TRIANGLE AMPLITUDE WITH OFF-SHELL COULOMB T-MATRIX FOR EXCHANGE-REACTIONS IN ATOMIC AND NUCLEAR-PHYSICS

The lowest-order rescattering contribution (triangle amplitude) in thr ee-body models of exchange reactions with charged particles contains t he off-shell two-body T matrix describing the intermediate-state Coulo mb scattering of charged subsystems. General properties of the exact e xchange triangle amplitude, when the incoming and outgoing particles a re on the energy shell, are derived. This includes the analytic behavi or, i.e., the positions and characters of its leading singularities, i n the cos theta plane, where theta is the scattering angle, in the vic inity of the forward- and backward-scattering directions. Since for co mputational reasons the Coulomb T matrix is usually replaced by the Co ulomb potential, the effects of such an approximation on the analytic properties are investigated. The theoretically established behavior of the exact and the approximate exchange triangle amplitudes is then il lustrated by numerical calculations, for both atomic and nuclear react ions, for energies below and above the corresponding three-body dissoc iation thresholds, for elastic and inelastic exchange.