Rotational inertia of superdeformed nuclei: Intruder orbitals, pairing, and identical bands
G. de France,
1
C. Baktash,
2
B. Haas,
1
and W. Nazarewicz
2–4
1
Centre de Recherches Nucle ´aires, IN2P3-CNRS/Universite ´ Louis Pasteur, F-67037 Strasbourg Cedex, France
2
Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
3
Department of Physics, University of Tennessee, Knoxville, Tennessee 37996
4
Institute of Theoretical Physics, Warsaw University, ul. Hoz ˙a 69, PL-00-681 Warsaw, Poland
Received 11 August 1995
The phenomenon of identical bands is studied by analyzing the distributions of fractional changes in the
dynamical moments of inertia of pairs of bands in superdeformed SD nuclei. These distributions are found to
exhibit a peak with a centroid at nearly zero. Their widths increase in going from the SD bands in the mass
A 150, to the SD bands in the mass 190, and to the normally deformed bands in the rare-earth region.
Consequently, there exists a significant excess of identical bands in SD nuclei compared to the normally-
deformed nuclei at low spins. This difference may be attributed to the weaker pairing correlations and the
stabilizing role of intruder orbitals on the structures of SD bands.
PACS numbers: 21.10.Re, 21.60.Jz, 23.20.Lv
Observation of rotational bands in different nuclei which
have nearly identical moments of inertia and, occasionally,
nearly identical -ray energies has been one of the most
exciting discoveries in low-energy nuclear physics in recent
years 1. These identical bands exist at both low and high
spins, and span a wide variety of shapes 2–9. The first pair
of superdeformed SD identical bands IB’s discovered was
an excited band in
151
Tb whose -ray energies are identical
to those in the yrast band of
152
Dy to within 1.5 keV over
20 transitions 2. This similarity implies that the dynamical
moment of inertia, J
(2)
, of the two bands are the same to
within a few parts per thousand. ( J
(2)
is defined as
4/ E
, where E
is the difference in the energies of two
consecutive rays in a band of stretched electric quadrupole
transitions. This is extremely surprising since the variation
just due to the mass difference between the two nuclei is
expected to be one order of magnitude larger. The discovery
of IB’s implies that, contrary to expectations, in some cases
the valence particles or holes have only a very weak effect
on the corresponding core. That is, they play the role of
weakly coupled spectators. So far, despite intense theoretical
efforts aimed at the understanding of the IB phenomenon, no
definitive scenario has yet emerged 1. An extensive bibli-
ography of both the experimental data and the theoretical
work related to the question of IB’s is reviewed in Ref. 1.
Since the advent of new and highly efficient -ray spec-
trometers such as Eurogam, Gammasphere, and Ga.Sp, nu-
merous pairs of IB’s have been discovered in the SD mass
regions A 130, A 150, and A 190 nuclei. With the avail-
ability of a relatively large set of data on IB’s, it is now
possible to investigate the following questions. First, is there
an excess of IB’s among superdeformed nuclei versus nor-
mally deformed nuclei? Second, if the distributions of the
moments of inertia of the SD and normally deformed bands
are significantly different, can the differences be traced to
any of the special properties of the SD bands such as the
presence of large shell effects or reduced pairing correla-
tions? The present study provides affirmative answers to both
of these questions.
In this work, we have adopted the general definition that
two bands are identical if they exhibit an anomalously small
difference as defined later in their J
(2)
. To assess the de-
gree of similarity between the J
(2)
of band ( n ) in nucleus
X , X ( n ), and the band ( m ) in nucleus Y , Y ( m ), we have
first evaluated the fractional change FC in their J
(2)
:
FC
X n , Y m
J
X n
2
-J
Y m
2
/ J
X n
2
= J
2
/ J
X n
2
.
1
The nucleus Y , to which the reference band belongs, was
taken to be the lighter of the two nuclei. The quantity FC has
the advantage of being independent of the absolute spin, I .
Instead, it depends only on the relative spin alignments of the
two bands defined as i ( ) =I
X( n )
( ) -I
Y ( m)
( ), where
=E
/2 is the rotational frequency. Since the absolute spin
values of SD bands have not yet been experimentally deter-
mined, one can alternatively use the effective spin alignment
i
eff
=i mod1. As shown in Ref. 10, the FC is related to the
effective alignment by the relation
FC
X n , Y m
=di / dI
X n
=di
eff
/ dI
X n
. 2
In situations where i
eff
is a linear function of I , the average
slope of this linear function yields the average fractional
change, FC. In this work, we have extracted FC via a linear
least-squares fit to i
eff
. This technique is particularly useful
when comparing J
(2)
of SD bands which typically consist of
long cascades of rays ( 15 transitions on average.
We imposed two successive conditions to select the IB’s.
First, to ensure that a good least-squares fit is obtained, we
required that the resulting standard deviation must be less
than 0.05. In calculating the standard deviation we have not
assigned any uncertainties to the reported -ray energies. In
situations where band interactions introduced local disconti-
nuities in J
(2)
, we excluded from the least-squares fit up to
20% of the data points. Second, in order for two SD bands
to be identical, we demanded that their FC value should be
less than half the expected change in the moments of inertia
of two rigid bodies due to their mass difference, A .
The data set considered for this analysis consisted of 18
highly deformed bands in the mass A 130 region, 54 SD
PHYSICAL REVIEW C MARCH 1996 VOLUME 53, NUMBER 3
53 0556-2813/96/533/10704/$10.00 R1070 © 1996 The American Physical Society