  In this article, we study the asymptotic fields of the Yukawa particle-field
model of quantum physics, in the semiclassical regime $\hslash\to 0$, with an
interaction subject to an ultraviolet cutoff. We show that the transition
amplitudes between final (respectively initial) states converge towards
explicit quantities involving the outgoing (respectively incoming) wave
operators of the nonlinear Schr\"odinger-Klein-Gordon (S-KG) equation. Thus, we
rigorously link the scattering theory of the Yukawa model to that of the
Schr\"odinger-Klein-Gordon equation. Moreover, we prove that the asymptotic
vacuum states of the Yukawa model have a phase space concentration property
around classical radiationless solutions. Under further assumptions, we show
that the S-KG energy admits a unique minimizer modulo symmetries and identify
exactly the semiclassical measure of Yukawa ground states. Some additional
consequences of asymptotic completeness are also discussed, and some further
open questions are raised.
