Nonlocal Potentials and Nuclear Resonance Scattering

In the theory of nuclear resonance scattering, nonlocal potentials play an important role, as they are the reflection of the many body character of a system involving identical constituents. The Schroedinger equation with such a potential has been the target of intensive research, and its solutions have been investigated. However, no formal method of analytically solving the Schroedinger equation with a separable, symmetric nonlocal potential has been presented. This thesis fills this gap by establishing a general solution to such an equation by the use of the Green's function. As the solution bears a wave localized near the center of a potential, it offers a clue to the nature of the interaction at close range. Also, the S -matrix, which is the coefficient of the spherically outgoing wave, is shown to be the ratio of the Fredholm determinants associated with the kernel of the integral equation. Resonance, which is a time dependent phenomenon, demands the construction of wave packets, as these are a time dependent solution to the Schroedinger equation. In this context, the analytic expression of the S-matrix we have derived establishes the relationship between a potential and the configuration of the outgoing wave packet. Also, in the wave packet picture, it is possible to investigate the time dependent behavior of the centrally localized wave. In this way, the nature of resonance phenomena can be better elucidated.