Application of the inverse Hamiltonian method to Hartree-Fock-Bogoliubov calculations

TL;DR

This paper introduces an inverse Hamiltonian method adapted from Dirac equation solutions to efficiently solve Hartree-Fock-Bogoliubov equations for spherical systems, expanding computational tools in nuclear physics.

Contribution

The paper develops and demonstrates a novel inverse Hamiltonian approach for solving HFB equations, applicable to bound and unbound Hamiltonians in nuclear structure calculations.

Findings

Method successfully solves HFB equations for spherical systems.

Applicable to Hamiltonians unbounded from above or below.

Demonstrates effectiveness beyond Dirac equations.

Abstract

We solve the Hartree-Fock-Bogoliubov (HFB) equations for a spherical mean field and a pairing potential with the inverse Hamiltonian method, which we have developed for the solution of the Dirac equation. This method is based on the variational principle for the inverse Hamiltonian, and is applicable to Hamiltonians that are bound neither from above nor below. We demonstrate that the method works well not only for the Dirac but also for the HFB equations.