Scattering of a spinless particle by an asymmetric Hulth{\'e}n potential within the effective mass formalism

TL;DR

This paper solves the effective mass Klein-Gordon equation for an asymmetric Hulthén potential, analyzing scattering, bound states, and transmission resonances with position-dependent and constant mass scenarios.

Contribution

It provides exact solutions using hypergeometric functions and derives conditions for transmission resonance, highlighting the impact of potential shape and particle energy.

Findings

Transmission resonance condition derived

Solutions for scattering and bound states obtained

Resonance dependence on energy and potential shape analyzed

Abstract

Effective mass Klein-Gordon equation for the asymmetric Hulth{\'e}n potential is solved in terms of hypergeometric functions. Results are obtained for the scattering and bound states with the position dependent mass and constant mass, as a special case. In both cases, we derive a condition for the existence of transmission resonance (T=1). We also study how the transmission resonance depends on the particle energy and the shape of the external potential.