Reorientation effect measurements in 124Te, 126Te and 128Te

I.E.3:2.H{

Nuclear Ph.vsics A248 (1975) 342--355; (~) North-ltolland Publishin9 Co., Amsterdam Not to be reproduced by photoprint or microfilm without v, ritten permission from the publisher

REORIENTATION EFFECT M E A S U R E M E N T S IN 124Te, lZ6Te AND 12aTe A. M. K L E I N F E L D 1. Physikalisches Institut der Unicersitiit :u Kdln and

G. M.g, G G I t a n d D. W E R D E C K E R ,t

htstitttt /iir Kernphysik der Unicersitiit zu Kb'ln, 5 Ko'ln 41 (Coloyne), 14/. German)' Received 3 March 1975 Abstract: C o u l o m b excitation probabilities o f the first 2 + states o f x2'~Te, tZ6Te and L28Te have been determined. The measurement was performed by resolving the inelastically and elastically backward scattered 4He and ~60 projectiles using an a n n u l a r surface barrier detector. Quadrupole m o m e n t s (Q2 *) as well as the B(E2, 0 + -+ 2 +) values were extracted by analyzing the excitation probabilities with the Winther-de Boer multiple C o u l o m b excitation program. The Q 2 - deduced for the positive sign o f the 2 +" interference term are --0.41 ___0.08 e • b, --0.14.-'0.11 e ' b a n d - 0 . 1 2 : t : 0 . 0 9 e ' b for t'+Te, ~26Te a n d ~28Te, respectively.

E

N U C L E A R R E A C T I O N S 12+. t26.12aTe(ct, ~,), E = 8.5-17 MeV; 12"t'126'~'ZaTe(t60, 160'), E = 39~,4 MeV; m e a s u r e d o(E, El60, ). Iz+'J26. t2aTe deduced Q2*, B(E2, 0 + --~ 2+). Enriched targets.

1. Introduction Considerable attention has recently been brought to bear on the problem of vibrational-like nuclei in the Z ~ 50 region t). One of the most puzzling aspects of such nuclei are the observed large values of the static quadrupole moments of the first 2 + states (Q2 *) [ref. 2)]. These results have been particularly difficult to understand in light of the nearly vibrational character of the level schemes and associated electromagnetic matrix elements. Most of the difficulty encountered in the theoretical description of such nuclei results from the simultaneous occurrence of large IQ2, I and small B(E2, 0 ÷ --. 2 +') values. Recently, however, the particle-vibrational coupling models have been successfully applied to explain the character of certain of these nuclei 3-6). While promising, the true tcst of this as well as any modcl awaits a detailed comparison with a wide range of nuclear properties. For this purpose, a set of accurately measured static quadrupole moments as a function of neutron number is particularly suitable. At the time the present work was begun one measurement each of the Q 2 ÷ of the isotopes ~2ZTe [ref. 7)], 126Te and 12STe [ref. s ) ] , and tZ°Te [ref. 9)] had been * Present address: SEL Stuttgart. t* Present address: lnstitut ftir Experimentalphysik II!, R u h r Universit/it, Bochum. ? The values quoted in the present w o r k have been corrected for the deorientation effect 28). 342

t,_+. l z~, i z8Te(ct, ~t')

343

reported. Both the previous work as well as the present investigation used the reorientation effect to) to determine Q2*. However, the ~22, 126, 12aTe measurements were performed using the particle-~ coincidence techniques and were not corrected for deorientation effects 1~). The effect of these corrections, as is now recognized ~2), is to reduce the Q2* determined in such measurements. In order to avoid these and other complications associated for example with the rather involved coincidence electronics used in such measurements, we chose to perform the present study by directly measuring the Coulomb excitation probabilities using surface barrier detectors. Recently, two new measurements of the Te isotopes have been reported 13, 14) and generally good agreement among the existing measurements is found. Preliminary results of this investigation were reported earlier t s). Included in the present paper are additional 4He experimental data, obtained since the earlier report, together with some of the details of the experiment and analysis. Our results are compared with other measurements and with existing relevant model calculations in the last section.

