Energies

In Fig. 6 are plotted the HF energies as functions of
spin for the 30 SD bands calculated in ^{32}S.
As it is often done in the cranking approach, we identify the average
projection of the angular momentum on the
cranking axis
with the total
angular momentum of the system, i.e., we set *I*=
.
(Within a more refined approximation some authors identify
*I*(*I*+1) with
[39],
what results in a standard (approximate) correction
*I*=
;
however, this is not implemented in the figures presented below.)

All the bands have been obtained within the cranking HF
formalism, with the rotational frequencies that start at
=0.4MeV and increase in steps of 0.2MeV.
For each band, the calculations were carried out up to the highest
rotational frequencies that did not induce any sudden
configuration change. Since almost all bands are crossed at
high rotational frequencies by the bands involving
the down-sloping [440]1/2(*r*=-*i*) orbital, cf. Figs. 1 and
2, and Ref. [28], such configuration
changes are in many cases inevitable. On the one hand, introducing an
upper limit of the frequencies of some calculated bands reflects a deficiency
of the method since the discussed crossings are in
general the physical ones. On the other hand, however, the
corresponding experimental results are expected
to deviate from regularity at the vicinity of the calculated limiting
values and are likely to manifest, e.g., an up- or even a
back-bending behavior there, thus offering a possibility of valuable tests
of the crossing frequencies anyway.

Let us remark in passing that within the HO model, when two protons and two
neutrons in the HO [440]1/2 states are added to the ^{32}S SD
configuration, one obtains the magic hyperdeformed HO
configuration in ^{36}Ar. Structures based on the [440]1/2(*r*=-*i*)
orbitals are abundant in ^{32}S, however, they should rather
be attributed to the hyperdeformed configurations, and are not
studied in the present article.

Bands shown in Fig. 6 have been separated into four
groups, plotted in four panels.
Figures 6(a), (b), (c), and (d)
show the 3^{n}3^{p} bands with *p*=*n*, *p*=*n*+1, *p*=*n*+2,
and *p**n*+3, respectively. Parities of bands are equal
to the products of parities of the proton and neutron configurations,
i.e., =
(-1)^{n+p} in our case,
and are denoted by full (=+1)
and open (=-1) symbols. Various forms of the symbols (circles, squares,
etc.) distinguish different values of *n*.
In order to further differentiate between various configurations,
we have to introduce a convention relating the line styles with the
signatures of neutron *and* proton subsystems, *r*_{n} and *r*_{p}.
Hence, long-short-dashed, solid, dotted, and dashed lines
denote (*r*_{n},*r*_{p})=(+,+), (+,-), (-,+), and (-,-)
signatures, respectively. Of course the total signature *r*of each band is always equal to *r*=*r*_{n}*r*_{p}.

Since we are mostly interested in the low energy configurations,
in Fig. 7 we show a blow-up of
the near-yrast region of energies, for a selection of bands being
closest to the yrast band. At *I*=
= 6
(with the standard spin correction
of
here subtracted), we
obtain in the 3^{0}3^{0} band the total energy of
*E*=-261.651MeV, which gives the calculated excitation energy
of *E*_{x}(*I*=)=8.349MeV, ridiculously close to the
experimental energy, 8.346MeV [31,32], of the
6^{+} yrast state in ^{32}S. Of course, an agreement on this level
of precision is to a large extent accidental, however, it gives us
confidence that a correct configuration is being followed at low
excitation energies.

At low spins, the yrast line is first
built upon the ground-state 3^{0}3^{0} configuration whose
energy increases very regularly up to the angular momentum of
*I*9
and excitation energy of *E*_{x}14.5MeV.
At *I*9-10,
the one-intruder
configurations 3^{0}3^{1} become yrast for a narrow region of spins.
These bands are next crossed at *E*_{x}16.2MeV by two
bands with *r*=+1, the 3^{1}3^{1} configurations,
which are yrast up to about *I*15.
At this
point (*E*_{x}25MeV) the yrast line has the structure of the magic
3^{2}3^{2} SD configuration. When extrapolated to zero spin, the magic SD
configuration corresponds to the excitation energy of *E*_{x}14MeV.

The spin (energy) range of up to *I*6
(10MeV)
can be very well described by the *sd* shell-model
calculations [32], and in the rest of this article we will
focus on the higher spin states.
[Some collective bands in the low spin (energy) range may be unstable with
respect to parity-breaking deformations [28]; we do not study those
effects either.]