This work is supported by the Division of Chemical Sciences, Office of Basic Energy Science, Office of Energy Research, and the U.S. Department of Energy.
Physical Review A
Electronic excitation -- Mathematical models, Electrons -- Capture, Dispersion relations
Results of calculations of double excitation of helium to n=2 states for fast projectiles of charge Z are presented. Nonzero Z3 contributions for single and double excitation occur only when time-ordering contributions from the second-order amplitude are nonzero. For double excitation, electron correlation must also be nonzero to obtain Z3 terms. The time-ordering effects arise from virtual off-energy-shell intermediate states. As with second-order amplitudes for Thomas singularities in electron capture, the energy-nonconserving amplitude is connected to the second-order energy-conserving amplitude by a dispersion relation. Comparison is made with experiment.
McGuire, J. H., and Jack C. Straton. "Double excitation of helium by fast particles of charge Z." Physical Review A 43.9 (1991): 5184. DOI: http://dx.doi.org/10.1103/PhysRevA.43.5184