2. Experimental details The experimental techniques and data reduction procedures are similar to those used in ref. ~6), where a detailed description of the method may be found. Only the special aspects of the present investigation will be discussed here. Beams of about 100 nA of 8.5-17 MeV 4He 2+ and about 50 nA of 39-44 MeV 16OS+ or 6+ were extracted from the K61n FN Tandem. These projectiles were used to b o m b a r d thin ( ~ 10 :tg/cm 2 for ~60 and ~ 30/~g/cm 2 for 4He) targets enriched in a given isotope and evaporated on to ~ 10 pg/cm 2 carbon backings. The assay of the target material obtained from the supplier (Oak Ridge Isotopes Div.) are given in table 1. Projectiles scattered from these targets were detected in an annular surface barrier detector positioned at a mean angle of ~ 175 °. The system resolution was sufficient to separate the inelasdcally from the elastically scattered projectiles. TABLE 1

Assay (in ,o~)of the samples used in target preparation ~-..

Target

124

126

128

0.50 0.60 93.90 1.70 1.40 1.10 0.80

0.05 0.20 98.69 0.81 0.24

0.06 99.46 0.48

Impurity ~""-- ..... 122 123 124 125 126 128 130

All material was obtained from Oak Ridge Separated Isotopes Divisions.

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Typical spectra together with the fits used in the analysis of the 160 data are shown in figs. I-3. Significant here are the excellent ratios of inelastic peak height to background (in all cases better than 20 : I) of the 160 spectra, and the resolution which ranged from .,~ 30 keV ( F W H M ) for 4He to ~- 150 keV ( F W H M ) for I~'O. In ordcr to determine the Q2, to within __+0.I e . b it is necessary to measure the excitation probability with an accuracy of about 1 ~ since the total effect of the Q2 ~ is only about 15 %/ per e" b. The experimentally determined excitation probabilities RCxp arc defined as the ratio of intensities of the 2 + peak to the sum of the elastic (0 +) and 2 + peaks,

R,,, = 4~/(/o÷ + 4 - ) . With data o f the type shown in figs. 1-3, the extraction of the inelastic peak intensities in the presence of the low energy elastic tail using the methods of ref. v6), presents no difficulty. Table 2 lists the Rexp used in the analysis, together with their associated errors, bombarding energies and scattering angles. More problematic are the effects ofcontaminates. In the left hand side of fig. 3 the solid line was obtained by summing both the inelastic and elastic contributions of the Te contaminates using the shape of the elastic peak of the primary isotope and the suppliers assay. The excellent agreement observed in all cases lends confidence to the assumption that the impurity peaks, which are not resolved (e.g. tZSTe in the spectrum of 124Te), are correctly accounted for. The possibility of contamination due to elastic peaks arising from impurities with masses lighter than about A ~ 120, was eliminated by consideration of the combination of 4He and ~60 spectra. Contributions from reactions with the carbon backings were investigated by accumulating

124. t26. ,ZSTe(~" ~.)

347

TABLE 2

The experimental excitation probabilities R.p and errors (in ~) Isotope 124

126

128

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E.ft (MeV)

10 3 R . p ( 2 ÷)

4He *He '*He "*He 4He ~60 16O 160 160

8.509 9.010 9.510 10.010 10.509 42.234 43.138 43.199 44.060

2.48 -- (3.0) 3.24-?(1.3) 4.34--(I.6) 5.65=_(1.0) 7.104-(1.1) 73.20-t- (2.2) 78.40 -.'-(2.4) 82.00 4- (3.0) 87.40 4- (1.4)

4He "He "He '*He 160 a60 160 a60 160 160

8.509 9.509 10.010 10.507 39.051 40.051 42.051 43.050 44.050 44.186

1.75 4- (8.0) 3.05 - (2.8) 4.18-(1.7t 5.25±(1.7) 36.60-'-(2.7) 44.80 4- (2.8) 58.00-- (3.9) 62.604-(2.7) 67.70-"-(3.2) 6 9 . 9 0 ~. (I.8)

19.-'-(12)

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8.508 9.009 9.046 9.509 10.011 10.510 40.045 42.050 43.037 44.046

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18~(15}

All data were obtained at a m e a n scattering angle o f a b o u t 175% E¢. denotes the effective b o m b a r d i n g energy. Also given are the s u m o f the 2 ~" and 4 + excitation probabilities.

spectra of 4He and 16 0 bombarding the backing alone. No evidence was obtained to indicate contamination from this source. One further source of experimental error which has to be carefully studied is associated with. the maximum "safe" bombarding energy. Excitation functions for inelastic and elastic 4He [ref. 17)] and inelastic 160 [ref. 18)] scattering on the Te isotopes have been measured. Typical results for the excitation probabilities of 4He on 1 2 4 T e are shown in fig. 4. It was found that the excitation probabilities deviate by 1 ~ from pure Coulomb excitation at bombarding energies greater than 10.5 MeV for 4He and 46-47 MeV for t 60. The Q z • and B(E2, 0 + --* 2 +) values were therefore evaluated only from data corresponding to bombarding energies less than or equal to these "safe" energies.

