Parameters and numerical details of the calculation

 

In all of the calculations reported here, we use a contact interaction (55) in the p-p channel, which leads to volume pairing correlations [7]. Following the discussion of Sec. 3.2, the pairing phase space has been defined by a cut-off energy (see Eq. (60)) of $\bar{e}_{\max}$=30MeV. This constitutes a very safe limit, for which all convergence properties are well satisfied (see the discussion in Refs. [7,42]). Within this phase space, the pairing strength V₀ (see Eq. (55)) has been adjusted in a manner analogous to the prescription used in Ref. [43], namely so that the average neutron pairing gap (53) for ¹²⁰Sn equals the experimental value of $\Delta _{n}$=1.245MeV. The resulting value is V₀=-206MeVfm³. As demonstrated in the Appendix of Ref. [7], changes in the cut-off parameter $\bar{e}_{\max}$, leading to a renormalization of the pairing strength V₀, can be safely disregarded when compared to all other uncertainties in the methods used to extrapolate to unknown nuclei.

Although our axially-deformed HFB+THO code is able to work with arbitrary axial oscillator lengths $L_\rho$ and L_z, we have used in these calculations a spherical basis defined by a single common oscillator length L₀ (25) (see Sec. 2.3). When optimizing the THO basis parameters L₀, a, and c (to minimize the total energy), we invariably find that for weakly-bound nuclei the resulting exponential decay constant (19) is very close to that given by the HFB estimate (54). Based on this observation, we have chosen to eliminate the THO parameter a and to fix it in such a way that the basis decay constant (19), at the self-consistent solution, is equal to the HFB decay constant (54). In this way, we only have two variational parameters in our calculations, L₀ and c. The minimizations were carried out independently for each nucleus. When describing each specific application, we will indicate the number of shells included both in the minimization that determines the LST parameters ( $N^{{\rm\scriptsize {par}}}_{{\rm\scriptsize {sh}}}$) and in the final calculations ( $N_{{\rm\scriptsize {sh}}}$).

All Gauss integrations were performed with 22 nodes in the $\rho$ direction and 24 nodes in the z direction (due to the reflection symmetry assumed with respect to the x-y plane, only 12 nodes for z>0 were effectively needed).