 0 . 1 1 0 1 8 + ® p ~ + .... A similar wave function is proposed by ref. 6). E2 matrix elements for the f~ and p~ neutron holes were taken from Donahue et al. ~9). Most of the reduction of Qcal as compared to the 8 + moment is due to the non-diagonal (p~-~lQl/~ ~) term. The high spins of the studied levels resulted in long quadrupole periods, To = 2rc/~o0, and only limited parts of the periods were observed. This, in addition to the complexity of the perturbations due to successive isomers, did not allow a precision quadrupole moment measurement of the high-spin isomers. There was evidence found, however, for an increased quadrupole moment of the 11- isomer in 2~°Po as compared with the 8 + quadrupole moment. The 13- quadrupole moment was found to be close to the value measured for the 8 ÷ state, and the quadrupole moment of the 2 ° 9 p o ( ~ - ) state was found to be reduced. These features are reproduced by the calculated shell-model quadrupole moments. The deviation between the experimental and calculated values is not very significant in view of the large experimental errors. They could result partially from differences between the true isomeric wave functions and the simplified forms used in the calculation. It is possible, however, that the quadrupole coupling constant for the 21°Po(8+) isomer in tin was slightly overestimated in our analysis, since a lower value would improve the overall agreement between the experiments and the calculation. We would like to thank W. Riel for skillful target fabrication and Dr. Y. Niv for helpful discussion concerning the data analysis.

References 1) H.-E. Mahnke, T. K. Alexander, H. R. Andrews, O. H~usser, P. Taras, D. Ward, E. Dafni and G. D. Sprouse, Phys. Lett. 8811 (1979) 48 2) T. Yamazaki, Phys. Rev. CI (1970) 290 3) T. Yamazaki and T. Nomara, Phys. Rev. Lett. 24 (1970) 317 4) J. Blomqvist, B. Fant, K. Wikstrom and I. Bergstrom, Phys. Scripta 3 (1971) 9 5) Y. Yamazaki, S. Nagamiya, T. Nomura, K. Nakai and T. Yamazaki, Phys. Lett. ,1411 (1973) 440 6) O. H~usser, T. K. Alexander, J. R. Beene, E. D. Earle, A. B. McDonald, F. C. Khanna and I. S. Toumer, Nucl. Phys. A273 (1976) 253 7) E. Dafni, Ph.D. thesis (1978), unpublished ; E. Dafni, M. H. Rafailovich, W. A. Little and G. D. Sprouse, Phys. Rev. C23 (1981) 90 8) T. Yamazaki, Nucl. Data A3 (1967) 1 9) E. Dafni, R. Bienstock, M. H. Rafailovich and G. D. Sprouse, At. Nucl. Data Tables 23 (1979) 315 10) E. Dafni et al., unpublished 11) R. M. Steffen, Angular correlations in nuclear disintegration, ed. H. van Krugten and B. van Hooyen (Rotterdam Univ. Press, 1971) 1

256

E. DaJhi et al. / Electric quadrupoh, moments

12) R. M. Steffen and H. Fraunfelder, in Proc. Uppsala Meeting on extranuclear perturbations in angular correlations, Uppsala (1963) 13) Tables of Isotopes, ed. C. M. Lederer and V. S. Shirley, appendix VII (Wiley, New York, 1978) 14) T. Yamazaki, Phys. Rev. C1 (1970) 290 15) J. Blomqvist and S. W. Wahlborn, Ark. Fys. 16 (1960) 545 16) G. Astner, I. Bergstrom, J. Blomqvist, B. Fant and K. Wikstrom, Nucl. Phys. A182 (1972) 219 17) V. Gillet, A. M. Green and E. A. Sanderson, Nucl. Phys. 88 (1966) 321 18) W. Baldridge, N. Freed and J. Gibbons, Phys. Lett. 36B (1971) 179 19) D. J. Donahue, O. H/iusser, R. L. Hershberger, R. Lutter and F. Reiss, Phys. Rev. C12 (1975) 1547