348

A . M . K L E I N F E L D et al.

3. Analysis The data were analysed by comparing the experimental excitation probabilities with those calculated using the de Boer-Winther computer code for multiple Coulomb excitation z o). These calculations were p¢rformed using the energy levels and electric quadrupole matrix elements

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shown in fig. 5. In order to determine the values of these matrix elements, the 2 +' ~ 0/ 2 +' --* 2 + branching and 2+'--* 2 + mixing ratios of Grabowski er al. ' ~ ) f o r tZ4Te and ~Z°Te as well as our own measurements of the sum of the 2 +' and 4 + excitation probabilities, given in table 2, were used. These data together with the value of Mt 3 obtained by Barrette el al. t4) for 124Te and by Stokstad and Hall 8) and reE ~4) for tZeTe enabled us to determine Mr4 and M24. In the case of lZ*Te we find somewhat smaller values of Mr4 and 3f24 than ref. t,), who obtain 0.11 e . b and 1.26 e . b for Mr4 and M24 respectively. For t2eTe we find better agreement with the values of

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+p~ompQ2+).

From a least squares fit to the ratios R expt/R ~" re=°) comp the B(E2, 0 + --+ 2 +) and a2+ values were determined. The final results and corresponding fits are given in table 3 and fig. 6, respectively. Several small corrections were taken into account. Effects of .screening due to the atomic electrons 21) as well as the polarization of the vacuum 22) were estimated by directly including these terms in the interaction potential. This results in a change in the excitation probability due to vacuum polarization which is about ½ that obtained from correcting the bombarding energy at the distance of closest approach. It was found that the vacuum polarization decreased the excitation probability for both 4He and 160 by about 0.6 °/:owhile the effect of screening was to increase the excitation probabilities by about 0.2 %. Therefore, the net effect of these two processes is to decrease the excitation probability by about 0.4 %, and thereby to increase the B(E2, 0 ÷ --+ 2 +) by 0.4 %. Corrections arising from the semiclassical approximation [ref. 23)] have also been taken into account. In our case these corrections are about the same for 4He and 1 6 0 and therefore have a negligible effect on the Q2÷. The

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interference term. The ratios have been n o r m a l i z e d (B(E2, 0 ÷ --~ 2 ÷) a dj us t e d) to o b t a i n an intercept at 1.0.

12,~.126,12STe(~t, ~,)

351

TABLE 3

The 0 2 + , B(E2, 0 + ---} 2 +) values and the associated normalized Z2 values obtained in the present w o r k , together with the Q2+ and B(E2, 0 + ~ 2 +) values from other measurements Isotope

Q2* ( e . b)

124

126

B(E2, 0 + ~ 2 +) (e 2. b 2)

zZ/d.f.

Sign of interference term

--0.41 ± 0 . 0 8

0.568±0.005

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B(E2, 0 + --} 2+), however, is increased by about 0.3 ~ for t24Te and about 0.1 ~o for X26Te and t28Te due to these quantum mechanical effects. N o corrections have been made for the influences of excitation modes of multipolarity other than ). = 2. We have, for example, made no corrections for the influence of the giant dipole resonance or the hexadecapole moments, whose appropriate matrix elements are unknown and presumed small. 4. Discussion of the results As is apparent from a perusal of table 3, the fit quality as measured by the X2 value is equally good for either sign of the interference term. We are therefore not in a position from this measurement alone to infer the sign of the product MI 2MI4M24. However, in much of the discussion that follows we will assume the positive signs. This is based in part on model predictions 24), and more significantly on the results of recent experimental studies of nuclei in this region, namely t t 4Cd [refs. 16. 25)] and aos. ltopd [ref. 26)].

352

A.M. KLEINFELD et al.

