Two-center harmonic oscillator basis for Skyrme-DFT calculations (I): formalism and Proof of Principle

TL;DR

This paper introduces a novel two-center harmonic oscillator basis method for solving Skyrme-DFT equations, improving the modeling of nuclear fission and fusion configurations with exact Coulomb exchange calculations.

Contribution

It develops a new formalism and implementation for two-center harmonic oscillator bases in Skyrme-DFT, enabling precise and efficient nuclear configuration studies.

Findings

Exact Coulomb exchange evaluation without Slater approximation

Successful implementation in { extsc hfodd} code

Proof-of-principle tests on $^8$Be and $^{24}$Mg

Abstract

We present a new method to solve the nuclear density functional theory (DFT) equations using a two-center harmonic oscillator for Skyrme-like functionals, incorporating pairing and Coulomb interactions. The goal is to efficiently determine the fission and fusion configurations in nuclei. The Coulomb exchange term is evaluated exactly, allowing for a novel approach to neck formation without the Slater approximation, commonly used in space coordinate-based approaches. The new method has been implemented in the code {\sc hfodd}, enabling direct comparison with standard one-center solutions. This first paper focuses on deriving and implementing a methodology based on stable, precise, and exact applications of harmonic oscillator bases for the two fragments, which can either overlap or be separated by arbitrarily large distances. The implementation is tested on two proof-of-principle examples using light nuclei, specifically, $^8$Be and $^{24}$Mg.