Solving the Dirac equation with nonlocal potential by Imaginary Time Step method

TL;DR

This paper presents an efficient imaginary time step method to solve the Dirac equation with nonlocal potentials, demonstrating its accuracy and simplicity through nuclear physics applications.

Contribution

It introduces a novel algorithm for solving the Dirac equation with nonlocal potentials using the imaginary time step method, applicable with or without localization.

Findings

The method accurately reproduces results from the shooting method.

The localized and nonlocalized approaches yield equivalent solutions.

The algorithm is efficient and reliable for nuclear structure calculations.

Abstract

The Imaginary Time Step (ITS) method is applied to solve the Dirac equation with the nonlocal potential in coordinate space by the ITS evolution for the corresponding Schr\"odinger-like equation for the upper component. It is demonstrated that the ITS evolution can be equivalently performed for the Schr\"odinger-like equation with or without localization. The latter algorithm is recommended in the application for the reason of simplicity and efficiency. The feasibility and reliability of this algorithm are also illustrated by taking the nucleus $^{16}$O as an example, where the same results as the shooting method for the Dirac equation with localized effective potentials are obtained.