Non-relativistic expansion of Dirac equation with spherical scalar and vector potentials by reconstituted Foldy-Wouthuysen transformation

TL;DR

This paper introduces a reconstituted Foldy-Wouthuysen transformation inspired by the similarity renormalization group, enabling fast convergence and accurate calculation of single-particle energies and densities in the Dirac equation within covariant density functional theory.

Contribution

It proposes a novel reconstituted FW transformation that improves convergence and accuracy in relativistic quantum calculations involving Dirac equations.

Findings

Fast convergence of single-particle energy spectrum.

Relativistic corrections significantly improve density accuracy.

Almost exact single-particle densities after corrections.

Abstract

Inspired by the reconstituted similarity renormalization group method, the reconstituted Foldy-Wouthuysen (FW) transformation is proposed. Applied to the Dirac equation in the covariant density functional theory, the reconstituted FW transformation shows a fast convergence of the spectrum of the single-particle energy. The single-particle densities and the single-particle scalar densities obtained by this new method are also investigated. In particular, the relativistic corrections to the densities from the picture-change error between the Schr\"odinger and Dirac pictures are discussed in detail. Taking these relativistic corrections into account, both the single-particle densities and the single-particle scalar densities are almost identical to their exact values.