The nucleus ~24Te. Two other measurements of the Q2 ÷ exist ~3,,4). All three

measurements are in good agreement. It should be noted that considerably larger values of M~4 and M24 were used in the analysis of refs. 13,14). In the measurement of Larsen et al. ~3), however, the i-values used in their measurement were appreciably larger (0.6-0.7) than used in the present investigation (0.33-0.43), and therefore their results are less sensitive to the choice of the relevant matrix elements. In the case of ref. ~4), however, the kinematic conditions were almost identical to ours. This accounts for the larger spread in Q2 corresponding to either sign of the interference term. As a result of a transcription mistake the B ( E 2 , 0 ÷ ~ 2 +) of ~24Te quoted in ref. 15) is in error. The correct value which also reflects the additional 4He data obtained since the appearence of ref. ~5), is given in table 3 and is seen to be in good agreement with the value of Barrette et al. 14). The nucleus ~26Te. As we mentioned in the introduction, the original measurements of ~26, 12STe [ref. s)] were performed using a particle-), coincidence technique. In this type of measurement the recoiling nuclei if not stopped in the target, will generally decay in vacuum and consequently the magnetic sublevel population of the state will be altered by the interaction with the hyperfine field of the atomic electrons - the so called deorientation effect. The size of this correction has been estimated 2s) for the measurement of Stokstad and Hall a). This was done using the attenuation coefficients of Ben-Zvi et al. 27), for backscattered 35 MeV oxygen ions. It is found that the 160 excitation probabilities should be reduced by about 1 ~ and 0.8 ~ for 126Tc and 12aTe, respectively. Applying this correction, the Q2÷ obtained in ref. s) are reduced by 0.08+0.04 e. b and 0.06+0.03 e" b for 126Te and 12STe, respectively. The corrected Q2 ÷, as seen in table 3, are in better agreement with the results of the present measurement. The authors of ref. ,4) have erroneously concluded that the earlier reported results ~5) for the Q2÷ of 126Te ( - 0 . 2 0 + 0 . 0 9 as opposed to the present value of - 0 . 1 4 + 0 . 1 1 e . b ) , and their own did not agree. Because of the above mentioned difference in the choice of the matrix elements M~4 and M24 used in the analysis, the discrepancy is only apparent. In fact, for the positive sign of the interference term both values are in agreement. Our considerably smaller IQ2÷ I for the negative sign of the interference term reflects the larger values of M14 and M24 used in our analysis, and not a discrepancy in the measurements. Both the B(E2, 0 + ~ 2 +) obtained in the present work and that found by Barrette et al. agree within errors. The nucleus 128Tt,. As mentioned above, the results of the present work and those of Stokstad and Hall 8), after correcting for deorientation effects, are in agreement. The value obtained by Barrette et al. 14), while also in agreement with ref. 8), is somewhat larger in magnitude (0.2 e- b) than the present result. The B(E2, 0 + ~ 2 +) values obtained in the present work and those of ref. 14) are in good agreement. All reported 8.9, ,3-~s) values of the Q2÷ of the doubly even Te isotopes obtained using the positive sign for the interference term are shown in fig. 7. Attention should be drawn to several aspects of this figure. First of all there is uniformly good agree-

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130

Fig. 7. The measured Qz+ corresponding to the positive sign of the interference term. (a) Ref. t3). (b) Ref. t4). (c) Present work. (d) Ref. 8). (e) Ref. 9). I

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Fig. 8. The average values of the measured Q2÷ shown in fig. 7, together with the predictions of the particle-vibrational coupling theory of ref. 6). The rotational values of Q2+ were calculated using the B(E2, 0* -~ 2 *) values of table 3. ment a m o n g the various measurements. S e c o n d l y the values are all negative a n d smaller t h a n the r o t a t i o n a l value. In a d d i t i o n , there a p p e a r s to be a definite t r e n d with n e u t r o n n u m b e r , the value o f (Q2*) decreasing as the closed n e u t r o n shell at 134Te is a p p r o a c h e d . The m o d e l s which a p p e a r most successful in explaining the p r o p e r t i e s o f the low lying levels o f the v i b r a t i o n a l - l i k e nuclei are the p a r t i c l e - v i b r a t i o n a l c o u p l i n g theories.

354

A . M . KLEINFELD et al.

