nucleus | force | ![]() |
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SLy4 | ![]() |
0.24 | 49 | 4.81 | 29.2 | 17.0 | 5.41 | 4.86 | 0.46 | 12.8 | ||
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0.24 | 49 | 5.50 | 37.1 | 21.3 | 5.45 | 5.16 | 0.37 | 13.2 | ||||
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0.24 | 49 | 4.16 | 29.4 | 19.9 | 5.49 | 5.20 | 0.59 | 16.8 | ||||
SkM* | ![]() |
0.23 | 47 | 5.86 | 31.3 | 17.9 | 5.43 | 5.01 | 0.43 | 13.0 | |||
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0.23 | 47 | 6.55 | 36.7 | 21.1 | 5.47 | 4.97 | 0.37 | 13.0 | ||||
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0.23 | 47 | 5.69 | 33.4 | 20.0 | 5.49 | 5.14 | 0.43 | 13.9 | ||||
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SLy4 | ![]() |
0.26 | 46 | 7.18 | 28.7 | 19.1 | 5.44 | 4.90 | 0.57 | 15.9 | 0.68 | 18.8 |
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0.26 | 46 | 8.45 | 36.0 | 23.7 | 5.60 | 5.21 | 0.47 | 16.4 | 0.60 | 20.3 | ||
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0.26 | 46 | 7.12 | 31.7 | 22.2 | 5.64 | 5.26 | 0.60 | 18.5 | ||||
SkM* | ![]() |
0.25 | 45 | 8.19 | 30.8 | 20.3 | 5.47 | 5.03 | 0.54 | 16.0 | 0.62 | 17.8 | |
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0.25 | 45 | 8.81 | 35.9 | 23.5 | 5.60 | 5.06 | 0.46 | 15.9 | 0.54 | 17.8 | ||
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0.25 | 45 | 8.37 | 34.0 | 22.4 | 5.63 | 5.21 | 0.50 | 16.5 | 0.58 | 18.5 | ||
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SLy4 | ![]() |
0.26 | 58 | 6.11 | 25.4 | 5.00 | 4.36 | |||||
oblate | ![]() |
0.26 | 58 | 7.21 | 31.3 | 4.92 | 4.84 | ||||||
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0.26 | 56 | 3.68 | 29.8 | 5.26 | 4.60 | |||||||
SkM* | ![]() |
0.23 | 22 | 18.5 | 28.1 | 20.7 | 5.38 | 5.28 | 0.91 | 25.0 | |||
triaxial | ![]() |
0.23 | 22 | 21.4 | 32.6 | 24.3 | 5.46 | 5.44 | 0.82 | 26.1 | |||
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0.23 | 22 | 20.7 | 30.8 | 24.8 | 5.52 | 5.57 | 1.08 | 32.7 | ||||
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SLy4 | ![]() |
0.25 | 53 | 24.7 | 4.62 | |||||||
oblate | ![]() |
0.25 | 53 | 30.3 | 5.38 | ||||||||
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0.25 | 52 | 29.0 | 5.05 | |||||||||
SkM* | ![]() |
0.22 | 19 | 15.0 | 27.5 | 12.4 | 5.32 | 5.38 | 0.56 | 14.8 | |||
triaxial | ![]() |
0.22 | 19 | 17.9 | 33.2 | 13.0 | 5.50 | 5.42 | 0.45 | 14.4 | |||
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0.22 | 19 | 17.4 | 29.8 | 13.4 | 5.51 | 5.53 | 0.56 | 16.1 |
As the first step, the HF calculations without cranking were performed to
find the
bandheads. Obviously,
the energetically most favored state of this configuration is
obtained if the valence proton particle and neutron hole occupy the
lowest and highest levels of the
multiplets, respectively.
Table 1 gives the obtained
and
deformations for each isotone and Skyrme parameter set. They
practically do not depend on the included time-odd terms, and remain
almost constant when cranking is applied later on in our calculations. Note
that the present values of
are up to 1.5 times larger than
those found in the PQTAC/SCTAC calculations quoted
in Section 3.1. Also the values of
are more distant from the maximum
triaxiality of
as compared to the earlier results by other authors.
In Pr and
Pm, two minima with the same
configuration were found, which differ by the occupation of
positive-parity states. The energetically lower minima have similar
positive-parity s.p. structure as in
Cs and
La, but they
correspond to almost oblate shapes of
-to-
. The
other minima have
-to-
, thus corresponding to
triaxial shapes. In the following, those two kinds of minima in
Pr and
Pm are conventionally referred to as oblate and triaxial.
Such a structure of minima and configurations appears for both interactions
studied here, SkM* and SLy4, and the corresponding sets of results are very similar
to one another. Therefore, to save space, below only the SkM* results are shown for
the triaxial minima, and only the SLy4 results for the oblate ones.
In Section 2, we introduced the intrinsic frame of a
nucleus as formed by the principal axes of the quadrupole tensor.
Below, by the short (), medium (
), and long (
) axes of our
triaxial solutions we understand the intrinsic axes indexed so that
,
where
is the Cartesian coordinate for axis
,
, or
.