VARIATIONAL PRINCIPLE FOR TIME-DEPENDENT INTERACTIONS

A Schwinger-type variational principle for time-dependent interactions is developed for the S matrix using a separable operator approach. The S matrix has an implicit fractional form by which we mean that an integral equation has to be solved to compute the wave function. This principle shares the important features of the fractional form of Schwinger's variational principle and reduces to it for time-independent interactions. We discuss the relationship with the Lippmann-Schwinger variational principle. The variational principle is generalized to treat direct and rearrangement processes in ion-atom collisions in both the time-dependent and time-independent representations. It is shown to yield the correct asymptotic form for capture. Using free states as trial functions, the channel-distorted strong-potential Born S matrix is obtained. the distortion potential is determined variationally and is found to have the correct form at large distances.