NEGATIVE-PARITY STATES OF N = 88 ISOTONES IN THE INTERACTING BOSON APPROXIMATION

Volume 163B, number 5,6 PHYSCIS LETTERS 28 November 1985

N E G A T I V E - P A R I T Y S T A T E S O F N ffi 88 I S O T O N E S I N T H E I N T E R A C T I N G B O S O N A P P R O X I M A T I O N

C.S. H A N , D.S. C H U U

Department of Electrophyszcs, Natwnal Chtao Tung Unwerstty, Hsmchu, Tatwan, Repubhc of China

S.T. H S I E H and H.C C H I A N G

Department of Phystcs, Natwnal Tsmg Hua Umverstty, Hsmchu, Tatwan, Repubhc of China

Received 6 December 1984, rewsed manuscript recewed 4 June 1985

The negative-panty states of N = 88 :sotones are stuched systemaUcally in terms of the interacting boson approxtmataon A mass-independent effectave interacting boson hanultoman reproduced energy levels very well Umfied E1 and E3 trans:taon operators are found The effect of p bosons on the energy spectra and electromagnetic transxtlons as chscussed

I n the lighter-mass end of the deformed A = 150-180 region the shapes of the nuclei change very rapidly. Since the N = 88 nuclex lie just outside the permanently deformed region which begins at N -- 90, they extublt transmonal character and thus attracts great interest in both experimental and theoretical investigations. Re- cently, i n - b e a m studies [1-6] of the N = 88 nude1 h a d identified some high-spin negative-panty odd-spin b a n d s Vanous models have been pro- p o s e d to explain these negaUve-pafity bands (NPB). The N P B seen in X52Gd [1,7] has been interpreted in terms of an octupole wbrat~on coupled either to a deformed or to a sphencal core. Zolnowski et al. [3] has investigated the N P B of the N = 88 nuclei using a quadrupole-octupole coupled model. The calculated energy levels are in good agreement with the experimental data except for the high-spin states in X56Er. Vogel [8] has pointed out that above a certam critical s p m value the N P B can no longer be treated as octupole states but become two-quasxpart~cle decoupled states. Sunyar et al. [9] interpreted the N P B in :56Er as a rotatxonal b a n d built on a two-quasiparticle state. However, Iachello and A r i m a [10,11] have shown that this couphng can

be treated in a simple way wltban the framework of the interacting boson approximation (IBA) model. De Volgt et al. [5] investigated the N P B of 15°Sm m terms of interacting quadrupole and octupole bosons. Satisfactory results are obtained. Scholten et al. [12] have studied the negatwe-parity energy levels and E l , E3 transitions of even-mass nuclei of Sm xsotopes. They used a mass-depen- dent interacting hamiltoman with s, d and f bosons. T h e energy levels can be well explained, b u t the E1 transitions faal to be reproduced unless the higher order terms m E1 transition operators were taken into account. In this letter, we shall study systematically the N P B of e v e n - e v e n N = 88 lsotones using the IBA model. It is hoped that the energy levels of the negative-panty states of this senes of isotones can be well reproduced b y an umfied set of parameters

In our model, the inert closed shells are taken at Z = 50 a n d N = 82. Extra core nucleons are considered to pair to active bosons. The effectxve h a m d t o n i a n between bosons is taken as the form

where H ~ is the harmltoman for s and d bosons, ef is the singie-boson energy of the f boson, Q~)

0 3 7 0 - 2 6 9 3 / 8 5 / $ 03.30 © Elsevier Science Pubhshers B.V. ( N o r t h - H o l l a n d Physics Pubhshlng Division)

