Octupole correlations in U and Pu nuclei
N. V. Zamfir
1,2,3
and Dimitri Kusnezov
4
1
Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut06520-8124
2
Clark University, Worcester, Massachusetts01610
3
National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania
4
Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut06520-8120
Received 11 September 2002; published 17 January 2003
We study the even-even U and Pu nuclei in the framework of the spdf interacting boson model. Analysis of
the systematics of positive and negative parity bands, together with the E 1, E 2, and E 3 transitions, suggests
that the properties of low-lying states can be understood without the introduction of stable octupole deforma-
tion. Double octupole phonon characteristics are also identified in certain low-lying 0
+
excited states in U
and Pu.
DOI: 10.1103/PhysRevC.67.014305 PACS numbers: 21.60.Fw, 21.10.Re, 23.20.Lv, 27.90.+b
I. INTRODUCTION
Octupole correlations in the actinides have attracted inter-
est since the predictions that octupole deformation would be
present in the Z 88 and N 134 region 1. These predic-
tions have been explored through a series of experimental
studies, which have centered on energy spectra and transition
properties 2. Numerous theoretical studies were dedicated
over the years to the octupole degree of freedom in nuclei
2,3. A suitable and versatile model for the description of
quadrupole-octupole collective degrees of freedom in even-
even nuclei is the interacting boson model IBM4. Re-
cently, an extensive study of the collective negative parity
states in the even-even Ra-Th nuclei was completed 5 in
the framework of the spdf IBM 6. In that study, a consis-
tent picture was obtained over the entire nuclear region of the
light actinides using a minimal Hamiltonian. The aim of this
work is to extend that analysis to U and Pu nuclei, providing
a consistent view of the systematics of the even and odd
parity states from Z =86 to Z =94.
We will examine the full systematics of all available data
on energies and electromagnetic transitions. The data are
from Refs. 7–19. The full spdf IBM Hamiltonian contains
over 50 interaction terms, however, simple physical consid-
erations can reduce the form of the Hamiltonian H 20. We
will use a four parameter model for H, which includes a
single quadrupole strength and three boson single particle
energies. The form of the Hamiltonian and transition opera-
tors are further constrained by the recent analysis of the Rn,
Ra, and Th nuclei. We would like to see whether octupole
deformation is an essential ingredient in the understanding of
the nuclei in this mass region.
II. spdf INTERACTING BOSON MODEL
The interacting boson model offers a phenomenological
approach of collective nuclear structure by introducing
bosons of a given spin, which are associated with the corre-
sponding multipole modes. The quadrupole vibrations and
deformations are described in terms of interacting s and d
bosons with L
=0
+
and L
=2
+
, respectively. Negative
parity states are described by introducing bosons with odd
values of angular momentum. In the sdf model, only f ( L
=3
-
) bosons are used 4,21,22, while in the spdf model,
both f and p ( L
=1
-
) bosons are included see, for example,
Ref. 5, and references therein. The spdf is the preferred
model since it is closer in spirit to the sd IBM, including the
same dynamical symmetry limits as well as the possibility of
octupole deformation.
We are interested in studying the behavior of negative
parity states in a region of large quadrupole deformation very
close to the SU
sd
(3) limit. This requires a minimal Hamil-
tonian to include a vibrational contribution and a quadrupole
interaction. The simplest form of such a Hamiltonian for
positive parity states is H =
d
n
ˆ
d
- Q
ˆ
sd
• Q
ˆ
sd
. The natural
extension of this Hamiltonian to describe both positive and
negative parity states simultaneously is realized in the spdf
model as
H =
d
n
ˆ
d
+
p
n
ˆ
p
+
f
n
ˆ
f
- Q
ˆ
spdf
• Q
ˆ
spdf
, 1
where
p
,
d
, and
f
are the boson energies and n
ˆ
p
, n
ˆ
d
, and
n
ˆ
f
are the boson number operators. This is the same Hamil-
tonian used to describe the transitional actinides in Ref. 5.
The spdf model space admits a SU
spdf
(3) limit which is the
natural extension of the SU
sd
(3) limit of the sd IBM. In the
spdf model, the quadrupole operator is given by
Q
ˆ
spdf
=Q
ˆ
sd
+Q
ˆ
pf
= s
†
d
˜
+d
†
s -
7
2
d
†
d
˜
(2)
+
3 7
5
p
†
f
˜
+ f
†
p
˜
(2)
-
9 3
10
p
†
p
˜
(2)
-
3 42
10
f
†
f
˜
(2)
.
2
This is related to the Casimir operator of the SU
spdf
(3) sub-
group. Note that the same strength of the quadrupole in-
teraction describes the sd bosons and the pf bosons.
The transition operators T ( E 1), T ( E 2), and T ( E 3) are
not all defined from dynamical symmetry considerations, so
PHYSICAL REVIEW C 67, 014305 2003
0556-2813/2003/671/0143058/$20.00 ©2003 The American Physical Society 67 014305-1