  We consider the massless Nelson model with two types of massive particles
which we call atoms and electrons. The atoms interact with photons via an
infrared regular form-factor and thus they are Wigner-type particles with sharp
mass-shells. The electrons have an infrared singular form-factor and thus they
are infraparticles accompanied by soft-photon clouds correlated with their
velocities. In the weak coupling regime we construct scattering states of one
atom and one electron, and demonstrate their asymptotic clustering into
individual particles. The proof relies on the Cook's argument, clustering
estimates, and the non-stationary phase method. The latter technique requires
sharp estimates on derivatives of the ground state wave functions of the fiber
Hamiltonians of the model, which were proven in the earlier papers of this
series. Although we rely on earlier studies of the atom-atom and
electron-photon scattering in the Nelson model, the paper is written in a
self-contained manner. A perspective on the open problem of the
electron-electron scattering in this model is also given.
