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Effective mass Klein-Gordon equation for the asymmetric Hulth{\'e}n potentialis solved in terms of hypergeometric functions. Results are obtained for thescattering 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 oftransmission resonance (T=1). We also study how the transmission resonancedepends on the particle energy and the shape of the external potential.

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