Relating pseudospin and spin symmetries through chiral transformation with tensor interaction

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.