Application of the gradient method to Hartree-Fock-Bogoliubov theory

TL;DR

This paper introduces a flexible and efficient computational code for solving Hartree-Fock-Bogoliubov equations using the gradient method, applicable to various nuclear configurations and symmetries.

Contribution

It presents a modular code implementation for HFB calculations that separates Hamiltonian specifics from the gradient method, enhancing flexibility and robustness.

Findings

Successfully applied to sd-shell nuclei with USDB Hamiltonian

Handles both even and odd particle number states

Demonstrates efficiency and adaptability of the gradient method

Abstract

A computer code is presented for solving the equations of Hartree-Fock-Bogoliubov (HFB) theory by the gradient method, motivated by the need for efficient and robust codes to calculate the configurations required by extensions of HFB such as the generator coordinate method. The code is organized with a separation between the parts that are specific to the details of the Hamiltonian and the parts that are generic to the gradient method. This permits total flexibility in choosing the symmetries to be imposed on the HFB solutions. The code solves for both even and odd particle number ground states, the choice determined by the input data stream. Application is made to the nuclei in the $sd$-shell using the USDB shell-model Hamiltonian.