Prealignment B(E2)-anomaly in 124Xe

Volume 133B, numbe 1,2 PHYSICS LETTERS 8 Decembe 1983 PREALIGNMENT B(E2)-ANOMALY IN 124Xe H. HANEWlNKEL, W. GAST, U. KAUP, H. HARTER, A. DEWALD, A. GELBERG, R. REINHARDT, P. yon BRENTANO lns i u a Ke nphysik, Uni e si i~ zu K6ln, Wes Ge many and A. ZEMEL, C.E. ALONSO 1 and J.M. ARIAS 1 Ke n ysisch Ve snelle lns i uu , Uni e si y o G oningen, The Ne he lands Recei ed 1 July 1983 Re ised manusc ip ecei ed 28 Sep embe 1983 Li e imes o 17 le els o 124Xe we e measu ed using he Recoil Dis ance Dopple Shi me hod. An anomalous E2- educ ion was obse ed, s a ing a I = 8 + and p = 5 + in he g ounds a e and in he quasi-gamma band espec i ely. This anomaly is discussed in e ms o he In e ac ing Boson Model. The i egula i ies in he y as cascades o e en-e en nuclei, known as backbending, a e nowadays common- ly unde s ood as a band c ossing phenomenon, domina - ed by he o a ion-alignmen (RAL) o a high-} b oken pai [ 1 ]. Acco ding o he band c ossing desc ip ion, he E2 ansi ion p obabili y be ween y as s a es mus sha ply d op a backbending, while he ansi ions below and abo e he c ossing should ha e he ull o a ional s eng h [2]. Howe e , he measu emen o B(E2) al- ues in 126Ba [3] and 130-134Ce [4] ha e displayed an anomaly, iz. he ansi ion s eng h is subs an ial- ly educed e en below he band c ossing. This anomaly can no be explained by Nilsson model band c ossing calcula ions [2], indica ing ha he backbending pa - e n and he B(E2) anomaly may ha e di e en o igins. A possible heo e ical explana ion was p o ided by D aaye e al. [5] who also coined he exp ession "p ealignmen B(E2) anomaly". The au ho s ca ied ou a pseudo-SU(3) shell model calcula ion o 126 Ba. The anomaly is p ima ily ela ed o he c ossing o wo SU(3) ep esen a ions. The aim o he p esen wo k has been o b ing new 1 P esen add ess: Depa men o A omic and Nuclea Physics, Uni e si y o Se illa, Spain. 0.031-9163/83/$ 03.00 © Else ie Science Publishe s B.V. (No h-Holland Physics Publishing Di ision) expe imen al in o ma ion on he p ealignmen B(E2) anomaly by s udying 124Xe and o pe o m a de ailed compa ison o he esul s wi h In e ac ion Boson Mod- el (IBM) calcula ions. The nucleus 124Xe was p oduced in he ollowing eac ions: 122Te (a, 2n) 124Xe (E~ = 24, 25 MeV), 108pd (19F, p2n)124Xe(E 19F = 60-75 MeV) and ll4Cd (13C, 3n) 124Xe(E 13C = 46-58 MeV). Gamma singles, 7-3' coincidences, angula dis ibu ions, exci- a ion unc ions and con e sion elec ons we e mea- su ed a he FN Tandem Van de G aa accele a o in Cologne in o de o es ablish an ex ended le el scheme. In he low spin pa i ag ees well wi h hose gi en elsewhe e [6,7]. A de ailed discussion will be gi en in a o hcoming pape [8]. The li e imes o 17 le els we e measu ed by means o he Recoil Dis ance Dopple Shi (RDDS) ech- nique, using he eac ion 114Cd (13C, 3n) 124Xe a E 13C = 54.4 MeV. The gamma- ays we e de ec ed by h ee la ge olume Ge (Li) de ec o s a 0 °, 160 ° and 305 ° ela i e o he beam axis. The in ensi ies o he shi ed and unshi ed peaks we e ex ac ed om he RDDS spec a by he p ocedu e desc ibed in e . [91. The esul ing B(E2) alues in WU a e gi en in ig. 9 Volume 133B, numbe 1,2 PHYSICS LETTERS 8 Decembe 1983 1. I should be men ioned ha ou esul o he B(E2, 2 ~ 0) di e s conside ably om ha gi en p e iously [10]. Mo eo e i does no i so well in o he end o he sys ema ic IBM calcula ions o e . [11 ]. Hence we checked e y ca e ully he alidi y o ou esul s. F om he independen analysis o he RDDS spec a aken a di e en angles deo ien a ion e ec s due o he hype ine ield could be excluded. No essen ial in luence om sho li ed side eeding componen s can be expec ed as om he de ailed le el scheme an uppe limi o 3% can be se on he ela i e in ensi y o unobse ed side eeding o he 2 + s a e. Fo he discussion o he le el s uc u e he exci - ed s a es we e en a i ely g ouped in o bands using he expe imen al B(E2) alues ( ig. 1). The g ounds a e band, whose ansi ions a e cha ac e ized by a he la ge B(E2)'s can be ollowed up o he 8 + s a e. The 10 + s a e appea s o be he head o a new band as in- dica ed by he small B(E2) alue o 24 WU o he 10 + ~ 8 + ansi ion. I is supposed o be a (Uhll/2) -2 exci a ion: i we calcula e he aligned angula momen- W 6- !