Theory of Scattering in Three-Particle System

Abstract

A theory of scattering in three· particle system is proposed. The Hamiltonian of the system is described in a coordinate system which is appropriate for representing the three· particle system. After a unitary transformation, the basic Hamiltonian satisfying the asymp­ totic condition is obtained. On the basis of this Hamiltonian, the orthogonality of the scat­ tering states for different channels is exhibited in an exact way. The S-matrix involves ex­ plicitly· the contribution from the indirect _interactions between two particles through the motion of the third P'!rticle. With the aid of the orthogonal character of the scattering states, a generalized optical theorem in three-particle system is derived. The integral equa­ tion for the scattering amplitude is transformed so as to be able to have a convergent series which does not involve any disconnected diagram.