45 Evolution of Nuclear Shapes at High Spins Noah R. Johnson
Downloaded via UNIV OF CALIFORNIA SANTA BARBARA on July 10, 2018 at 05:19:25 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
Oak Ridge National Laboratory, Oak Ridge, TN 37831 Outstanding progress has been made during the past ten years on an understanding of the properties of nuclei excited into states of high angular momentum. Much of the experimental progress has resulted from γ-γ coin cidence measurements u t i l i z i n g complex detector arrays. Many of the proper ties of the yrast and near-yrast bands in nuclei revealed in these measure ments have become reasonably well explained by current theory. Both cranked shell model (CSM) and cranked Hartree-Fock Bogoliubov (CHFB) calculations have enjoyed considerable success in accounting for many aspects of high spin behavior. However, for a detailed understanding of the structure of these high spin states and for a stringent test of these models, i t is necessary to resort to measurements of their static and dynamic electromagnetic multipole moments. During the past few years we at Oak Ridge have concentrated on stu dies of the latter quantity, the dynamic electric quadrupole (E2) moments which are a direct reflection of the collective aspects of the nuclear wave functions. For t h i s , we have carried out Doppler-shift lifetime measurements u t i l i z i n g primarily the recoi1-distance technique. The nuclei with neutron number Ν « 90 possess many interesting proper t i e s . These nuclei have very shallow minima in their potential energy sur faces, and thus, are very susceptible to deformation driving influences. It is the evolution of nuclear shapes as a function of spin or rotational fre quency for these nuclei that has commanded much of our interest in the l i f e time measurements to be discussed here. There is growing evidence that many deformed nuclei which have prolate shapes in their ground states conform to t r i axial or oblate shapes at higher spins. Since the E2 matrix elements along the yrast line are sensitive indicators of deformation changes, mea surements of lifetimes of these states to provide the matrix elements has become the major avenue for tracing the evolving shape of a nucleus at high spin. Of the several nuclei we have studied with Ν « 90, those to be dis cussed here are i60,i6i [FEW82], [J0H82], [FEW82], [FEW85] and Er [0SH84a], [0SH84b]. In addition, we will discuss briefly the preliminary, but interesting and surprising results from our recent investigation of the Ν = 98 nucleus, W [RA085]. 1 5 8
Yb
172
0097-6156/ 86/0324-0298S06.00/ 0 © 1986 American Chemical Society Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
45.
Nuclear Shapes at High Spins
JOHNSON
II.
Experimental Both
its
1 6 0
inverse
case.
Aspects
Yb
^Ti (
and 1 1 6
1 6 1
and Data
It
C d , x n ) , at a c e n t e r - o f - m a s s
which a c t s
p o s s i b l e t o g a t e on g i v e n
as a t o t a l - e n e r g y
channel.
of
puter
p r o g r a m , LIFETIME [WEL85] w h i c h i n c l u d e s
[STU76] t o t h e d a t a .
population
γ-ray
intensities
lifetimes
fits
each
is discussed
In t h i s
in
a 25-cm χ way i t
was
e n e r g y s p e c t r u m and g e t a
by t h e
o f t h e usual
corrections
features
of the level
scheme, one
t o account
The program t h e n s o l v e s t h e
lifetimes
and i n i t i a l
t o t h e decay c u r v e s .
are used i n t h e f i t t i n g
com
all
cascade s i d e f e e d i n g t o each l e v e l
from undefined t r a n s i t i o n s .
o b t a i n the best
145 MeV i n
r e s u l t i n g decay c u r v e s
Knowing t h e g e n e r a l
equations while adjusting the to
γ-ray
and
8
times.
were e x t r a c t e d f r o m t h e
u s u a l l y models a t w o - s t e p
C d ( ** Ti , x n )
S p e c t r a were o b t a i n e d f o r
total
Lifetimes
filter.
of the t o t a l
reaction
flight
1 1 6
i n s i d e t h e annular opening of
regions
enhancement o f t h e d e s i r e d 17 d i f f e r e n t
energy of
d e v i c e used i n t h e measurements
was d e s i g n e d t o f i t
25-cm Nal c r y s t a l
Analyses
Y b were p r o d u c e d by t h e r e a c t i o n s
The r e c o i 1 - d i s t a n c e
[J0H81].
