# Non-relativistic expansion of Dirac equation with spherical scalar and vector potentials by similarity renormalization group

## TL;DR

This paper extends the similarity renormalization group (SRG) method to higher orders for the Dirac equation with spherical potentials, demonstrating improved convergence and accuracy through re-summation techniques.

## Contribution

It provides an analytic ${1}/{M^4}$ order expansion of the Dirac equation using SRG and introduces a reconstituted SRG method with faster convergence.

## Key findings

- Re-summation accelerates the convergence of SRG.
- Reconstituted SRG yields densities close to exact values.
- Analytic ${1}/{M^4}$ order expression verified for convergence.

## Abstract

By following the conventional similarity renormalization group (SRG) expansion of the Dirac equation developed in [J.-Y. Guo, Phys. Rev. C \textbf{85}, 021302 (2012)], we work out the analytic expression of the ${1}/{M^4}$ order and verify the convergence of this method. As a step further, the reconstituted SRG method is proposed by using the re-summation technique. The speed of convergence of the reconstituted SRG becomes much faster than the conventional one, and the single-particle densities with the reconstituted SRG are also almost identical to the exact values.