EXACT AND APPROXIMATE TRIANGLE AMPLITUDES FOR (IN-)ELASTIC 3-BODY PROCESSES WITH CHARGED-PARTICLES

The triangle amplitudes, which within the framework of the multiple-sc attering approach represent the leading contribution to the amplitude for three-body elastic and inelastic reactions, contain the off-shell Coulomb T-matrix T-C describing the intermediate-state scattering of t he projectile off each of the target particles. We present results of the exact numerical calculation of that amplitude in which the rescatt ering particles have charges of opposite sign ('attractive case'), for several atomic processes. This is facilitated by a 'new' representati on of the Coulomb T-matrix which turns out to be very effective for nu merical purposes. One interesting result is that the charge sensitivit y of the full triangle amplitude apparently disappears at the elastic threshold, for all scattering angles. Furthermore, we propose a new ap proximation for the triangle amplitudes which can be viewed as a 'reno rmalization' by a simple analytic expression, of the well known approx imation which consists in replacing T-C by the potential V-C. While th e latter is known to be generally inadequate, this new approximation i s shown to yield results in excellent agreement with the numerically c alculated exact amplitude, for atomic elastic reactions, over a wide r ange of (medium to high) projectile energies and scattering angles (in cluding the near-forward-scattering direction). An even simpler approx imate amplitude is derived which contains no quadratures at all. It yi elds similarly good results provided the masses of the two particles e xperiencing intermediate-state rescattering are of the same order of m agnitude but differ from that of the spectator particle. In addition, the explicit forms of the approximate amplitudes are used to derive a variety of interesting theoretical results.