-) -] ~,8-~ -F Xe-12L --- J bond ,~ ~ -J- s uc u e ----" __~ 32 2;,o. '3'19- , 2~ 70~_ ~7" >21 ,c , 6" 45 :,3 * 120 , /." I 2* 109 2" quasi "/-bond 8~ O" gs. band Fig. 1. Assumed band s uc u e o 124Xe: numbe s le o he a ows indica e B (E2) alues in Weisskop uni s (WU). u n o he wo h 11/2 quasipa icles by using he me h- od gi en in e . [12], we ind he alue i = 7.1/i which is ypical o a si ua ion whe e he hll/2 subshell is pa ially illed; he ex apola ed gsb was used as e e - ence line. This sugges s ha we deal wi h an aligned wo-neu on s a e. An addi ional suppo o his in e - p e a ion may be p o ided by he ac ha in he h11/2 neu on bands o 121Xe and 123Xe [8] no backbending has been obse ed. The pa e n o exci a ion ene gies and B(E2) al- ues ( ig. 2) is e y simila o ha o he iso ope 126Ba [3], and he p ealignmen B(E2) educ ion is clea ly e iden . We ied o achie e a consis en desc ip ion o bo h ene gies and ansi ion a es in 124Xe and 126Ba by using he model desc ibed in e . [13], which o) b) ~0 ~ 1.5. 1.0. .5' 1.0' ¢1 LU <) .5 A-2 P "I Vl3u/2}, ll " ~ ,..L ~Z • g ounds a e ~',( g,,2)~'~ band J. ',~,' J. s g ounds o e e'" IBA- 2 bond /" s ° j1 e~ 'I~ . X Exp. / "~-~_.* o -o.-.- IBA-2* 2qp ( h,~2) 2 (ng 71~ )2 / : ~ 8 I"o 1~ "u~J Fig. 2. (a) Expe imen al E2 ansi ion s eng hs compa ed wi h he p edic ions o he IBA2 + 2 qp model. Fo he wo quasi- pa icles he con igu a ions ( h u/2) and (T gT/2 ) a e conside ed. The ansi ion p obabili ies a e no malized o he B (E2, 2 + -* 0 ÷) alue. (b) Compa ison o he esul ing ansi ion ene gies wi h expe imen . 10 Volume 133B, numbe 1,2 PHYSICS LETTERS 8 Decembe 1983 cons i u es an ex ension o he IBM [14] and o p e- ious mo e simple minded calcula ions [15] ; a model simila o ha o e . [13] was gi en in e . [16]. One co e boson can be b oken in o wo pa icles which a e ecoupled o o m a pai wi h highe angula momen- um. Thus in addi ion o he space o N bosons, he model space includes s a es in which he pa icle pai is coupled o N - 1 bosons o he co e. This model was shown o accoun well o he salien ea u es o backbending [ 13,7] as a as exci a ion ene gies a e conce ned, bu i ails o ep oduce he anomalous beha iou o he ansi ion a es. Hence he calcula- ions o e . [13] ha e been ex ended by conside ing mixing wi h bo h wo-neu on and wo-p o on bands. In one calcula ion a b oken ( gT/2) pai has been con- side ed alongside o a (Vhll/2) pai . The model hamil onian is [13] H = H B + H F + H BF , whe e H B is he ene gy o he boson co e, H F ha o he wo e mions. The in e ac ion o he co e wi h he e mions is gi en by BF = KQ~ "Q whe e Q is a gene alized quad upole ope a o Qp = Qp (boson) + ap [a~a~] (2) +/3p [ [apap] (4)alp ] (2) -- [Jpa~[['ap'ap](4)] (2) (/9 =/ , V), wi h aj+m being he nucleon c ea ion ope a o [aim = (-1)j-ma/_m) and d + he d-boson c ea ion ope a- o ; he quad upole coupling pa ame e K has he same alue as in H B. The pa ame e s o H B o 124Xe and 126Xe we e aken om e . [11 ]; hose o he 122Te co e we e i - ed o he low spin s a es o 122Te. The pa ame e s o V BF we e K --- -0.1430, % = 1.06, a = 1.76,/3~ =/~ = 0.032 (all alues in MeV). The diagonal ma ix elemen s o H F we e: E(4) = 1.716, E(6) = 2.553 o (ng7/2) 2 and E(4) = 1.804, E(6) = 2.223, E(8) = 3.144, E(10) = 3.694 o (Uhll/2) -2 (angula momen um o he s a e in pa an hesis). This choice o pa ame e s al- lowed o ep oduce he 124Xe le els, as well as he B(E2) alues ( ig. 2). The a emp o i ene gies and B(E2)'s in 126Ba wi h he same pa ame e s was much less success ul. The squa ed ampli udes o he pu e boson and o he wo-pa icle