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.

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.


Within the cutoff prescription and regularization scheme we have calculated the series of eveneven 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.