The Nilsson diagrams, shown in
Figs. 1-3, have been
obtained by diagonalizing the self-consistent mean-field Hamiltonians
corresponding to the states that were constraint to a sequence of values of the
axial mass quadrupole moment [60],
. Then,
by using a simple phenomenological formula [61],
FigSHE01.eps |
FigSHE02.eps |
FigSHE03a.eps
FigSHE03b.eps
FigSHE03c.eps
FigSHE03d.eps |
As we can see, for all considered EDFs, the overall positions and
deformation-dependence of single-particle levels is fairly
similar. In particular, deformed shell gaps, which appear near
ground-state deformations of ,
occur at particle numbers of
,
and
and/or
in the majority of the functionals. The only exception is the functional NL3*,
which is characterized by additional gaps at
and
. Another deformed gap at
is observed for
. Moreover,
significant differences in important details are also visible. The
proton deformed shell gaps appear consistently above the one at
that is tentatively inferred from the experimental data,
see discussion in Refs. [8,21].
Interestingly, although different EDFs show similar deformed
neutron shell closures, we observe dramatic differences in the shell structure at
sphericity between the Skyrme EDF UNEDF2 and the other ones, as shown in
Fig. 1. Compared to SLy4, spherical orbital
(
) is lowered (raised) by about 2MeV,
and thus their relative positions are inverted, resulting in
the spherical shell gaps at
and 170, whereas other EDFs predict
shell gaps at
.
The strong rearrangement of spherical neutron shells observed for UNEDF2
as compared to all other EDFs is a consequence of its rather large
and
coupling constants of the spin-current tensor
terms of this parameterization [27]. In the
region,
the inversion of the spherical level sequence substantially increases the
number of filled spherical shells for which the spin-orbit partner is empty,
thereby increasing the size of the spin-current terms. In fact, such behaviour is
often found at mid-shell for parameterizations with large attractive tensor
terms [65,66].
The relativistic NL1 and NL3* functionals have the unique feature that they
predict a large spherical gap of about 3MeV that is absent in
all non-relativistic calculations. As the sequence of spherical subshells
is different, for NL1 this gap is located between the
and
levels, whereas for NL3* it is found between the
and
levels.
Jacek Dobaczewski 2015-08-21