  The Schroedinger equation for N particles interacting through effective pair
potentials is derived from the massless Nelson model with ultraviolet cutoffs.
We consider a scaling limit where the particles are slow and heavy, but, in
contrast to earlier work [6], no ``weak coupling'' is assumed. To this end we
prove a space-adiabatic theorem without gap condition which gives, in
particular, control on the rate of convergence in the adiabatic limit.
