Microscopic nuclear mass model for r-process nucleosynthesis

Self-consistent mean-field (SCMF) theories based on Hartree-Fock-Bogolyubov (HFB) variational approach with energy density functionals (EDF) were actively developing in the recent decades and have proven successful in systematic studies of low-energy nuclear structure. In particular, current HFB-based mass models are found to be on the similar accuracy level in describing experimental masses as the more phenomenological mass formulas. In order to further increase the descriptive and predictive power of HFB models, we have addressed three particularly important topics that are generally inherent to all EDF approaches with either Skyrme, Gogny, or relativistic mean-field interactions. Firstly, we analyzed the convergence properties of results obtained with the SCMF calculations based on the Gogny EDF. While in the case of binding energies one generally has to implement prohibitively large harmonic oscillator working bases to ensure convergence, the extracted separation energies are found to be virtually converged even in a relatively modest basis dimension. Nevertheless, by properly controlling the numerical convergence, we have removed the artificial noise that was found in some of the previously published databases for binding and neutron-separation energies. We have also employed and systematically benchmarked one of the recently proposed infrared energy-correction techniques to extrapolate our results to the limit of an infinite model space. We found that this extrapolation scheme can be reliably applied only in the region of well-bound nuclei. \smallskip Thereafter, using the same Gogny EDF, we extended the HFB formalism by implementing such beyond-mean-field (BMF) methods as particle-number and angular-momentum symmetry restorations, as well as axial quadrupole shape mixing without assuming the commonly used Gaussian-overlap approximation. We performed global BMF calculations both with D1S and D1M parametrizations of Gogny interaction, and compared binding, separation, and $2^+$--excitation energies of the calculated doubly even nuclei to the available experimental data set. We found that the BMF effects amount to 5-6 MeV of correlation energy, and tend to decrease the shell effects particularly in the region of light nuclei. Moreover, the BMF calculations tend to reduce the shell gaps at Z = N = 20, 28, but we could not reproduce the reported quenching for the remaining shell gaps. As for the 2^+--excitation energies, we did not find any significant differences between D1S and D1M parametrizations, while both versions of Gogny interaction tend to overestimate the experimental values. Finally, we introduced all the necessary tools for performing self-consistent blocking calculations of the odd-A and doubly odd nuclei. We presented results of the global Gogny-HFB survey up to the neutron drip line from Z = 8 up to Z = 134 with explicit treatment of the time-odd fields. We also compared our results to the experimental data, as well as values obtained with the widely used PQPA method of approximative blocking. The overall pairing strength of the D1S functional is found to be adequate and provide a good qualitative level of description for the main features of pairing gaps. The calculations with explicit T-odd fields were generally found to capture more subtle traits of the observed odd-even staggering effects. Analysis of the global systematics showed, however, a noticeable deviation of the calculations from the reported mass-dependence of experimental pairing gaps.