  We investigate Anderson transitions for a system of two particles moving in a
three-dimensional disordered lattice and subject to on-site (Hubbard)
interactions of strength U. The two-body problem is exactly mapped into an
effective single-particle equation for the center of mass motion, whose
localization properties are studied numerically. We show that, for zero total
energy of the pair, the transition occurs in a regime where all single-particle
states are localized. In particular the critical disorder strength exhibits a
non-monotonic behavior as a function of |U|, increasing sharply for weak
interactions and converging to a finite value in the strong coupling limit.
Within our numerical accuracy, short-range interactions do not affect the
universality class of the transition.
