Effective-Mass Dirac Equation for Woods-Saxon Potential: Scattering, Bound States and Resonances

TL;DR

This paper derives approximate solutions for the one-dimensional effective-mass Dirac equation with Woods-Saxon potential, analyzing scattering, bound states, and resonances, and compares results with the constant mass case.

Contribution

It provides new analytical expressions for transmission resonances and bound states in the effective-mass Dirac equation with Woods-Saxon potential.

Findings

Transmission and reflection coefficients calculated

Analytic expression for transmission resonance obtained

Results agree with existing literature

Abstract

Approximate scattering and bound state solutions of the one-dimensional effective-mass Dirac equation with the Woods-Saxon potential are obtained in terms of the hypergeometric-type functions. Transmission and reflection coefficients are calculated by using behavior of the wave functions at infinity. The same analysis is done for the constant mass case. It is also pointed out that our results are in agreement with those obtained in literature. Meanwhile, an analytic expression is obtained for the transmission resonance and observed that the expressions for bound states and resonances are equal for the energy values $E=\pm m$.