The problem of finding a phenomenological separable interaction from the S-matrix has been resolved by M. Gourdin and A. Martin who gave exact and explicit formulae relating the interaction to the phase-shift and bound state binding energy (1,2). We generalize their method to the case where the interaction is the superposition of a non-local separable interaction and a local one, both of them being central(3).The local part of the interaction is supposed to be known. We show how the separable part can be determined by the S-matrix. Except for a few modifications, the method and results are analogous to those of 1and. The main result is that, given the local part of the interaction, the phase-shift and the bound states binding energies, it is then possible to determine exactly the separable part of the interaction if the phase shift has a good behaviour(4).
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