Tensor coupling and relativistic spin and pseudospin symmetries with the Hellmann potential

TL;DR

This paper analytically solves the Dirac equation with the Hellmann potential, revealing how tensor interactions influence spin and pseudospin degeneracies, and explores specific cases including non-relativistic and Coulomb potentials.

Contribution

It introduces an approximate analytical solution for the Dirac equation with the Hellmann potential incorporating tensor interactions under spin and pseudospin symmetries.

Findings

Tensor interaction removes degeneracies between spin and pseudospin doublets.

Energy levels for non-relativistic and Coulomb potential cases are derived.

Analytical solutions are obtained using the NU method.

Abstract

The Hellmann potential is a superposition potential that consists of an attractive Coulomb potential and a Yukawa potential. By using the generalized parametric Nikiforov-Uvarov (NU) method, we have studied the approximate analytical solutions of the Dirac equation with the Hellmann potential including a Coulomb-like tensor potential for arbitrary spin-orbit quantum number k under the presence of exact spin and pseudo-spin (p-spin) symmetries. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. As particular cases, we found the energy levels of non-relativistic case and also the pure Coulomb potential energy levels.