Nuclear surface energy solving Hartree-Fock equations with Gogny interactions using Lagrange mesh

TL;DR

This paper introduces an efficient Lagrange mesh method to solve Hartree-Fock equations with Gogny interactions for nuclear surface energy, achieving high accuracy and exploring effects of spin-orbit coupling.

Contribution

It presents a novel, faster numerical algorithm for solving Hartree-Fock equations with finite-range interactions, improving accuracy and enabling detailed analysis of Gogny interactions.

Findings

The Lagrange mesh method outperforms the Numerov algorithm in speed and accuracy.

Large computational boxes reduce Friedel oscillation effects, improving surface energy precision.

Including spin-orbit terms decreases surface energy by 1.2-1.9 MeV.

Abstract

Hartree Fock equations for finite range interactions in a slab of nuclear matter are presented and solved using an algorithm based on the Lagrange mesh method. This approach is faster and more efficient than the Numerov algorithm commonly used in the literature. Thanks to the improved numerical accuracy, we were able to perform calculations with sufficiently large boxes to minimize the impact of Friedel oscillations on the final results, achieving a precision on the surface energy within a few dozens of keV. Results are presented for several Gogny interactions that have not been previously discussed. In addition, the inclusion of the spin orbit term is examined, showing a net reduction of 1.2-1.9 MeV in the surface energy.