  We analyze the Bragg regime of the two-particle Kapitza-Dirac arrangement,
completing the basic theory of this effect. We provide a detailed evaluation of
the detection probabilities for multi-mode states, showing that a complete
description must include the interaction time in addition to the usual
dimensionless parameter w. The arrangement can be used as a massive
two-particle beam splitter. In this respect, we present a comparison with
Hong-Ou-Mandel-type experiments in quantum optics. The analysis reveals the
presence of dips for massive bosons and a differentiated behavior of
distinguishable and identical particles in an unexplored scenario. We suggest
that the arrangement can provide the basis for symmetrization verification
schemes.
