  We study the problem of two Dirac particles interacting through
non-relativistic potentials and confined to a two-dimensional sheet, which is
the relevant case for graphene layers. The two-body problem cannot be mapped
into that of a single particle, due to the non-trivial coupling between the
center-of-mass and the relative coordinates, even in the presence of central
potentials. We focus on the case of zero total momentum, which is equivalent to
that of a single particle in a Sutherland lattice. We show that zero-energy
states induce striking new features such as discontinuities in the relative
wave function, for particles interacting through a step potential, and a
concentration of relative density near the classical turning point, if
particles interact via a Coulomb potential. In the latter case we also find
that the two-body system becomes unstable above a critical coupling. These
phenomena may have bearing on the nature of strong coupling phases in graphene.
