In this section, we present results obtained by using the regularization
method proposed by A. Bulgac and Y. Yu [9]. Calculations
have been made with the same box size and integration step as
in the previous section, and the partial waves have been included up to .
The effective force used is SLy4, see table 1,
combined with the mixed pairing force with
parameters given in table 2.
When evaluating the densities, contributions of quasiparticle states are
included up to the maximum equivalent
energy
, see Eq. (47),
but once this maximum energy is high enough the
global properties of the nucleus do not depend on it.
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It appears that the stability of results is
very satisfying, even
for a very exotic nucleus. This is shown in Figure 6, where
the total energy and mean neutron gap are displayed as functions
of
for
Sn and
Sn.
For
greater than 60 MeV, where the total energy does
not show any significant evolution, we have evaluated its asymptotic
limit
, and the analogous limit of the neutron mean pairing gap
, by averaging their respective
values over the interval ranging from 60 to 80 MeV. The results are
MeV and
MeV for
Sn, and
MeV and
MeV for
Sn.
In this interval, the energies are scattered within
keV and the
gaps within
keV.
Since the increase of
from 60 MeV to
80 MeV does not change the results in a significant way, the
choice of
MeV has been made for the rest of this study.
In principle, this value should be readjusted in other mass
region or when using a different effective force.
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Within the cut-off prescription and regularization scheme we have calculated
the series of even-even tin isotopes by using the
SLy4
force.
The left part of Fig. 7 displays the
binding energies per particle and the right part the deviation between the calculated binding
energies and the experimental ones [25]. One can see that
both methods give very similar results.
The neutron mean gap are plotted on the left part of
Fig. 8. In the two sets of calculation,
the strengths of the pairing force have been adjusted
in order to give the same gap in
Sn.
Again, we do not observe here
any significant change when using or not the regularization
scheme, although the gap is slightly reduced in heavy
tin isotopes.
Finally, the right part of Fig. 8
compares the differences between the neutron and proton rms radii
plotted with respect to that in
Sn; once again the two methods
give extremely similar results.