Hamiltonian flow equations for a Dirac particle in large scalar and vector potentials

TL;DR

This paper introduces a novel expansion method for solving Dirac Hamiltonian flow equations with large scalar and vector potentials, achieving high accuracy in reproducing solutions for particles and antiparticles.

Contribution

The paper presents a new expansion technique based on the inverse Dirac effective mass, improving efficiency and accuracy in solving Dirac Hamiltonian flow equations.

Findings

High accuracy in reproducing Dirac solutions with few expansion terms

Effective reduction to nonrelativistic Hamiltonians for particles and antiparticles

Potential to bridge relativistic and nonrelativistic nuclear theories

Abstract

An efficient solution of the Dirac Hamiltonian flow equations has been proposed through a novel expandsion with the inverse of the Dirac effective mass. The efficiency and accuracy of this new expansion have been demonstrated by reducing a radial Dirac Hamiltonian with large scalar and vector potentials to two nonrelativistic Hamiltonians corresponding to particles and antiparticles, respectively. By solving the two nonrelativistic Hamiltonians, it is found that the exact solutions of the Dirac equation, for both particles and antiparticles, can be reproduced with a high accuracy up to only a few lowest order terms in the expansion. This could help compare and bridge the relativistic and nonrelativistic nuclear energy density functional theories in the future.