Volume 171, number 2,3 PHYSICS LETTERS B 24 April 1986
OCTUPOLE EXCITATIONS IN 0(6) NUCLEI
J. ENGEL
A. IV.. Wright Nuclear Structure Laboratory, Yale University, New Haven, CT06511, USA
Received 20 January 1986
The coupling is discussed of an octupole boson to an 0(6) core in the interacting boson approximation, and the results are
applied to several platinum isotopes.
Many of the low-lying negative-parity states in the
rare-earth region of the periodic table have been suc-
cessfully interpreted as octupole (L 7r = 3-) shape vi-
brations around a spherical or quadrupole deformed
ground-state shape. These vibrations have been dis-
cussed in different contexts; a quasiparticle RPA was
applied [1] systematically throughout a large part of
the rare-earth region and f bosons have been incorpo-
rated into the interacting boson approximation
(IBA) to describe negative-parity excitations phe-
nomenologically. In the latter model, the coupling
of an f boson to the usual s and d bosons in the U(5)
and SU(3) analytic limits was discussed very early on
[2] and successfully applied in a description of
samarium isotopes [3]. However, an analysis of the
coupling to an 0(6) [4] core - that is, a "r-unstable or
triaxial nucleus - has never appeared. In what follows
we discuss this case and apply the results to the low-
spin negative-parity states in 190pt-196pt.
The collective positive-parity states in many nuclei
have been fit by an 0(6) IBA hamiltonian of the form
H = -r Qsd. Qsd + r'L "L , (1)
where
QSd = d;s + std., (2)
L u = ~ (2a, 2~ll~u)d?od¢ ,
d, = (-)"d_u ,
and the dot stands as usual for the scalar product of
148
two tensors. The spectrum associated with this
hamiltonian is shown in ref. [4] ; a characteristic fea-
ture is a low-lying 7 band. In the spirit of previous
IBA studies of f coupling, we have added to the above
hamiltonian an additional piece
H' = enf + [3Qf " Qsd , (3)
where
Qu f = ~ (3a, 3/312#)f~ , (4)
at3
and nf is the number of f bosons. Although we were
not able to diagonalize this interaction analytically,
we examined the results numerically for several dif-
ferent sets of parameter values; the states organize
themselves into a regular pattern, an example of
which appears in fig. 1. This result is reminiscent of
that obtained when coupling a particle of half-integer
spin to an 0(6) core in the interacting boson-fermion
approximation [5].
We now turn to the nuclei 190pt-196pt, where
0(6) is known [6] to provide a reasonable approxi-
mation to the positive-parity energy levels and a good
description of transition rates. These isotopes were
studied some years ago [7] in terms of a "semi-de-
coupled model" in which the negative-parity states
could be expressed as linear combinations of two-
quasiparticle states in a triaxial one-body field. The
results of these calculations indicate that states with
J ~< 4 are essentially of octupole phonon type (cohe-
rent coupling of quasiparticles to L = 3) while those
with J/> 5 have different structure. This conclusion
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