L o p a c 4) a n d A l a g a et al. 5) have d e m o n s t r a t e d , in isolated cases, t h a t the experim e n t a l l y o b s e r v e d sign a n d m a g n i t u d e o f the Q2 ÷ as well as the small 2' --* 0 crossover t r a n s i t i o n p r o b a b i l i t i e s arc consistent, within the f r a m e w o r k o f this model. These c a l c u l a t i o n s s h o w e d t h a t in the case o f the Te isotopes the sign a n d m a g n i t u d e o f the Q2 • was the result o f the c o m p e t i t i o n a m o n g the c o n t r i b u t i o n s o f the available shell m o d e l states o f the two valence p r o t o n s plus a c o n t r i b u t i o n due to the e n h a n c e m e n t . by the p a r t i c l e - v i b r a t i o n a l coupling, o f the p r o t o n effective charge. T h e value o f these shell c o n t r i b u t i o n s d e p e n d s quite sensitively on t h e p o s i t i o n o f the single-particle states. In p a r t i c u l a r , the p o s i t i o n o f the 2d~ state is f o u n d to be critical as regards the Te isotopes. It follows that the o b s e r v e d decrease in [Q2 ÷ I with increasing neutron n u m b e r is consistent with the o b s e r v e d increase o f the 2d~r energy in the Sb i s o t o p e s Recently, D e g r i e c k a n d V a n d e n Berghe 6) c a l c u l a t e d the structure o f the even t e l l u r i u m isotope using the p a r t i c l e - v i b r a t i o n a l c o u p l i n g model. In fig. 8 we have p l o t t e d the average e x p e r i m e n t a l value o f Q2 ÷ t o g e t h e r with the results o f the calculations o f r e f . 6) a n d for c o m p a r i s o n purposes, the r o t a t i o n a l values. The p r e d i c t e d t r e n d with n e u t r o n n u m b e r agrees r e m a r k a b l y well with the e x p e r i m e n t a l results. The significance o f this a g r e e m e n t must, however, be t e m p e r e d by, e.g. the existence. o f certain discrepancies between the p r e d i c t e d a n d o b s e r v e d e l e c t r o m a g n e t i c transition rates. In p a r t i c u l a r the p r e d i c t e d B ( E 2 , 2 +' ~ 2 +) values are for 124Te three times s m a l l e r a n d for 126Te two times smaller t h a n the m e a s u r e d values o b t a i n a b l e from fig. 5, while the c a l c u l a t e d B ( E 2 , 2 +' ~ 0 +) values overestimate the e x p e r i m e n t a l l y d e t e r m i n e d values (fig. 5) by a b o u t a factor o f three a n d a factor o f two for 124Te a n d ~2 6Te ' respectively.

References I) Proc. Topical Conf. on nuclear vibrations, Zagreb, 1974, ed. V. Paar (North-Holland, to be published) 2) A. Christy and O. H/iusser, Nucl. Data Tables 11 (1973) 281 3) G. Alaga, Rendiconti, Scuola lnternazionale, Varenna, XL Corso, 1967 4) V. Lopac, Nucl. Phys. A155 (1970) 513 5) G. Alaga, V. Paar and V. Lopac, Phys. Lett. 43B (1973) 459 6) E. Degrieck and G. Vanden Berghe, Nucl. Phys. A231 (1974) 141 7) P. H. Stelson, in Proc. Summer Study Group on the physics of the emperor tandem Van de Graaff region (BNL, Upton) 8) R. G. Stockstad and I. Hall, Nucl. Phys. A99 (1967) 507 9) A. Christy, I. Hall, R. P. Harper, I. M. Nagiband and B. Wakfield, Nucl. Phys. AI42 (1970) 591 10) J. de Boer and J. Eichler, in Advances in nuclear physics, ed. M. Baranger and E. Vogt, vol. I (Plenum Press, New York, 1968) p. I ; O. H/tusser, in Nuclear spectroscopy 11, ed. 1. Cerny (Academic Press, New York. 1974) 11) J. J. Simpson and U. Smilansky, Phys. Lett. 26B (1968) 581 12) A. M. Kleinfeld, J. D. Rogers, J. Gastebois, S. G. Steadman and J. de Boer. Nucl. Phys. Ai58 (1970) 81 13) R. D. Larsen, W. R. Lutz, T. V. Ragland and R. P. Scharenberg, Nucl. Phys. A221 (1974) 26 14) J. Barrette, M. Barrette. R. Haroutunian, G. Lamoureux and S. Monaro, Phys. Rev. 10 (1974) 1166 15) A. M. Kleinfeld, G. M/iggi and D. Werdecker, Proc. Int. Conf. on nuclear moments and nuclear structure, Osaka, 1972

124, tz6. l, aTe(or, ~t')

355

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