Relating pseudospin and spin symmetries through chiral transformation with tensor interaction

TL;DR

This paper explores how the Dirac equation's solutions under spin and pseudospin symmetries relate through chiral transformation, especially with tensor interactions, providing solutions for Cornell potentials.

Contribution

It demonstrates a simple method to derive solutions for Dirac equations with spin and pseudospin symmetries using chiral transformation, including tensor interactions.

Findings

Derived solutions for Dirac equation with spin and pseudospin symmetries

Applied method to scalar, vector, and tensor Cornell potentials

Provided correct solutions for complex potential interactions

Abstract

We address the behavior of the Dirac equation with scalar ($S$), vector ($V$) and tensor ($U$) interactions under the $\gamma^{5}$ discrete chiral transformation. Using this transformation we can obtain from a simple way solutions for the Dirac equation with spin ($\Delta=V-S=0$) and pseudospin ($\Sigma=V+S=0$) symmetries including a tensor interaction. As an application, the Dirac equation with scalar, vector and tensor Cornell radial potentials is considered and the correct solution to this problem is obtained.