Calculations for deformed nuclei

In our previous study [44], we calculated the complete HFB mass chart of even-even nuclei by performing the PNP of paired ground states determined by the LN method. At this point, when performing the PNP calculation in each individual nucleus, one should take care of the cases when one of the poles $z_n$ turns out to be near the standard $r_0=1$ integration circle (unit circle).

In order to produce the ground state masses for all even-even nuclei lying between the two-nucleon drip lines, one has to calculate about 6000 nuclei. Moreover, each nucleus has to be calculated three times, by starting from oblate, spherical, and prolate initial shapes. We have found that among these 6000 nuclei, about 100 have a neutron or proton state with occupation numbers near 1/2. Therefore, the standard PNP method yields about 100 questionable results across the mass chart. However, the situations is much more serious when performing the constrained HFB calculations discussed in the following sections.