General many-channel variational principles for multiparticle scattering

Abstract

A general multichannel scattering formalism based on Schwinger-type variational principles and capable of treating rearrangements was recently presented by Tobocman. The approach involved combining variational functionals for individual transition operators with new coupled integral equations for these operators derived recently by Baer and Kouri and by Kouri and Levin. In this paper, we present general variational principles whose Euler equations are precisely the new coupled channel $T_{\alpha \beta }$ operator equations obtained by Kouri and Levin. The results are expressions which are stationary with respect to variations in all the $T_{\alpha \beta }$ simultaneously rather than just for a single $T_{\alpha \beta }$ operator. It is shown that such matrix generalizations may be obtained for a variety of functionals. With the specific choice of a channel permuting array (as discussed by Tobocman and by Kouri and Levin), the present formalism provides a valid computational basis for general many-body (e.g. nuclear) reactions, since then the iterated kernels of the resulting coupled channel $T_{\alpha \beta }$ operator equations are completely connected.