Separable Representations of Two-Body Interactions

Consideration is given to the approximation in which an arbitrary potential is replaced by a separable potential. A method is presented which permits the construction of a rank-N separable potential which has the property that the resulting T matrix is exact on the energy shell and half off the energy shell at N selected bound state and/or continuum energies. This construction yields a T matrix that is correct off the energy shell in the vicinity of the N on-shell points.