Absorption cross sections and the use of complex potentials in coupled-channels models

We give a simple and transparent derivation of a result obtained recently by Kim, Udagawa, and Tamura for the loss of flux occurring in the coupled-channels scattering problem when a complex potential is used. The loss of flux, or absorption cross section, consists of three components: absorption from the elastic channel, absorption from the nonelastic channels, and absorption occurring during the elastic-nonelastic transitions. Some discussion is given of these results and their application to fusion reactions