  The bipolaron are two electrons coupled to the elastic deformations of an
ionic crystal. We study this system in the Fr\"{o}hlich approximation. If the
Coulomb repulsion dominates, the lowest energy states are two well separated
polarons. Otherwise the electrons form a bound pair. We prove the validity of
the Pekar-Tomasevich energy functional in the strong coupling limit, yielding
estimates on the coupling parameters for which the binding energy is strictly
positive. Under the condition of a strictly positive binding energy we prove
the existence of a ground state at fixed total momentum $P$, provided $P$ is
not too large.
