Coupled channels optical theorem and non-elastic cross section sum rule

Within a coupled channels framework a theorem, similar to the optical theorem, is proved which provides a new formula for total non-elastic (inelastic, rearrangement and absorption) cross sections. An approximate cross section energy sum rule is also developed in terms of the trace of the imaginary part of an energy independent, but non-local optical potential. Corrections to sum rule are found small indicating that the result is a good approximation. The theorem and sum rule are applied to the Lane model describing charge exchange reactions.