299
populations
Both t h e s h i f t e d
procedure.
of the and
levels
unshifted
Uncertainties
were d e t e r m i n e d by t h e method o f t h e s u b r o u t i n e
for
Bateman
in
the
MINOS, d e s c r i b e d
in
[JAM75]. Excited 1 2 8
Te(
large tors
3 4
S,4n)
1 5 8
at
Er
nuclei
f o r t h e s e s t u d i e s were p r o d u c e d v i a t h e
a bombarding e n e r g y o f
155 MeV.
In these experiments
Nal d e t e c t o r was removed i n o r d e r t o p l a c e an a r r a y o f a t 90° w i t h
t o the t a r g e t .
r e s p e c t t o t h e beam d i r e c t i o n T h i s was done i n o r d e r t o t e s t
c i d e n c e measurement tation
could o f f e r
of the experimental
analyses
problems a s s o c i a t e d w i t h
contribution
of
if
separations
statistical
i n t h e 0° d e t e c t o r Lifetimes different
quality
is
158Ε
γ
a
t
f o r the y r a s t
(6 cm) coin
and
interpre
respect t o s i m p l i f y i n g Direct
the
s i d e f e e d i n g makes no
g a t e d by band members
a
total
of
14 t a r g e t - s t o p p e r
spectra taken at f o u r of
shown i n F i g . 1 .
and r e v e a l
as a r e s u l t
with
the spectrum i s
A p o r t i o n of the t o t a l - p r o j e c t e d
target-stopper
a high-efficiency
in the analysis
the
Ge d e t e c
interest.
Measurements were t a k e n on tances.
if
side f e e d i n g .
t o a γ-ray t r a n s i t i o n
higher than the t r a n s i t i o n
cellent
especially
five
and a t c l o s e geometry
simplifications
data,
reaction
These s p e c t r a a r e o f
a favorable
peak-to-background
o f u s i n g t h e Compton s u p p r e s s i o n sequence o f
sets of coincidence d a t a :
1) t h a t
1 5 8
Er
ex ratio
shield.
were d e t e r m i n e d f r o m
f r o m g a t i n g on t h e
dis
the
first
Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
four
300
NUCLEI OFF THE LINE OF STABILITY ORNL-DWG 8 5 - 9 8 9 2
ORNL-DWG 89-9602
d=20/xm 30,000
h 1 6
10,000
Π
1 4
n
20,000 | -
n
12*
π
-Π Π II L
Fig. 1. Illustrative " t o t a l p r o j e c t e d " coincidence spectra of E r c o v e r i n g t h e 400-650 keV r e g i o n f o r f o u r o f t h e f o u r t e e n d i s t a n c e s measured. 1 5 8
transition 2) t h a t
above t h e one o f
f r o m t h e sum o f a l l
below t h e t r a n s i t i o n 4) t h a t
1 5 8
interest; gates
from t h e t o t a l - p r o j e c t e d
cidences.
Although side feeding
the state of i n t e r e s t
40
F i g . 2 . Decay c u r v e s f o r mem b e r s o f t h e y r a s t sequence i n Er. The p o i n t s r e p r e s e n t the experimental data w i t h the appropriate corrections. The s o l i d curves are t h e f i t t e d time d i s t r i b u t i o n s determined by t h e program LIFETIME.
interest;
of i n t e r e s t ;
20
FLIGHT TIME (pe)
f r o m g a t i n g on t h e second
transition 3) t h a t
above t h e one o f
0
and coin to
i s n o t e l i m i n a t e d i n t h e l a s t two t y p e s o f d a t a ,
have an advantage i n b e i n g o f e x c e l l e n t
statistical
quality.
they
I n f a c t , we
f o u n d t h a t t h e program LIFETIME h a n d l e d t h e i r more complex s i d e f e e d i n g ditions data. fits
quite well,
based on c o m p a r i s o n s o f l i f e t i m e s
I n F i g . 2 a r e shown e x p e r i m e n t a l t o these For t h e
from a l l
con
four sets
of
d a t a f o r each s t a t e and t h e program
data. 1 7 2
W studies, the
beam energy o f E|_
aD
= 230 MeV.
12i
*Sn
(
5 2
C r , 4n) r e a c t i o n was u t i l i z e d
The e x p e r i m e n t a l
arrangement was s i m i l a r
Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
at a to
45. that
for
tors
a t 90° f o r c o i n c i d e n c e g a t i n g .
