It is shown that use of the plane-wave approximation to describe (non-relativistic) fast particles does not always lead to the correct transition amplitudes, even in the high-energy limit. As an illustration of the possible difficulties, the photoionisation process is analysed in detail. It is found that use of the plane-wave approximation can lead to high-energy transition amplitudes which are incorrect by a factor of two or more, depending on the atomic potential and also on which form of the electromagnetic interaction is used.
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Cordes et al. (1980) studied this question.
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