Approximate Dirac solutions of complex -symmetric P\"oschl-Teller potential in view of spin and pseudospin symmetries

TL;DR

This paper develops an approximate analytical method to solve the Dirac equation with complex P"oschl-Teller potentials, revealing energy spectra under spin and pseudospin symmetries, and expressing solutions via hypergeometric functions.

Contribution

It introduces an exponential approximation scheme for the centrifugal term, providing new solutions for complex PT potentials in the context of spin and pseudospin symmetries.

Findings

Derived real bound-state energy eigenvalues.

Wave functions expressed in hypergeometric functions.

Identified shared spectra for Dirac and Klein-Gordon equations under symmetries.

Abstract

By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for spin- particle subject to the complex -symmetric scalar and vector P\"oschl-Teller (PT) potentials with arbitrary spin-orbit -wave states in view of spin and pseudospin (p-spin) symmetries. The real bound-state energy eigenvalue equation and the corresponding two-spinor components wave function expressible in terms of the hypergeometric functions are obtained by means of the wave function analysis. The spin- Dirac equation and the spin- Klein-Gordon (KG) equation with the complex P\"oschl-Teller potentials share the same energy spectrum under the choice of (i.e., exact spin and p-spin symmetries).