1 5 8
distances
Er
measurements, e x c e p t here we used s i x l a r g e volume Ge d e t e c Data were c o l l e c t e d f o r
r a n g i n g f r o m 16un t o 7mm.
analyses are a v a i l a b l e
To t h i s
only f o r the t o t a l
t h e sums o f g a t e s below t h e t r a n s i t i o n III.
transition
t h e reduced e l e c t r i c t o the
these Q
of
interest.
of Q
t
=
^
probabilities,
B(E2),
2
Q
2 t
states
values f o r the y r a s t
g r o u n d band o f tunately,
stretching
The d a t a f o r 1 6 0
Yb are,
effect
In F i g .
t
trend
with
values
somewhat s i m i l a r l y the rotational
^
r
^
of
Q
t
1
dif
bands,
21/2*
Û
γ*
1
f 1
with
values
Γ
ι
25/2
\
+
I
29/2+
behaving
as a f u n c t i o n
of
Likewise,
rather
similar
As seen i n F i g . 4 ,
J
L_ 0.2
0.3
In f a c t ,
(MeV)
the
v a l u e s a l s o show a d r o p o f f
i n the s band.
I
17/2*
Λω
behavior.
an
increasing
frequency.
bands w i t h
d a t a show c l e a r
of
Y b shows o n e - and t h r e e - q u a s i
particle
The l a t t e r
i n t h e ground band as e x p e c t e d f o r
Yb
1 6 0
Y b t h e r e are t h r e e
each showing Q
for
F i g u r e 4 shows a p l o t
the
bands i n b o t h
two-quasiparticle
Er.
Yb.
there
feature
Y b show an o v e r a l l
1 6 0
1 5 8
1 6 1
unfor
A most i n t e r e s t i n g
For
Y b and
the
is present
loss of c o l l e c t i v i t y
1 6 0
3,
frequency
indicate
the data in F i g . 3 i s t h a t quasiparticle
in
sequence o f
too l i m i t e d to
whether t h i s
Er
according
,
i s a Clebsch-Gordon c o e f f i c i e n t .
and n e a r - y r a s t
Ν = 90 n u c l e u s .
ferent
from
t
< I 2 0 0 | 1-2 0 >
evidence of c e n t r i f u g a l
1 6 1
q u a d r u p o l e moments, Q , were o b t a i n e d
v a l u e s are p l o t t e d as a f u n c t i o n o f t h e r o t a t i o n a l
t
some y r a s t
1 5 8
lifetime
p r o j e c t e d c o i n c i d e n c e s p e c t r a and
quadrupole t r a n s i t i o n
where t h e t e r m i n b r a c k e t s
1 6 1
p o i n t , the preliminary
flight
expression B(E2:I-I-2)
ω.
18 r e c o i l
Discussion Experimental
and
301
Nuclear Shapes at High Spins
JOHNSON
the
f o r t h e 8 " , 9" and s bands
F i g . 3. T r a n s i t i o n quadrupole moments o f some y r a s t and n e a r y r a s t s t a t e s o f 160, i e i r o t a t i o n a l frequency.
Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
Y b
v s
302 of
NUCLEI OFF THE LINE OF STABILITY 158£
s
Γ
n
o
w
r e d u c i n g t r e n d when p l o t t e d as a f u n c t i o n o f r o t a t i o n a l
a
quency, although
i t i s l e s s pronounced t h a n i s t h e d a t a o f F i g . 3 .
mon a l i g n e d q u a s i p a r t i c l e orbital
with parity
bands i n
1 6 0
(ττ,α) = ( + , + 1 / 2 ) .
and ( - , - 1 / 2 )
h
9
/
Y b and t h e 8 " and 9 " bands i n
behavior of Q (+,+1/2)
i n a l l o f t h e s e bands i s t h e l o w e s t energy i
and s i g n a t u r e
coupled t o t h e ( - , + 1 / 2 )
with
t
2
orbitals 1 5 8
Er.
influence
x
3
/
This q u a s i p a r t i c l e
2
is
t o f o r m t h e 6 " and 9 " s i d e The s i m i l a r i t i e s
ω f o r t h e s e bands s u g g e s t t h e p o s s i b i l i t y
q u a s i n e u t r o n has a dominant
fre
The com
in the
that the i 1 3 / 2
on t h e c o r e .
