Variational Methods in Charged-Particle Collision Theory

Abstract

A variational principle of the Kohn type is formulated for the scattering of three charged particles, with particular attention given to the breakup process. In addition, an effective-potential theory, which also allows for variational formulation, is derived for the three-body system with long-ranged Coulomb interactions properly accounted for. These results generalize previous work done for systems with short-ranged interactions; the difference lies, essentially, in the use of Coulomb-modified plane waves to describe the asymptotic states. To establish the physical justification for this modified version of scattering theory a section is included containing a time-dependent description of the collision process in which the wave packets follow classical, Coulomb-modified, trajectories in the initial and final states.