  Motivated by anomalies in cosmic ray observations and by attempts to solve
questions of the Standad Model of particle physics like the (g-2)_mu
discrepancy, U(1) extensions of the Standard Model have been proposed in recent
years. Such U(1) extensions allow for the interaction of Dark Matter by
exchange of a photon-like massive force carrier \gamma' not included in the
Standard Model. In order to search for \gamma' bosons various experimental
programs have been started. One approach is the dedicated search at
fixed-target experiments at modest energies as performed at MAMI or at the
Jefferson Lab. In these experiments the process e(A,Z)->e(A,Z)l^+l^- is
investigated and a search for a very narrow resonance in the invariant mass
distribution of the l^+l^- pair is performed. In this work we analyze this
process in terms of signal and background in order to describe existing data
obtained by the A1 experiment at MAMI with the aim to give accurate predictions
for exclusion limits in the \gamma' parameter space. We present a detailed
theoretical analysis of the cross sections entering in the description of such
processes.
