Rearrangement-Channel Operator Approach to Models for Three-Body Reactions. I

Abstract

The channel operators ${\tau }_{\gamma \alpha }$ describing scattering from configuration $\alpha$ to configuration $\gamma$ are utilized in considering a model for three-body rearrangement scattering. The ${\tau }_{\gamma \alpha }$ are those defined by $V_{\alpha }+V_{\gamma }{(E-H+i\epsilon )}^{-1\mathrm{}}{V}_{\alpha }$. Two well-known forms of integral equations for the ${\tau }_{\gamma \alpha }$ obtained from this expression are explicitly solved for the model potential surface. Using these explicit solutions, results are examined in the limit that no dissociative continuum is present. It is found that the integral equations in which the ${\tau }_{\gamma \alpha }$ are not explicitly coupled do not yield the correct results for this limiting case. Integral equations explicity coupling the ${\tau }_{\gamma \alpha }$ give limiting results in agreement with those obtained by more-common boundary-matching techniques. These results indicate that the major effects of the dissociative continuum may be accounted for by considering the coupled equations for the ${\tau }_{\gamma \alpha }$ (at least so long as one is well below threshold for the production of three free particles).