  We show asymptotic completeness of two-body scattering for a class of
translation invariant models describing a single quantum particle (the
electron) linearly coupled to a massive scalar field (bosons). Our proof is
based on a recently established Mourre estimate for these models. In contrast
to previous approaches, it requires no number cutoff, no restriction on the
particle-field coupling strength, and no restriction on the magnitude of total
momentum. Energy, however, is restricted by the two-boson threshold, admitting
only scattering of a dressed electron and a single asymptotic boson. The class
of models we consider include the UV-cutoff Nelson and polaron models.
