The ground state of the 32S nucleus, obtained within the
HF approach with the SLy4 force,
corresponds to a spherical-shape configuration that contains,
on top of the closed 16O core, the
1d5/2 and 2s1/2 orbitals filled, both for the neutrons and protons.
With an increase in the prolate deformation, the
negative-parity Nilsson orbitals originating from the spherical
16O core stay occupied (see Fig. 2.21a in Ref. [39]
for a qualitative illustration). The same is true for the
positive-parity valence orbitals, except for the orbital
[202]5/2 (the up-sloping extruder orbital), which originates
from the spherical 1d5/2 shell, and rapidly grows up in energy
with increasing deformation. After this orbital is crossed
by the [330]1/2 orbital (the down-sloping intruder orbital),
which originates from the spherical 1f7/2 shell, one obtains a
large, about 2.5MeV gap that corresponds to a SD
configuration in the 32S nucleus. Therefore, the SD states in such a
light system as 32S, formally correspond to the 4p-4h excitation
with respect to the spherical ground state.
However, our calculations presented in detail below indicate that the SD
configurations
have extremely large quadrupole deformations, 0.7, and the
implied structures of the SD, ND (normal deformed), or spherical wave
functions have so little similarities that the notion of particle-hole
excitations with respect to the spherical ground-state is not very useful.
Figures 1 and 2 show the neutron and proton
single-particle routhians, as functions of the cranking
frequency
.
One can see that over a very
large range of the rotational frequencies, there exists an
important gap in the single-particle HF spectrum at
the neutron and proton numbers N=Z=16. By definition, in the underlying 32S
SD configuration all the neutron and proton levels lying
below the gaps at N=16 and Z=16 are occupied, and
all those above the gaps are empty.
As a result of the presence of those large gaps in the single-particle 32S proton and neutron spectra, we refer to the corresponding lowest-energy SD state as to the magic SD configuration.
A characteristic result visible from Figs. 1 and 2
is that the over-all single-particle structure of the HF orbitals near the
Fermi level is remarkably simple. First of all, the dependence of the
single-particle routhians on the
rotational frequency is very regular, and there is only one clear-cut
crossing caused by the down-sloping routhians [440]1/2(r=-i),
originating from the N0=4
shell. Second, the density of levels appearing in the figures is very low
as compared, e.g.,
to those in the mass A150 region of SD nuclei.
The negative parity states are represented only by two N0=3 intruder
orbitals [330]1/2(r=
)
below, and two intruder orbitals [321]3/2(r=
)
above the Fermi level. Similarly, in the positive
parity there are only two states [211]1/2(r=
)
below, and two
extruder states [202]5/2(r=
)
above the Fermi level.
Signature splitting of the extruder states [202]5/2(r=
)
is very weak, because they carry high K=5/2 angular momentum projection,
whereas splitting between the intruder levels [321]3/2(r=
)
is more pronounced. It becomes well visible at rotational
frequencies of about 0.8MeV. Below the Fermi level,
orbitals [330]1/2(r=
)
and [211]1/2(r=
)
have K=1/2, hence both
are strongly split.