Few-body Systems the Few-body Coulombian Problem

Recent advances in the treatment of scattering of charged composite particles are reviewed. In a rst part I report on developments of the theory. Speciically I describe the recent completion of the derivation of the coordinate space asymptotic behaviour of the wave function for three charged particles in the continuum. This knowledge is increasingly being made use of in attempts tòderive' three-Coulomb particle wave functions to be used in all of connguration space which are solutions of the Schrr odinger equation, though not everywhere but at least in one or preferably all of the asymptotic regions. Their practical application in approximate calculations of ionisation and breakup processes is pointed out. The asymptotic three-charged particle wave functions nd further use in investigations of asymptotic and analytic properties of matrix elements of the three-body Coulomb resolvent. An important example is the nonper-turbative derivation, valid for all energies, of the large-distance behaviour of the optical potential. In the second part I describe a renewed attempt to establish the few-body approach as a valuable tool for calculating (energetic) atomic collision processes. At the end I brieey touch upon the recent successful above-breakup-threshold calculation of proton-deuteron elastic scattering for a realistic potential. Knowledge of the asymptotic form of the wave function is required, e.g., as boundary condition for selecting the physical solution of the Schrr odinger equation (SE) for energies above the ionisation threshold, and for deriving asymp-totic and/or analytic properties of quantities which are matrix elements of the three-body Coulomb resolvent, such as the optical potential or the kernel of momentum space integral equations for charged particles (for a discussion of