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PARTICLE OCTUPOLE EXCHANGE COUPLING IN
THE YRAST LINES OF TERBIUM AND
DYSPROSIUM NUCLEI
P. Kleinheinz
To cite this version:
JOURNAL DE PHYSIQUE CoZZoque C I O , suppZe'ment au n022, Tome 4 1 , de'cembre 1980, page ~ 1 0 - 4 3
PARTICLE OCTUPOLE EXCHANGE COUPLING I N THE YRAST L I N E S OF TERBIUM AND DYSPROSIUM NUCLEI
P . Kleinheinz.
I n s t i t u t fiir Kemphysik, KFA JiiZich, Jiilieh, F . R. Germany.
An a n a l y s i s o f high-spin p a r t i c l e - h o l e e x c i t a t i o n s l ) neighbourhood o f 1.6 MeV. The unexpectedly l a r g e i n t h e N=82 nucleus 1 4 6 ~ d has i n d i c a t e d t h a t t h e r e .77 Meli energy s p l i t i s due t o the dominant i s a l a r g e gap i n t h e s i n g l e p a r t i c l e spectrum a t c o n t r i b u t i o n o f t h e 1 4 6 ~ d core octu- Z=64, and i n several r e c e n t
investigation^^'^)
we pole. (The analogous energy s e p a r a t i o n o f the 13/2+ c o u l d show t h a t t h e y r a s t s p e c t r a o f few-valence- and 15/2' members of t h e h X 3- s e p t u p l e t i n20g~i i s 140 keV). 9/2 p a r t i c l e n u c l e i around 1 4 6 ~ d can be w e l l described
w i t h i n the s p h e r i c a l she1 l model u s i n g e m p i r i c a l one- and two-nucleon i n t e r a c t i o n energies. S i m i l a r techniques have e a r l i e r 4 ) been s u c c e s s f u l l y a p p l i e d t o analyze t h e h i g h s p i n s t a t e s o f n u c l e i c l o s e t o t h e doubly closed '08pb. One t h u s f i n d s t h a t the
-
f u l l y o r near f u l l y a l i g n e d-
f e w - p a r t i c l e y r a s t c o n f i g u r a t i o n s have r a t h e r s i m i l a r c h a r a c t e r i s t i c s i n t h e 2 0 8 ~ b and 1 4 6 ~ d regions. However, t h e proper- t i e s o f t h e phonons' d i f f e r s t r o n g l y i n t h e two core n u c l e i . The 3- as w e l l as t h e 2' s t a t e i n 1 4 6 ~ d occur a t much l o w e r e x c i t a t i o n than i n '08pb.Furthemore, i n c o n t r a s t t o 208~b, where many p r o t o n and neutron p a r t i c l e - h o l e e x c i t a t i o n s c o n t r i b u t e 5 ) t o t h e 2.6 MeV 3- s t a t e , t h e 1 4 6 ~ d o c t u p o l e has a dominant dll/2d;)2 component; a p r e l i m i n a r y RPA
c a l c u l a t i o n 6 ) g i v e s s.75 f o r t h e ~ ~ h ~ ~ ~ ~ d ; : ~ ampli- tude o f t h e 1.6 MeV 3- s t a t e . One t h e r e f o r e expects t h a t t h e c o u p l i n g modes o f hllf2 valence protons t o t h e 146~d 3 s t a t e w i l l be s t r o n g l y i n f l u e n c e d by t h e P a u l i p r i n c i p l e .
MeV I L45E
F i g . 1: Y r a s t l e v e l s of 1471% observed in (cr,8n) and
c a l c u l a t e d s h e l l model y r a s t s t a t e s ( r e f . 2 ) .
tiamamoto 5 , has considered t h e problem o f -tile coupling o f a s i n g l e p a r t i c l e ( o r h o l e ) t o t h e octupole v i b r a t i o n i n '08pb and has presented t h e lowest-order diagrams which c o n t r i b u t e t o t h e We have r e c e n t l y i n an (a,8n) experiment i n v e s t i - energy s h i f t s i n a p a r t i c l e p l u s phonon m u l t i p l e t . gated2) t h e o n e - p a r t i c l e nucleus 147~b, which has The diagram a p p r o p r i a t e t o t h e case o f t h e 1 4 7 ~ b an h2Ill p r o t o n i n i t s ground s t a t e ( f i g . 1 ) . The
1 4 7 ~ b d p l h y r a s t s t a t e s i n t h e 2.5 t o 3.5 MeV r e g i o n p r o v i d e one example f o r t h e a p p l i c a b i l i t y o f t h e s p h e r i c a l s h e l l model f o r t h e n u c l e i around 146~d. Rather good agreement w i t h experiment i s found f o r t h e energies c a l c u l a t e d w i t h e m p i r i c a l two-nucleon i n t e r a c t i o n s taken from t h e known 1,7) l e v e l s p e c t r a o f 14%d and 148~y.