A d d r e s s i n g t h e i d e a s d i s c u s s e d a b o v e , t h e group a t Lund has r e p o r t e d [BEN83] r e s u l t s calculations
of self-consistent
o f t h e shape o f
1 6 0
f i n d t h a t t h e 1 1 3 / 2 alignment
c r a n k e d H a r t r e e - F o c k - B o g o l i u b o v (HFB)
Y b as a f u n c t i o n o f a n g u l a r momentum.
produces a quadrupole d e f o r m a t i o n
near t h e g r o u n d - s t a t e v a l u e and w h i c h remains a p p r o x i m a t e l y spin. about tion, tive
However, t h e t r i a x i a l i t y
p a r a m e t e r γ shows a s t e a d y
10° by I = 1 8 , t h e h i g h e s t
spin they
+
of a prolate
with
increase,
reaching
( I n t h e Lund c o n v e n
ellipsoid
and γ = 60° c o r r e s p o n d s t o n o n c o l l e c rotations
o f an o b l a t e
Another t h e o r e t i c a l
and i t i n v o l v e s
ORNL-DWG 8 5 - 1 1 3 6 3
Ί
Γ
ellipsoid.) approach
has a l s o been t a k e n [LEA83]
cal
2
constant
γ = 0° c o r r e s p o n d s t o c o l l e c rotations
tive
reported.
They
ε which i s
O g BAND
[FRA83]
•
s BAND
a more p h e n o m e n o l o g i -
examination of the e f f e c t s
of the
γ degree o f freedom on t h e e n e r g y o f the quasiparticles cranked s h e l l
and t h e c o r e .
model
The
"5 *
(CSM) i s used t o
calculate the quasiparticle
energies
w h i c h a r e added t o t h e e n e r g y o f t h e r o t a t i n g c o r e as a f u n c t i o n o f γ . t h e N~90 t r a n s i t i o n quasiparticles
region, the i
qualitatively,
consistent
results
CSM r e s u l t s but w i l l
3
/
2
drive the equilibrium
v a l u e o f γ t o around 5 ° . least
x
In
So, at
both t h e s e l f -
for
1 6 0
L
SPIN
Y b and t h e
(calculated f o r
be v e r y s i m i l a r
J 12
for
1 6 0
Yb,
1 5 8
Er)
F i g . 4 . T r a n s i t i o n quadrupole moments o f y r a s t s t a t e s i n Er.
Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
1 5 8
45.
Nuclear Shapes at High Spins
JOHNSON
303
a r e seen t o be i n agreement w i t h o u r e x p e r i m e n t a l l y tivity
at high r o t a t i o n a l
we p o i n t
out t h a t
frequencies
should a l l
of the loss of c o l l e c t i v i t y
be a t t r i b u t e d t o t r i a x i a l i t y , o f 20° a t s p i n
observed l o s s of
in the q u a s i p a r t i c l e
it
is
bands.
i n t h e s e two
necessary t o invoke values of
If
is strongly
it
lies
l o w e s t energy f o r
low i n t h e s h e l l , t h e n t h e h i g h - j γ > 0.
to collective
rotations
n e u t r o n Fermi
surface
When t h e Fermi giving
surface
excess
mation d r i v i n g
it
lies
potential
resistant
of
has γ
conforming
a n u c l e u s whose
near t h e m i d d l e o f t h e 1*13/2 s h e l l
i s e x p e c t e d t o be r e l a t i v e l y
surface
near mid s h e l l ,
Admittedly,
w e l 1 - d e f o r m e d r o t o r w i t h a pronounced minimum i n i t s and, t h e r e f o r e ,
deformation
quasiparticle
rise to t r i a x i a l i t y
o f an o b l a t e e l l i p s o i d .
lies
the
a f f e c t e d by t h e l o c a t i o n o f t h e Fermi
t e n d s t o move t o t h e n e g a t i v e s e c t o r ,
s h o u l d be a energy
to t r i axial
surface defor
influences.
I n measuring t h e l i f e t i m e s is
nuclei
+
An i n t e r e s t i n g a s p e t o f t h e CSM approach above i s t h a t
its
γ in
18 .
d r i v i n g tendency a nucleus.
collec
However,
of h i g h - s p i n
states
in
1 7 2
W
(N = 9 8 , w h i c h
near t h e m i d d l e o f t h e i 1 3 / 2
s h e l l ) , we d i d not a n t i c i p a t e
a
significant
collec
tivity
difference
at spins
18-20 i n t h e
sequence f r o m t h a t ground band.
in the
yrast
f o u n d low i n
At t h i s
[RA085] have o n l y p a r t i a l l y
completed
t h e d a t a a n l a y s e s , but t o o u r p r i s e , the Q
t
values of
in Fig. 5 display
1 7 2
a very
W
very
This
sur shown
similar
b e h a v i o r t o t h e much s o f t e r near Ν = 9 0 .
the
p o i n t we
result
nuclei
raises
i n t e r e s t i n g questions
some
relating
t o w h i c h degrees o f freedom a r e c h a n g i n g t o produce t h i s viously,
additional
ments o f n u c l e i important;
effect.
lifetime
Ob
measure
near Ν = 96-100 a r e
but t h e search f o r
better
t o a c c o u n t f o r such p h e __ nomena i s e q u a l l y demanded.