--(3-) ml- 3 Exp 1L'8 Nd 1,41 ~3- ~3- '3- Jl- -3- 1,42 1505m ~(17-) ~17 - --15- 15- 17- ~15- ~,13- --13- --13- 11 - 11- --.11 - --9- 9- 5- --7- ,, 7- --2- 3- 3- 2g ~ 2- 7- 5- --3- ~3- 3-- Exp H I M 2 Fzg 1 Exp 152Gd --17 - ~17- --15- 15- --13- .13- --.13- --11 - ~11 - 9- ~9- 7- ~7- ~2- --5- 5- .<: 0 L,o ~17- g --15- -11- 9- L'-' L"I"J '7- ,2- 1 ~3- ~3- ~3- 1,41 1,42 to oo Z oo

Volume 163B, n u m b e r 5,6 PHYSICS LETTERS 28 November 1985 6 5 4 3 ~ r I.iJ 2 1 o E x p . 1 5 - m 1 3 - 9 - m 7 - 2 - 5 - 3 - 154 Dy hl I 15 13- 11- m 9 - 7 - 1 - ~ 3 ~ m l S - 1 3 - m 1 1 - 9 - 7 - 2 - - - 5 - - - 1 - ~ 3 - M 2 Fig 2 ~ ( 2 0 - ) ~ , ( 1 9 - ) ~ 1 7 - -15- ~ 1 3 - w l l ~ 9 - 7 - 2- 5 - I - 3 - E x p 156 E r M I ~ 2 1 - ~ 1 9 - ~ 1 7 - ~ 1 5 - - - 1 3 - 11- 1 9 - ~ 7 - i ~ 3 - ~ 2 1 - ~ . 1 9 - ~ 1 7 - '-15- ~ 1 3 - 9- 7- m 2 -5 ~ 3 - M 2 2 9 7

V o l u m e 163B, n u m b e r 5,6 PHYSICS LETTERS 28 November 1985

a n d Q~2) are the quadrupole operators for s, d and f bosons defined as follows"

0(2) _sd [ d + × ~ + s + × d](2)_ ½v~-[d+× a7](2),

Q~2) = C l [ f +

X f](2)

T h e p a r a m e t e r s in Hsd are taken from a previous

calculation for the positxve-parlty states of the N = 88 lSOtones [13]. The remaining two parame- ters ef and C 1 are determined from a least-squares fitting to forty-three negauve-parlty states of five N = 88 lsotones 148Nd, 15°Sm, 152Gd, l~4Dy and ~56Er. We find that accurate fits to the energy spectra can be obtained by using an effecuve hamlltonlan without any exphclt b o s o n - n u m b e r dependence in the parameters The overall root- m e a n - s q u a r e devlaUon is 0.119 MeV with the p a r a m e t e r s (in MeV) ef = 1.123, C1 = 0.028. The results (referred to as M1) are shown m figs. 1 and 2. In general, the calculated values are in good agreement with the observed ones, except the 1 - states for all nuclei. The calculated 1 - states he m u c h hagher than the observed ones, so that the energy spacings between 1 - and 3 - states are almost doubled as compared to the observed values. F r o m in-beam spectra of the (A, x n) reaction, high-spin negative-panty states have been ldenUfied up to 1 5 - for tS°Sm and 154Dy and to 1 7 - for lS2Gd and 156Er. These htgh-spm levels are all well reproduced m our calculations

T o test the wave funcUon, we also calculated the electromagneuc transitions. The one-body E1 a n d E3 transition operators in the space of s, d and f bosons can be written as

T(E1) =

d] (1>,

T(E3) = a 3 [ s + X f + f + X g](3)

+ fl3[d+x f + f+x d] 0~

It is found that the unified parameters a 3 = 0.12 a n d f13 = - 0 70 can reproduce the B(E3) values quite well. T h e results are shown in table 1. However, the calculated values for B(E1) cannot fit the observed values with either a mass-indepen- dent p a r a m e t e r a~ or mass-dependent p a r a m e t e r

~t I .

