Spin and Pseudo-Spin Symmetries in Radial Dirac Equation and Exceptional Hermite Polynomials

TL;DR

This paper extends solutions of the radial Dirac equation under spin and pseudospin symmetry to include exceptional Hermite polynomials, introducing new rational potential models that generalize nonlinear isotonic potentials and depend on energy.

Contribution

It introduces a novel approach by incorporating exceptional Hermite polynomials into the radial Dirac equation, leading to new energy-dependent potential models.

Findings

Derived new solutions using exceptional Hermite polynomials.

Developed generalized rational potential models.

Extended the class of solvable Dirac equations.

Abstract

We have generalized the solutions of the radial Dirac equation with a tensor potential under spin and pseudospin symmetry limits to exceptional orthogonal Hermite polynomials family. We have obtained new general rational potential models which are the generalization of the nonlinear isotonic potential families and also energy dependent.