Pairing gaps in Hartree-Fock Bogoliubov theory with the Gogny D1S interaction

TL;DR

This paper introduces a new gradient-based method for calculating odd-A nuclei in Hartree-Fock-Bogoliubov theory using Gogny interactions, and assesses its impact on neutron pairing gaps across various nuclei.

Contribution

Developed a robust gradient method for HFB minima in odd-A nuclei that includes time-odd fields, providing systematic survey capabilities and insights into pairing gaps with Gogny D1S.

Findings

Time-odd fields have minimal effect on pairing gaps.

The Gogny D1S interaction yields reasonable overall pairing gap predictions.

Systematic discrepancies exist between calculated and experimental gaps, especially in heavy and deformed nuclei.

Abstract

As part of a program to study odd-A nuclei in the Hartree-Fock-Bogoliubov (HFB) theory, we have developed a new calculational tool to find the HFB minima of odd-A nuclei based on the gradient method and using interactions of Gogny's form. The HFB minimization includes both time-even and time-odd fields in the energy functional, avoiding the commonly used "filling approximation". Here we apply the method to calculate neutron pairing gaps in some representative isotope chains of spherical and deformed nuclei, namely the Z=8,50 and 82 spherical chains and the Z=62 and 92 deformed chains. We find that the gradient method is quite robust, permitting us to carry out systematic surveys involving many nuclei. We find that the time-odd field does not have large effect on the pairing gaps calculated with the Gogny D1S interaction. Typically, adding the T-odd field as a perturbation increases the pairing gap by ~100 keV, but the re-minimization brings the gap back down. This outcome is very similar to results reported for the Skyrme family of nuclear energy density functionals. Comparing the calculated gaps with the experimental ones, we find that the theoretical errors have both signs implying that the D1S interaction has a reasonable overall strength. However, we find some systematic deficiencies comparing spherical and deformed chains and comparing the lighter chains with the heavier ones. The gaps for heavy spherical nuclei are too high, while those for deformed nuclei tend to be too low. The calculated gaps of spherical nuclei show hardly any A-dependence, contrary to the data. Inclusion of the T-odd component of the interaction does not change these qualitative findings.