2 + 6 8 10
16 18 20
SPIN
theories
F i g . 5. T r a n s i t i o n quadrupole moments of y r a s t s t a t e s i n W.
Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
1 7 2
304
NUCLEI OFF THE LINE OF STABILITY
Acknowledgments The f o l l o w i n g c o l l a b o r a t o r s a r e t o be t h a n k e d f o r t h e i r r o l e s i n c a r r y i n g out the research discussed here: Hattula,
I.Y.
M.P. F e w e l l , F.K. McGowan, J . H .
L e e , C. B a k t a s h , Y. S c h u t z , J.W. J o h n s o n , J . C . W e l l s ,
L.L.
R i e d i n g e r , M.W. G u i d r y , S . C . P a n c h o l i , M. Oshima, R.V. R i b a s , M.N. Rao, K. E r b , J.W. McConnell and A. L a r a b e e .
References [BEN83] R. Bengtsson, Y-D. Chen, J-S. Zhang and S. Aberg, Nucl. Phys. A405, 221 (1983). [FEW82] M.P. Fewell, J . Hattula, D.R. Haenni, N.R. Johnson, J.W. Johnson, I.Y. Lee, F.K. McGowan, L . L . Riedinger, J.C. Wells, and S.C. Pancholi, B u l l . Am. Phys. Soc. 27, 522 (1982). [FEW82] M.P. Fewell, J.S. Hattula, N.R. Johnson, I.Y. Lee, F.K. McGowan, H. Ower, S.C. Pancholi, L . L . Riedinger, and J.C. Wells, in Proc. of the Conf. on High Angular Momentum Properties of Nuclei, Oak Ridge, TN, Nov. 1982, ed. by N.R. Johnson, Nuclear Science Research Conf. Series, Vol. 4 (Harwood Academic, New York, 1983), p. 69. [FEW85] M.P. Fewell, N.R. Johnson, F.K. McGowan, J.S. Hattula, I.Y. Lee, C. Baktash, Y. Schutz, J.C. Wells, L . L . Riedinger, M.W. Guidry, and S.C. Pancholi, Phys. Rev. C, 31, 1057 (1985). [FRA83] S. Frauendorf and F.R. May, Phys. Lett. 125B, 245 (1983). [JAM75] F. James and M. Roos, Comput. Phys. Commun. 10, 343 (1975). [JOH81] N.R. Johnson, J.W. Johnson, I.Y. Lee, J . E . Weidley, D.R. Haenni, and J.R. Tarrant, ORNL Phys. Div. Prog. Report No. ORNL-5787, 1981, p. 147. [JOH82] N.R. Johnson, in Proc. of the 1982 Inst. for Nuclear Study Intnl. Symposium on Dynamics of Nuclear Collective Motion, ed. by K. Ogawa and K. Tanahe (Inst. for Nuclear Study, Univ. of Tokyo, 1982), p. 144. [LEA83] G.A. Leander, S. Frauendorf and F.R. May, Proc. Conf. on High Angular Momentum Properties of Nuclei, Vol. 4, Nuclear Science Research Conf. Series, ed. by N.R. Johnson (Harwood Academic Publishers, New York, 1983) p. 281. [OSH84a] M. Oshima, N.R. Johnson, F.K. McGowan, I.Y. Lee, C. Baktash, R.V. Ribas, Y. Schutz, and J.C. Wells, B u l l . Am. Phys. Soc. 29, 1043 (1984). [OSH84b] M. Oshima, N.R. Johnson, F.K. McGowan, I.Y. Lee, C. Baktash, R.V. Ribas, Y. Schutz, and J . C . Wells, ORNL Phys. Div. Prog. Report, ORNL-6120 (1984) p., 77. [RAO85] M.N. Rao, N.R. Johnson, C. Baktash, F.K. McGowan, I.Y. Lee, K. Erb, J.W. McConnell, M. Oshima, J.C. Wells, A. Larabee and L . L . Riedinger, unpub. [STU76] R . J . Sturm and M.W. Guidry, Nucl. Instrum. Methods 138, 345 (1976). [WEL85] J.C. Wells, M.P. Fewell and N.R. Johnson, ORNL/TM-9105 (1985). RECEIVED July 15, 1986
Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.
