Non-Relativistic Models at High Energies

Abstract

Abstract In this chapter, we shall be concerned with charge exchange at high impact velocities for which methods based on perturbation or distorted wave series are appropriate, but for which a non-relativistic formulation remains accurate. This high-velocity region cannot be precisely defined, but as a guide we can take v0/ve 3 4 where v0 is the incident velocity and ve the Bohr velocity of the active electron in the target. Relativistic corrections for collisions between light ions become significant when v0 ≤ 60 a.u. and we shall consider the modifications required to the theory to take account of these in the next chapter. It is interesting to consider the mechanisms which allow the capture of an electron from a target atom (B + -e ) by a very fast ion A. (A very full analysis has been given by Shakeshaft and Spruch (1979)). In a reference frame centred on the ion A, the initial electronic energy (kinetic) of V6/2 is large, while the final electronic energy, after capture, of the atom (A+ e-) is small. The different mechanisms for capture correspond to different means of effecting this change of energy. The first possibility is radiative capture, A + (B + e-) -> (A + e-) + B + hv. At sufficiently high energies, the ion B acts as a spectator and the cross section is effectively that for radiative capture of a free electron by the moving ion A. This process will be discussed in Chapter 11. All that needs to be noted here is that although the cross section for radiative capture is small at low impact velocities it decreases less rapidly (like E- i or v0 2) than non-radiative capture cross sections and is the dominant process at high energies. This occurs at impact energies in excess of ~ 10 MeV/a.m.u. for collisions between light ions.