Reduction of the Finite-Range Three-Body Problem in Two Variables

Abstract

It is shown explicitly that for finite-range two-body forces which contribute significant interactions in only $L+1$ orbital angular momentum states, the Faddeev equations for the three-body $T$ matrix with total angular momentum $J$ can be reduced to well-defined integral equations for functions of two continuous variables with $3(L+1)\ifmmode\times\else\texttimes\fi{}min(2J+1, 2L+1)$ components. Hence numerical calculation for realistic interactions, and analytic investigation of the dependence on two-body dynamics (which is explicitly separated from the geometrical part of the problem), become possible.