Equivalent local potentials for a coupled-channel system and the Feshbach optical potential

Abstract

Explicit formulas of all equivalent local potentials for a coupledn-channel problem are calculated. The general equivalent local potentials constitute a $$[(_2^{2^n } ) - 1]$$ -complex-parameter family of local potentials. For a definite input elastic channel, the uniqueness of the equivalent local potential is shown. The equivalent local potential of the Feshbach optical potential coincides with the equivalent local potential of then-channel system. The construction of the Feshbach optical potential is a reduction to the dimensionality of the coupled-channel problem, the construction of the equivalent local potential is a diagonalization of the coupled-channel problem, both constructions are compatible manipulations on the set of the coupled-channel system. The properties of the Feshbach optical potential can be used for the study of the properties of the equivalent local potential.