New integral equations for the transition operators of many-body systems

Abstract

A new set of coupled integral equations for the transition operators of a nonrelativistic quantum-mechanical $n$- body system is presented. These equations are a generalization to the many-body system of a special case of a set suggested for the three-body problem by Kouri, Baer, and Levin. The Kouri-Baer-Levin formalism effectively couples together the Lippmann-Schwinger integral equations for the transition operators for all open channels thus simultaneously imposing all asymptotic boundary conditions. The effect of our specialization of these equations is to make the kernel of the integral equations connected so that the resulting equations appear to be a suitable basis for many-body calculations.