A Sasakawa approach to three-particle scattering

An idea introduced by Sasakawa is used to convert the Faddeev equations into integral equations in which the inhomogeneous term contains the amplitudes for inelastic scattering and rearrangement collisions. The kernels are thereby modified and made nonsingular for energies below the three-particle break-up threshold. The equations are derived for a system of three nonidentical spinless particles interacting through central two-particle potentials. An iterative method for solving the modified equations is developed. It is shown how to symmetrize the equations for a system of three identical spinless particles. The equations are written out in detail for the angular-momentum-zero state of three identical spinless particles interacting through an s-wave two-particle force which produces only one two-particle bound state. The lowest-order approximation to the solution of the equations for this simple system is worked out. It is found that this approximation satisfies unitarity for energies below the three-particle break-up threshold.