Triangle amplitude with off-shell Coulomb T matrix for exchange reactions in atomic and nuclear physics.

Abstract

The lowest-order rescattering contribution (triangle amplitude) in three-body models of exchange reactions with charged particles contains the off-shell two-body T matrix describing the intermediate-state Coulomb scattering of charged subsystems. General properties of the exact exchange triangle amplitude, when the incoming and outgoing particles are on the energy shell, are derived. This includes the analytic behavior, i.e., the positions and characters of its leading singularities, in the cos\ensuremath{\vartheta} plane, where \ensuremath{\vartheta} is the scattering angle, in the vicinity of the forward- and backward-scattering directions. Since for computational reasons the Coulomb T matrix is usually replaced by the Coulomb 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 illustrated by numerical calculations, for both atomic and nuclear reactions, for energies below and above the corresponding three-body dissociation thresholds, for elastic and inelastic exchange. \textcopyright{} 1996 The American Physical Society.