On the impulse approximation in atomic collision physics

Abstract

Application of the quantum-mechanical impulse approximation in atomic collision physics leads to special problems caused by the long range of the Coulomb interaction between the individual particles. These problems are discussed using the exact T matrix as a starting point for the analysis. The discussion leads to a new variant of the restricted impulse approximation in which multiple scattering terms involving more than one target particle are disregarded. Free-free Coulomb scattering is correctly described by this variant of the impulse approximation and not by the conventional one. Our version of the restricted impulse approximation is shown to have an almost identical range of validity as the Born approximation in atomic collision physics, in contrast to the situation encountered in nuclear physics. It is further shown that the plane-wave impulse, plane-wave Born, binary-encounter and classical impulse-approximation cross-section formulae can be derived from the quantum-mechanical impulse-approximation formulae by making successive approximations.