The .measured E3 t r a n s i t i o n r a t e o f 31 t 6 U.U. f o r t h e 1266 keV ground s t a t e t r a n s i t i o n c h a r a c t e r i z e s t h e 15/2' s t a t e as an o c t u p o l e e x c i t a t i o n , and we i n t e r p r e t t h e 2038 keV l e v e l as t h e 1712' member o f t h e "hl2 ll X 3- s e p t u p l e t expected i n t h e
hl
lf2 X 3- coupling, w i t h two hll f 2 p a r t i c l e s and one dg12 h o l e i n t h e i n t e r m e d i a t e s t a t e i s shown i n f i g . 3, bottom l e f t . When t h e hlE lf valence pro.- t o n i s added t o t h e 3- s t a t e o f t h e core, t h e l a r g e "h11f2d;j2 component o f t h e o c t u p o l e s t a t e w i l l be e f f e c t i v e l y blocked o u t by t h e P a u l i p r i n c i p l e i n some coupled states, and t h e i r energies w i l l conse- q u e n t l y be much h i g h e r than t h e unperturbed
3-
energy.
In
second o r d e r p e r t u r b a t i o n t h e o r y t h e energy s h i f t saw
gi'ven by:c10-44 JOURNAL DE PHYSIQUE
where W i s a Racah c o e f f i c i e n t . F o r the s t a t e w i t h maximum angular momentum, I = 17f2, t h e geometric c o e f f i c i e n t 7W i s +17/2,i.e. p o s i t i v e and l a r g e , and the s t a t e i s pushed up i n energy. For t h e I = 15/2 s t a t e t h e c o e f f i c i e n t i s -7f22. The n e g a t i v e s i g n imp1 i e s t h a t t h e Paul i p r i n c i p l e enhances r a t h e r than reduces t h e h2:2d;ill component i n the 3- phonon, because t h e two hllL2 protons occur more i n an antisymmetric than a symmetric arrangement. I n the 1 4 7 ~ b le v e l spectrum the 17/2+ and 15/2+ l e v e l s a r e s h i f t e d from 1.58 MeV i n the expected d i r e c t i o n s , and the r a t i o o f the energy s h i f t s i s 1.45 compared t o t h e t h e o r e t i c a l r a t i o o f 22/12 ( c f . f i g . 3). This approximate agreement must be considered s a t i s f a c t o r y , s i n c e the s i t u a t i o n i s c h a r a c t e r i z e d by s t r o n g coupling, where h i g h e r than second-order e f f e c t s may be important. Nevertheless, the 1 4 7 ~ b le v e l energies p r o v i d e an experimental number f o r t h e exchange c o u p l i n g strength. From t h e observed 722 keV 15/2 t o 17/2 s p l i t t i n g t h e energy f a c t o r o f eq. (1) becomes
which we w i l l use l a t e r t o c a l c u l a t e energy s h i f t s of m u l t i p l e t members i n 148~y,
The h i g h s p i n l e v e l spectrum o f t h e two-proton nuc- 16
leus 1 4 8 ~ y i n (a,8n) and ( 0,4n) i n - beam experiments i s presented i n f i g , 2. Below 3 MeV t h e e x c i t a t i o n s are o f two-proton character. I n the y r a s t decay t h e complete ~ h : ~ / ~ m u l t i p l e t i s populated, t o g e t h e r w i t h 5- and 7- two-proton
s t a t e s which i n v o l v e s2il and d3/2 valence p a r t i c l e s . A t I = 10 the 148~y valence s p i n i s exhausted and h i g h e r y r a s t s t a t e s must i n v o l v e breaking o f t h e 1 4 6 ~ d core. Since t h e 3- o c t u p o l e i s t h e lowest core e x c i t a t i o n , t h e y r a s t l i n e can be expected t o continue by e x c i t a t i o n s o f t h e type 10' X
3-.
