  Invariant mass spectra of di-electrons stemming from bremsstrahlung processes
are calculated in a covariant diagrammatical approach for the exclusive
reaction D p \to p_{\rm sp} n p e^+ e^- with detection of a forward spectator
proton, p_{sp}. We employ an effective nucleon-meson theory for parameterizing
the sub-reaction n p \to n p e^+ e^- and, within the Bethe-Salpeter formalism,
derive a factorization of the cross section in the form {d\sigma_{D p \to
p_{\rm sp} n p e^+ e^-}}/{dM}= {d\sigma_{n p \to n p e^+ e^-}}/{dM} \times
kinematical factor related solely to the deuteron (M is the e^+ e^- invariant
mass). The effective nucleon-meson interactions, including the exchange mesons
\pi, \sigma, \omega and \rho as well as excitation and radiative decay of
\Delta(1232), have been adjusted to the process pp \to pp e^+ e^- at energies
below the vector meson production threshold. At higher energies, contributions
from \omega and \rho meson excitations are analyzed in both, NN and Dp
collisions. A relation to two-step models is discussed. Subthreshold
di-electron production in Dp collisions at low spectator momenta is
investigated as well. Calculations have been performed for kinematical
conditions envisaged for forthcoming experiments at HADES.
