Exact solutions of a spatially-dependent mass Dirac equation for Coulomb field plus tensor interaction via Laplace transformation method

TL;DR

This paper provides exact analytical solutions for the spatially-dependent mass Dirac equation with Coulomb and tensor potentials using Laplace transformation, revealing how tensor interactions influence bound state degeneracies.

Contribution

It introduces an exact solution method for the Dirac equation with spatially-dependent mass and tensor interactions, extending previous models with new analytical results.

Findings

Tensor interaction removes degeneracy in spin doublets.

Spatially-dependent mass affects bound state energies.

Closed-form energy eigenvalues and wave functions obtained.

Abstract

The spatially-dependent mass Dirac equation is solved exactly for attractive scalar and repulsive vector Coulomb potentials including a tensor interaction potential under the spin and pseudospin (p-spin) symmetric limits by using the Laplace transformation method (LTM). Closed forms of the energy eigenvalue equation and wave functions are obtained for arbitrary spin-orbit quantum number Some numerical results are given too. The effect of the tensor interaction on the bound states is presented. It is shown that the tensor interaction removes the degeneracy between two states in the spin doublets. We also investigate the effects of the spatially-dependent mass on the bound states under the conditions of the spin symmetric limit and in the absence of tensor interaction