Hartree-Fock mass formulas and extrapolation to new mass data

Abstract

The two previously published Hartree-Fock (HF) mass formulas, HFBCS-1 and HFB-1 (HF-Bogoliubov), are shown to be in poor agreement with new Audi-Wapstra mass data. The problem lies first with the prescription adopted for the cutoff of the single-particle spectrum used with the $\delta$-function pairing force, and second with the Wigner term. We find an optimal mass fit if the spectrum is cut off both above $E_F+15\mathrm{}\hspace{0.5em}\mathrm{MeV}$ and below $E_F-15\hspace{0.5em}\mathrm{MeV},$ $E_F$ being the Fermi energy of the nucleus in question. In addition to the Wigner term of the form $V_W\hspace{0.5em}\exp (-\lambda |N-Z|/A)$ already included in the two earlier HF mass formulas, we find that a second Wigner term linear in $|N-Z|$ leads to a significant improvement in lighter nuclei. These two features are incorporated into our new Hartree-Fock-Bogoliubov model, which leads to much improved extrapolations. The 18 parameters of the model are fitted to the 2135 measured masses for $N,Z>~8$ with an rms error of 0.674 MeV. With this parameter set a complete mass table, labeled HFB-2, has been constructed, going from one drip line to the other, up to $Z=120.\mathrm{}$ The new pairing-cutoff prescription favored by the new mass data leads to weaker neutron-shell gaps in neutron-rich nuclei.