Improved Minimum Principle for Multichannel Scattering

Abstract

If the open-channel target states are known, the minimum principle formulation of scattering theory provides a systematic approach whereby one can, to arbitrary precision, monotonically approach the reactance matrix K. The scattering wave function and the Green's function for the open-channel approximation, that in which the closed channels are not taken into account at all, must be solved numerically. An explicit method for constructing the Green's function is given. The minimum principle approach is probably limited at present, in practice though not in principle, to the three-body problem with just a few open channels. A very useful simplification is possible at the threshold for a new channel; one need not there include the new channel in the euqations that must be solved exactly.