SPACE AND TIME CORRELATION IN HIGH-VELOCITY MULTIPLE ELECTRON TRANSITIONS

In collisions of high velocity projectiles of charge Z and velocity v, perturbations expansions in Z/v usually converge when Z/v < 1. Under these conditions Z3 contributions to cross sections for two electron transitions (e.g. double excitation) may arise if there is interference between first order and second order contributions to the probability amplitude. Non-zero Z3 terms in two electron excitation or ionization cross sections occur if spatial electron correlation is present. For double excitation non-zero Z3 contributions require a correlation in time as well. This time correlation corresponds to quantum time ordering arising from virtual off-energy-shell intermediate states. As with second order amplitudes for Thomas singularities in single electron capture, the energy nonconserving amplitude is connected to the energy-conserving amplitude in second order in Z by a dispersion relation. Generalization to higher order transitions (e.g. triple excitation) is discussed.