Particle identity and the optical potential for elastic two-fragment collisions

The permutation symmetries resulting from particle identity are incorporated into a complete and consistent set of scattering integral equations which are partition labeled and which also possess a multiple scattering structure. These equations are applied to the investigation of the optical potential for elastic two-fragment collisions including all identity effects. It is found that, among the standard off-shell extensions for the transition operators, only the one proposed by Alt, Grassberger, and Sandhas is entirely satisfactory for the definition of the optical potential. A dynamical integral equation for the symmetrized optical potential is derived. Several alternative forms of this equation are developed. Various low-order approximations to these equations are proposed.