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
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12