  We consider the Dirac equation for the classical spinor field placed in an
external, time-dependent electromagnetic field of the form typical for
scattering settings:
$F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$, where the
current producing $F^{\mathrm{ret}/\mathrm{adv}}$ has past and future
asymptotes homogeneous of degree $-3$, and the free fields
$F^{\mathrm{in}/\mathrm{out}}$ are radiation fields produced by currents with
similar asymptotic behavior. We show the existence of the electromagnetic
gauges in which the particle has 'in' and 'out' asymptotic states approaching
free field states, with no long-time corrections of the free dynamics. Using a
special Cauchy foliation of the spacetime we show in this context the existence
and asymptotic completeness of the wave operators. Moreover, we define a
special 'evolution picture' in which the free evolution operator has
well-defined limits for $t\to\pm\infty$, thus the scattering wave operators do
not need the free evolution counteraction.
