Hard-Core Potentials and the Three-Body Problem

Abstract

A method is presented for treating hard-core potentials within the framework of the Lippmann-Schwinger scattering-theory formalism. Using the method, a procedure is developed for constructing separable expansions of the $t$ matrix arising from potentials containing hard cores. Such expansions reduce the Faddeev equations to equations in one continuous variable. The rate of convergence of the expansion is illustrated by using it in a calculation of the binding energy of a system of three identical spinless particles interacting via square-well potentials with hard cores.