It m a y be interested to study whether the 1 -

Table 1 Nucleus J, ~ Jf B(E3) [ e 2 b 3 ] experiment theory 15°Sin 0 +---~ 3/- 0 36 a) 0 39 0 + ~ 32 0 15 a) 0 11 152Gd 0 +---, 3/- 0 32 b) 0 42 0 +---, 32 0 0 7 b) 0 12 a)Ref [14] b)Ref [15]

including the p boson. To check this point, we m o d i f y our h a m l l t o m a n to the following form to i n c o r p o r a t e the effects of p bosons:

H = Hsd + ef + ep +

[O~) ,o(2)1

w h e r e ep lS the s, ngle boson energy for p bosons

a n d

Q(2)

ep = C l [ f + x f](:~ +

G[p+x/~] (2>

+C3[f+×~+p+Xf] (2),

T h e energy spectra fitting with an R M S deviation of 0.102 M e V can be obtained with the following unified l n t e r a c u o n parameters (in MeV) e f --- 1.106, ep = 1.260, C 1 = 0.019, C2 = - 0 . 0 0 2 , C 3 = 0.003. T h e results (referred to as M2) are also presented in figs. 1 a n d 2. It can be seen that the 1 - states are all lowered down and thus the 1 - - 3 - energy spacings b e c o m e very close to the experimental data. In order to test the effects of the p boson on E1 a n d E3 transition rates we also include two terms, i l l [ s + × / 3 + p + × ~](1) and ,/l[d+ x/3 + p + x d] (1), in the T(E1) operator and a term

"r3[d+× ~ +

B(E1) t r a n s m o n rates agree reasonably well with the experimental data with a umfied set of p a r a m e t e r s a 1 = - 0 . 2 8 , 131 = - 0 50, ~1 = 1.80 for all lSOtones. T h e calculated and experimental values for some N - - 88 lsotones are shown in table 2. T h e inclusion of the "/3 [ d+ × P + P + × d] o) t e r m does not change the values of B(E3) a p p r e c i a b l y for a wide range of values of Y3, thus we p u t Y3 = 0. In shell-model language, it is intended to interpret the p-boson as a two-particle pair within the valence shell having J - values as

Volume 163B, number 5,6 PHYSICS LETTERS 28 November 1985 Table 2

Nucleus J, ~ Jf B(E1) ratxos

experiment theory 14SNd 3{- ~ 4{/27 1 5 + 0 2 a) 37 I x- ~ 2?/07 2 6 + 0 3 a~ 2 1 xS°Sm 3~- ~ 4 ? / 2 ? 0 78 b) 0 74 11- ~ 27/07 2 07 b) 1 98 11- --., 0~/07 0 63 b) 0 05 5{ ---, 4 ? / 6 ? 1 0 c) 5 1 152Gd 3~- ~ 4 ? / 2 ? 0 59 b) 0 35 1 x- ~ 2?/07 1 62 b) 1 84 1{ ~ 0~-/07 0 48 b) 0 04 a)Ref [16] b)Ref [17] C)Ref [18]

a m o u n t of s p u r i o u s c e n t e r - o f - m a s s moUon, whtch is, however, n o t treated i n o u r calculation. T h e r e f o r e , we w o u l d lake to emphasxze that the success i n fittings of 1 - energy levels a n d B(E1) t r a n s i t i o n rates s h o u l d b e i n t e r p r e t e d i n a p h e n o m - e n o l o g i c a l sense.

I n c o n c l u s i o n , the N P B of N -- 88 lsotones c a n b e e x p l a i n e d i n terms of the m t e r a c t m g b o s o n a p p r o x i m a t i o n model. A m a s s - i n d e p e n d e n t h a m - d t o n i a n c a n b e used for d e s c r i b i n g the whole series of l s o t o n e s . T h e E M t r a n s i t i o n s c a n b e r e p r o d u c e d q u i t e s a t i s f a c t o r y b y a umfied set of parameters. I t is also f o u n d t h a t the i n c l u s i o n of the p b o s o n i m p r o v e s t h e fittings m 1 - states a n d the E1 t r a n s i t i o n rates a l t h o u g h the s p u n o u s center-of-

m a s s m o t i o n of p b o s o n pairs are n o t treated m a n y way.

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