Non-relativistic models for inelasticities in the ND−1 equations

Inelasticities in non-relativistic, many-channel scattering problems, due to the existence of non-explicit further channels of the system, are studied in the framework of the matrix ND^?1 representation of partial-wave scattering amplitudes, using the concept of a generalised phase-space matrix. For a system of coupled two-fragment channels driven by an absorptive, effective-potential matrix, general, exact expressions for the phase-space matrix are derived in terms of a matrix generalisation of the Kowalski-Noyes half-off-shell extension factor. Analytically soluble coupled-channel models based on finite-rank interactions are used to illustrate the general formulas, to discuss the problem of CDD singularities, and to numerically test approximation schemes based on Born expansions of the half-off-shell factors. It is concluded that for a large class of problems, the regular part of the phase-space matrix can be calculated in a practical way from low-order Born or multiple-scattering terms, in much the same way as usually done for the left-hand singularities.