Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential

TL;DR

This paper analyzes how Klein-Gordon particles scatter in a generalized symmetric Woods-Saxon potential, incorporating surface interactions, and derives solutions using hypergeometric functions to study transmission and reflection probabilities.

Contribution

It provides new analytical solutions for Klein-Gordon scattering in a generalized potential including surface effects, extending previous models.

Findings

Transmission and reflection probabilities depend on potential parameters.

Solutions are expressed in terms of hypergeometric functions.

Behavior differs for positive and negative energy particles.

Abstract

Recently, it has been shown that the generalized symmetric Woods-Saxon potential energy, in which surface interaction terms are taken into account, describes the physical processes better than the standard form. Therefore in this study, we investigate the scattering of Klein-Gordon particles in the presence of both generalized symmetric Woods-Saxon vector and scalar potential. In one spatial dimension we obtain the solutions in terms of hypergeometric functions for spin symmetric or pseudo-spin symmetric cases. Finally, we plot transmission and reflection probabilities for incident particles with negative and positive energy for some critical arbitrary parameters and discuss the correlations for both cases.