  Luminous X-ray binaries (>1E34 erg/s, LMXBs) have a neutron star or black
hole primary, and in globular clusters, most of these close binaries are
expected to be have evolved from wider binaries through dynamical interactions
with other stars. We sought to find a predictor of this formation rate that is
representative of the initial properties of globular clusters rather than of
the highly evolved core quantities. Models indicate the half-light quantities
best reflect the initial conditions, so we examine whether the associated
dynamical interaction rate, proportional to L^1.5 r^-2.5, is useful in
understanding the presence of luminous LMXBs in the Galactic globular cluster
system. We find that while LMXB clusters with large values of L^1.5 r^-2.5
preferentially host LMXBs, the systems must also have half-mass relaxation
times below about 1E9 yr. This relaxation time effect probably occurs because
several relaxation times are required to modify binary separations, a timescale
that must be shorter than cluster ages. The frequency of finding an LMXB
cluster is enhanced if the cluster is metal-rich and if it is close to the
bulge region. The dependence upon metallicity is most likely due either to
differing initial mass functions at the high mass end, or because bulge systems
evolve more rapidly from tidal interactions with the bulge. This approach can
be used to investigate globular cluster systems in external galaxies, where
core properties are unresolved.
