Annual Report 2012 - Latvijas Universitātes Cietvielu fizikas institūts

much higher than that predicted by model calculations. Such increased level density
indicates non-axial deformation, at least for some of 188 Re states. A possibility of nonaxial
deformation for nuclear states including neutron orbits with high orbital moment j
values, e.g., 11/2[615] and 9/2[505], in A~190 region tungsten and osmium isotopes has
been considered also in [2].
In order to resolve that problem, we have performed extensive model calculations
employing the modified oscillator particle-plus-rotor model [3]. When γ≠0, particle's
angular momentum j projection on the nuclear core symmetry axis Ω is not conserved,
and the particle wave function includes all N shell oscillator state components |Nljs>
with corresponding projections j z. It means that one can employ the asymptotic quantum
numbers Ω π [Nn z Λ] for nuclear state classification only approximately. Calculations
have been performed both for the odd-odd nucleus 188 Re (Z=75,N=113), and for its odd
neutron neighbor 187 W (Z=74,N=113). The dependence of quasiparticle energies and
wave functions on the core non-axiality angle γ value have been studied for all low-lying
valence proton and neutron orbits. The polarization energy and the γ stability for each
particle state has been determined. It has been found that most orbits with high j values,
e.g., i 13/2 neutron orbit 11/2[615], or h 11/2 proton orbit 9/2[514], are γ stable. On the
contrary, the energy of neutron orbits 3/2[512] (f 5/2 ) and 9/2[505] (h 9/2 ) changes
drastically. For some low j value states increased fragmentation results even in the
change of particle orbit, e.g., the main component of the p 3/2 orbit 1/2[510] changes to
that of the f 5/2 orbit 1/2[521] already at γ=10º.
In the case of odd-odd nuclei, the resulting level scheme depends considerably also on
the residual (i.e., not included in the nuclear mean field) NN-interaction between valence
particles. Proton and neutron pairs form level multiplets with energy difference
(Gallagher-Moszkowski (GM) splitting) depending on singlet or triplet orientation of
particle spins. Other important effects of the residual NN-interaction are: a) the odd-even
spin level energy shift (Newby shift) in K=0 rotational bands; b) the ΔK=0 mixing
between two-quasiparticle states. In the scope of our model calculations, we have
studied the behavior of residual NN-interaction matrix elements on the nuclear nonaxiality
angle γ value. The values of corresponding V np matrix elements have been
calculated using expressions and parameter values given in [4]. It has been found that in
order to reproduce the experimentally observed GM-splittings in 188 Re, one should
include in the V np both the short and the long range central interaction components, as
well as the terms accounting for the polarization of nuclear core. Study of the γ-
dependence of residual NN-interaction has shown that, because of increased
fragmentation of particle wave functions, the values of most V np matrix elements
become smaller, though the well-known GM-rule (i.e., the spin triplet state has lower
energy value in odd-odd nuclei) remains true also in the case of non-axial deformation.
However, the behavior in dependence on γ of the matrix elements responsible for ΔK=0
mixing is chaotic. Since the role of ΔK=0 mixing in non-axial nuclei is greater than in
axially-symmetric ones due to increased number of states with same K value, the
resulting fragmentation of two-quasiparticle states in the case of non-axial deformation
becomes very complex.
In general, our results show that the traditional particle-plus-rotor model interpretation
of odd-odd transitional nuclei level schemes at energies above 500 keV is questionable.
The only confident characteristics of excited levels are their energy, spin, and parity. If
one intends to use for classification of nuclear levels the rotational bands based on
Nilsson two-quasiparticle states, one should check for γ stability of involved states, as
well as for possible fragmentation.
The results of our level energy and electromagnetic transition calculations in the case of
odd 187 W have shown that one cannot regard the existence of positive parity “inverted
bands”, observed in the level schemes of odd 183,185,187 W nuclei, as a firm indication of
non-axial deformation. Observed levels can be interpreted as the band heads based on
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