I nt h e experiment, t h e s t r o n g 1061 key E l t r a n s i t i o n i s found8) t o populate t h e 148~y
lot
isomer from a 3980 keV 11- l e v e l , which we i n t e r p r e t as t h e l o w e s t member o f t h e octupole m u l t i p l e t b u i l t on t h e 2 nhl l, 2 10' s t a t e .I n t h e 148~y
l o t
s t a t e a t 2919 keV,two
21llhprotons a r e a l i g n e d and i n t h i s case one can expect t h e l o w e s t member o f t h e octupole m u l t i p l e t t o be two u n i t s i n s p i n l e s s than t h e maximally a l i g n e d 13' member. The particle-phonon exchange diagram a p p r o p r i a t e t o t h e =him X 3- coupling,
w i t h t h r e e hll,* p a r t i c l e s and one dgI2 h o l e i n
the intermediate s t a t e , i s shown i n f i g . 3 t o t h e r i g h t . I n second o r d e r p e r t u r b a t i o n theory, the energy s h i f t s f o r members o f the octupole m u l t i - p l e t i n 148~y are given by
where X i s a 9j symbol, and
I '
s p e c i f i e s the c o u p l i n g o f t h e two h2lIl protons i n t h e i n i t i a l s t a t e . The c r u c i a l p o i n t here i s t h a t the energy f a c t o r <I H
1
> 2 / ~ ~ c o n t a i n i n g the i n t e r a c t i o n m a t r i x element i s t h e same as i n the 1 4 7 ~ b case, and t h e r e f o r e one can use t h e e m p i r i c a l energy f a c t o r (2) from the o n s - p a r t i c l e phonon c o u p l i n g t o des- c r i b e t h e exchange i n t e r a c t i o n o f two p a r t i c l e s w i t h the phonon. With t h e value of 85k keV f o r t h a t energy f a c t o r , d e r i v e d above from t h e observed 772 keV s p l i t t i n g o f t h e 1 5 ~ 2 ' and 1712' l e v e l s i n 147~b, we have c a l c u l a t e d t h e expected energy s h i f t s2 f o r t h e f o u r h i g h e s t s p i n members o f t h e hllL2 X 3- m u l t i p l e t i n 148~y. (The I' = 10 and 8 couplings b o t h c o n t r i b u t e t o t h e 11- and 10- s t a t e s , and t h e t h e o r e t i c a l energies shown are t h e lower energy s o l u t i o n s obtained by d i a g o n a l i z i n g the i n t e r a c t i o n i n t h i s two-dimensional b a s i s ) . I n f i g . 3 the c a l - c u l a t e d l e v e l energies a r e compared w i t h t h e experi- mental r e s u l t s . The good agreement w i t h the observed 11-, 12- energies provides s t r o n g support f o r t h e i n t e r p r e t a t i o n o f these s t a t e s as octupole m u l t i - p l e t members, I n f u t u r e experiments i t may be p o s s i b l e t o l o c a t e a d d i t i o n a l members o f t h e 2 h l l L 2 X 3- mu1 t i p l e t , p a r t i c u l a r l y t h e 13- member which should be an y r a s t s t a t e .
The f a c t t h a t the e x c i t a t i o n energy o f t h e 3- octu- p o l e s t a t e i s h i g h e r i n 148~y than i n 1 4 6 ~ d can a l s o be understood as a P a u l i i n t e r f e r e n c e e f f e c t .
Tn t h i s case, t h e geometric,al b l o c k i n g c o e f f i c i e n t 14(21a t
l)X
f o r I' = 0 equals 2/12 assuming t h a t two o f t h e twelve hllf2 protons a r e p r e s e n t i n t h e 148~y 0' ground s t a t e . N i t h t h e same e m p i r i c a l m a t r i x element, t h e c a l c u l a t e d energy s h i f t i sThis s l i g h t l y smaller increase of the 3- energy in
148~v is not unexpected since the proton pair in
the 148~y ground s t a t e also p a r t i a l l y occupies the
slj2 and dgj2 o r b i t a l s .
MeV
nh,;2.3- L -
F i g . 2: Yrast l e v e l s of 148Dy observed i n ( a , 8 n ) and ( 160,4n) and s h e l l model c o n f i g u r a t i o n s ( r e f s
.
7 , 8 )As f a r as we know,
t h i stype of p a r t i c l e phonon
exchange coupling involving two p a r t i c l e s has not
been observed before; i t i s encouraging t h a t the
empirical coupling strength derived from the one-
p a r t i c l e case describes the more complex s i t u a -
tion so well.
It
i s noteworthy t h a t octupole y r a s t s t a t e s w i t h
A I <
3 systematically occur
i nthe nuclei above
146~d. In the Tb isotopes with N>82 low lying octu-
pole s t a t e s a r e found, which due t o Pauli i n t e r -
ference have AI
=2, analogous t o the 1266 keV
-
excitation i n 147~b82
discussed above. Such s t a t e s
have been i d e n t i f i e d i n
148~bg3(Ex
=1006 keV,
1"
=11-, Ref. 2). 149~b84 (1094 keV, 151
zt,
Ref.
151
9 ) . 150~bg5
(874 key, 11-, Ref. lO), and
Tbg6
(1097 keV, 15/2',
Ref. 21).
