  In studying encounters between binaries and single stars, one is interested
in three classes of events: exchanges of stars, hardening of the original
binary by a third star, and the production of merged objects. We present a
means for computing cross sections for these three outcomes for an arbitrary
binary and single star as might be found in the core of a globular cluster. The
cross sections for a number of binaries in various stellar populations are then
computed. We consider multiple encounters and the ultimate fate of a population
of binaries fed into the cores of different globular cluster models. We see
that the presence of only a relatively small number of binaries (containing
10\% of the stars) will boost the production rate of
astrophysically-interesting objects by a factor of at least a few over the
rates expected from encounters between single stars. In particular, the ratio
of smothered neutron stars to low-mass X-ray binaries (LMXBs) may be greatly
increased, possibly explaining, in part, the excess of millisecond pulsars
compared to LMXBs.
