Scattering of a Klein-Gordon particle by a Woods-Saxon potential
Clara Rojas, Victor M. Villalba
TL;DR
This paper analytically solves the Klein-Gordon equation with a Woods-Saxon potential, deriving conditions for transmission resonances and exploring how potential shape affects zero-reflection scenarios.
Contribution
It provides exact scattering solutions using hypergeometric functions and analyzes the influence of potential shape on transmission resonances.
Findings
Transmission resonance conditions derived
Zero-reflection depends on potential shape
Analytical solutions obtained in closed form
Abstract
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional Woods-Saxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission resonances is derived. It is shown how the zero-reflection condition depends on the shape of the potential.
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