Octupole t r a n s i t i o n s with AI
=1 a r e found
i n
the
y r a s t cascades of the Dy isotopes above
3MeV ex-
c i t a t i o n , where the two hllj2 valence protons a r e
aligned. For example,
i n the three p a r t i c l e nucleus
14'oys3
recent experimentsL) identif led a 984 keV
2
E l
t r a n s i t i o n feeding the 2661 keV (nhllj2 vf7f2)2712-
s t a t e , suggesting a (27/2-
X3-)29(2+ configuration
f o r the 3645 keV level. In 150~y84 a 742 keV
E lt r a n s i t i o n deexci tes12) .the 5813 keV 19- octupole
2
s t a t e t o the (rhlliZ vf7i2hgf2)18+ l e v e l , and i n
2
151Dy
the (rhlll2 ~ h ~ ~ ~ f ~ ~ ~ ) 4 1 / 2 -
s t a t e i s fed13)
by an 839 keV
E lfrom the (41/2-
X3-)4312' y r a s t
s t a t e a t 5743 keV. In a l l cases these octupole
THEORY EXPMT THEORY EXPMT
P
Fig. 3: One-particle-phonon and two-particle- phonon exchange c o u p l i n g i n v o l v i n g t h e 1579 keV octupole e x c i t a t i o n i n t h e 1 4 6 ~ d c o r e . Zxperi- mental and c a l c u l a t e d n h l l / p X 3- and
nhfllf!
X 3-m u i t i p l e t members i n 1 4 7 ~ and 14*Ey a r e shown.
excitations are b u i l t on y r a s t s t a t e s i n which a l l
available
~ h ~~f~~~ and
~ / ~ vhgf2 ,valence spins
are f u l l y aligned. The f a c t t h a t octupole core
excitation competes successfully with l i f t i n g of
a neutron i n t o the ilSf2 orbital reemphasizes the
rather high single p a r t i c l e energy of t h a t o r b i t a l
noted
i n earl ier14) spectroscopy studies
.
References
1 ) P. Kleinheinz, R. Broda, P.J.Daly,
S.Lunardi,
M.
Ogawa, J . Blomqvist, Z. Physik A290 (1979)
279
2 ) R.
Broda,
M.Behar,
P. Kleinheinz, P.J. Daly,
J . Blomqvist, Z. Physik A293 (1979) 135
3)
P.Kleinheinz, Proc. ASHPIN, Argonne (1979),
ANL
f PHY-79-4, p. 125
4) See e.g. I. Bergstrom, Proc. XVI I n t . Winter
Meeting on Nuclear Physics, Bormio, Jan. 1978,
I . Iori ed.
,
Vol. 11, p. 636 and r e f s . given
therein
5)
I.
Hamamoto, Phys. Reports 10 (1974) 64
6) J.S. Dehesa, J . Speth,
P.
Kleinheinz, unpub-
lished
7 )
P.J. Daly,
P. Kleinheinz,
R.
Broda, A.M.
Stefanini, S. Lunardi,
H. Backe,
L .Richter,
R.
Willwater, F. Weik,
2.Physik A288 (1978)
c10-46 JOURNAL DE PHYSIQUE
8) P.J. Daly, P. Kleinheinz, R. Broda, S. Lunardi, H. Backe, J. Blomqvist, Z. Physik A, i n press, and c o n t r i b u t i o n t o t h i s conference (p. 61) 9) M. Ogawa, S. Lunardi, M.R. Maier, P. Kleinheinz,
Proc. I n t . Symp. on High Spin States and Nucl. Structure, Dresden, 1977, ZfK-336, p. 31 10) R. Broda, M. Ogawa, P. Kleinheinz, R.K. Sheline,
L. Richter, Proc. ASHPIN, Argonne (1979), ANL/ PHY-79-4, p. 401
11) P. Kemnitz, L. Funke, F. Stary, E. G l i l l ,
G. Winter, S. Elfstrom, S.A. H j o r t h , A. Johnson,
Th. Lindblad, itiucl. Phys. A311 (1978) 11
12) S. Lunardi
,
M. Ogawa, H. Backe, M. P i i p a r i n e n , Y. Nagai, P. Kleinheinz, Proc. ASHPIN, Argonne (1979), ANL/PHY-79-4, p. 40313) M. P i i p a r i n e n , S. Lunardi, P. Kleinheinz, H. Backe, J. B l o q v i s t , Z. Physik A290 (1979) 337. (Recent conversion e l e c t r o n measurements a t J u l i c h c o n f i r m t h e 839 keV
El
m u l t i p o l a r i t y suggested by T.L. Khoo i n Proc. ASHPIN, Argonne (1979), ANL/PHY-79-4, p. 95)14) S. Lunardi, M. Ogawa, M.R. Maier, P. Kleinheinz, Proc. ASHPIN, Argonne (1979)
