  We investigate interactions of stellar binaries in galactic nuclear clusters
with a massive black hole (MBH). We consider binaries on highly eccentric
orbits around the MBH that change due to random gravitational interactions with
other stars in the nuclear stellar cluster. The pericenters of the orbits
perform a random walk, and we consider cases where this random walk slowly
brings the binary to the Hills tidal separation radius (the so-called empty
loss-cone regime). However, we find that in a majority of cases the expected
separation does not occur and instead the members of the binary merge together.
This happens because the binary's eccentricity is excited by tidal interactions
with the MBH, and the relative excursions of the internal eccentricity of the
binary far exceed those in its internal semimajor axis. This frequently reduces
the pericenter separation to values below typical stellar diameters, which
induces a significant fraction of such binaries to merge ($\gtrsim 75\%$ in our
set of numerical experiments). Stellar tides do not appreciably change the
total rate of mergers but circularise binaries, leading to a significant
fraction of low-eccentricity, low-impact-velocity mergers. Some of the stellar
merger products will then be tidally disrupted by the MBH within $\sim 10^6$
years. If the merger strongly enhances the magnetic field of the merger
product, this process could explain observations of prompt relativistic jet
formation in some tidal disruption events.
