In the framework of first-order theory, differential cross sections for e--H scattering in the presence of a laser field have been calculated. In the calculation, the dressed wavefunction of Byron and Joachain was used. The effect of exchange was taken into account explicitly. Both the dressing and the exchange effects are sensitive to the direction of the laser field. In a sufficiently intense laser field, the effect of exchange is virtually absent, i.e. the incident electron seems to be distinguishable from the target electron.

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