One-flux theory of a nonabsorbing barrier

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Abstract
Equations of the one-flux method are integrated to obtain the scattering matrix for a nonabsorbing barrier with an arbitrary potential profile. Earlier solutions for a field-free and uniform-field region are recovered as special cases of a general result. An important expression representing the results of the Monte-Carlo simulations for the “downstream” backscattering coefficient in a strong field is derived directly from the one-flux method. The generalized Bethe criterion is obtained formally within a general context.