componen s a e gi en in able 1. I Table 1 P obabili ies o componen s o y as s a es in 124Xe (in %) I N bosons (N - 1) bosons (N - 1) bosons only @ ( gT/2) @ ( h I I/2 )-2 0 99.99 0.01 0 2 99.98 0.02 0 4 99.88 0.11 0.01 6 99.07 0.91 0.02 8 35.06 64.91 0.02 10 1.38 17.11 81.51 12 0.01 0 99.99 14 0 0 100.00 can be seen ha he 8 + and 10 + s a es ha e a compli- ca ed s uc u e. Fo bo h spins, pai s o nea ly de- gene a e le els should exis , in disag eemen wi h ex- pe imen . The magne ic momen s o he 8 + and 10 + s a es a e expec ed o de ia e s ongly om he collec i e alues: he 8 + s a e should ha e a la ge posi i e con i- bu ion om (7 g7/2) 2 , whe eas a small nega i e alue o g(10 +) should ollow om he con ibu ion o (Vhl 1/2)-2" An expe imen al de e mina ion o hese momen s is he e o e highly desi able. The disc epan- cies men ioned abo e show ha his desc ip ion is no comple ely sa is ac o y. I is ob ious ha he model is o e simpli ied. Only one pai has been b oken. Howe e , i has been shown [17], ha he sca e ing o se e al pai s om he co e o he alence shell mus be aken in o accoun in a co ec desc ip ion o backbending. Will 1.0 .5 g ounds a e T numbe o bosons band 1 N = 5 ~"~~'~ IBA- 1 l B(E2, 2? 0") ~ { ~" Fig. 3. Expe imen al E2 ansi ion s eng hs compa ed wi h heo e ical alues om he collec i e IBM calcula ion; s a es wi h I > 8 which a e mixed ha e no been ep esen ed. 11 Volume 133B, numbe 1,2 PHYSICS LETTERS 8 Decembe 1983 A di e en app oach has been conside ed [18], based on a mic oscopic calcula ion. While in IBM he boson cu o is mainly due o he ini e numbe o alence pa icles, he e ec o he Pauli p inciple has been conside ed explici ly. The esul s o he calcula- ion a e equi alen o in oducing an e ec i e boson numbe a ound N = 5. The in luence o his educ ion o he e ec i e boson numbe o he ansi ion p ob- abili ies be ween collec i e s a es calcula ed by means o IBM can be seen in ig. 3. The au ho s would like o hank F. Iachello o his in e es and s imula ing discussions and T. O suka o pu ing his wo-pa icle p og am o ou disposal. Two o he au ho s (C.E.A. and J.M.A.) acknowledge wi h hanks he discussions wi h M. Lozano, as well as he kind hospi ali y o he KVI. This esea ch has been pe o med as pa o he esea ch p og am o FOM wi h inancial suppo o ZWO. The wo k was also sup- po ed by he BMFT. Re e ences [1 ] F.S. S ephens, Re . Mod. Phys. 47 (1975) 43, and e e - ences he ein. [2] M. Reinecke and H. Rude , Z. Phys. A282 (1977) 407. [3] G. Seile -Cla k, D. Husa , R. No o ny, H. G ~/ and D. Pel e, Phys. Le . 80B (1979) 345. [4 ] D. Husa , S.J. Mills, H. G , U. Neumann, D. Pel e and G. Seile -Cla k, Nucl. Phys. A292 (1977) 267. [5 ] J.P. D aaye , C.S. Han, K.J. Weeks and K.T. Hech , Nucl. Phys. A365 (1981) 127. [6] Ch. D os e e al., Z. Phys. A284 (1978) 297; H. Kusaka i, N. Yoshikawa, H. Kawakami, M. Ishiha a, Y. Shida and M. Sasaki, Nucl. Phys. A242 (1975) 13; J. Ha ula, H. Helppi and A. Luukko, Phys. Sc ip a 26 (1982) 205. [7] H. Kusaka i, K. Ki ao, K. Sa o, M. Sugawa a and H. Ka su agawa, o be published. [8] W. Gas e al., o be published; W. Gas , Ph.D. Thesis, Uni e si y o K61n (1982), un- published. [9] A. Dewald e al., Phys. Re . C25 (1982) 226. [10] D.M. Go don, L.S. Ey el, H. de Waa d and D.E. Mu nick, Phys. Re . C12 (1975) 628. [11 ] G. Puddu, O. Schol en and T. O suka, Nucl. Phys. A348 (1980) 109. [12] B. Bane jee, H.J. Mang and P. Ring, Nucl. Phys. A215 (1973) 366; R. Beng sson and S. F auendo , Nucl. Phys. A327 (1979) 139. [ 13 ] N. Yoshida, A. A ima and T. O suka, Phys. Le . 114B (1982) 86. [14] A. A ima and F. Iachello, Ann. Re . Nucl. Pa . Sci. 31 (1981) 75, and e e ences he ein. [15] A. Gelbe g and A. Zemel, Phys. Re . C22 (1980) 937. [16] I. Mo ison, A. Faessle and C. Lima, Nucl. Phys. A372 (1981) 13. [17] F. G iimme , K.W. Schmid and A. Faessle , Nucl. Phys. A326 (1979) 1. [18] U. Kaup and G. Holzwa h, o be published. 12