Boundary Conditions and Time-Dependent States

Abstract

In a previous paper, a phenomenological description of nuclear reactions by means of boundary conditions was introduced. These boundary conditions that connect the several stages of the reaction (initial particles, compound nucleus, etc.) apply to time-dependent, as well as to stationary states. It is possible to discuss then the time development of any state specified initially. In the present paper a time-dependent description is obtained for the single-level $S$-wave scattering of two spinless particles, and for the process of disintegration of a compound particle. The only parameters on which this time-dependent description depends are the poles of the scattering matrix. The connection between the position of the poles of the scattering matrix in the complex plane, and the time-dependent behavior of the scattering and disintegration processes, is discussed. The form of the transient scattered current is also obtained. The generalized Hankel transforms on which the present developments are based, will be shown in a following paper to be a consequence of the expansion theorems for states in Fock space.