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.
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McGuire et al. (1991) studied this question.
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