Off-Energy-ShelltMatrix for Local Potentials with Singular Core Interactions

As a preliminary to studying three-body problems involving local two-particle potentials with singular core interactions, we derive and numerically study an integral equation for the complete off-energy-shell $t$ matrix for the associated two-particle scattering. The core interaction is described by the boundary-condition model (specified energy-independent logarithmic derivative of the radial wave function at the core radius). Numerical solutions of the integral equation for the special case of the Herzfeld potential (hard core with a square well outside) are found to agree well with the exact $t$ matrix.