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.

• Received 30 November 2004

DOI:https://doi.org/10.1103/PhysRevA.71.052101