Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. II. Role of the effective mass

We have constructed four new complete mass tables, referred to as (Hartree-Fock-Bogoliubov) HFB-4 to HFB-7, each one including all the 9200 nuclei lying between the two drip lines over the range of $Z$ and $N⩾8$ and $Z⩽120$. HFB-4 and HFB-5 have the isoscalar effective mass $M_s^{*}$ constrained to the value $0.92M$, with the former having a density-independent pairing, and the latter a density-dependent pairing. HFB-6 and HFB-7 are similar, except that $M_s^{*}$ is constrained to $0.8M$. The rms errors of the mass-data fits are 0.680, 0.675, 0.686, and $0.676\text{MeV}$, respectively, almost as good as for the HFB-2 mass formula, for which $M_s^{*}$ was unconstrained. However, as usual, the single-particle spectra depend significantly on $M_s^{*}$. This decoupling of the mass fits from the fits to the single-particle spectra has been achieved only by making the cutoff parameter of the $\delta$-function pairing force a free parameter. An improved treatment of the center-of-mass correction was adopted, but although this makes a difference to individual nuclei it does not reduce the overall rms error of the fit. The extrapolations of all four new mass formulas out to the drip lines are essentially the same as for the original HFB-2 mass formula.