Evaluation of off-shell matrix elements of Faddeev equations

Abstract

The first-order exact off-shell matrix elements for the scattering processes to a three-body Coulomb system with arbitrary masses in which three-particle states are made of two-body bound states and a third free-particle state have been evaluated. These elements are required if one is interested in applying the tractable form (Sloan and Moore) of the Lovelace-Faddeev equations. The amplitudes have been obtained for both the direct and rearrangement channels. The two-body bound states in both the initial and final states are, however, restricted to be the ground states. It may be mentioned that one can always get the amplitudes for higher excited states by appropriate parametric differentiations. Two other approximate forms of the amplitudes have also been given. In all, the forms the matrix elements in the direct channel are found to be singular in the forward scattering angle. The expressions devoid of singularities have been obtained in the present investigation.