Scattering of a spinless particle by an asymmetric Hulthen potential within the effective mass formalism

Effective mass Klein-Gordon equation for the asymmetric Hulthen 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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758926]