The solution of the s-wave Bethe–Goldstone equation with a standard hard core potential

Abstract

This paper extends the results of an earlier article [J. Math. Phys. 27, 1154 (1986)] to include the solution of the s-wave Bethe–Goldstone equation for the interaction of two nucleons characterized by a potential with an infinite repulsive core and a nearby attractive well. The solution again exhibits band-limiting behavior and is obtained in closed form via the prolate spheroidal wave functions. It is shown that the attractive part of the interaction potential perturbs the far-field scattered wave so that healing of the nucleon wave function is achieved only when the attractive part is weak. Finally, asymptotic results for the case of small core radius are also calculated.