On the reliability of proxies for globular cluster collision rates
  (Abridged) Proxies for the stellar collision rates in globular clusters are
often used. We present comparisons between these proxies and the full
integrated collision rate for King models. Gamma, defined to be rho_0^3/2
r_c^2$, where $\rho_0$ is the central cluster density, and r_c is the core
radius, is an accurate representation of the collision rate from the King model
to within about 25% for all but the least concentrated clusters. Gamma_h,
defined to be rho_h^3/2 r_h^2, where rho_h is the average density within the
half-light radius, and $r_h$ is the half-light radius, is only marginally
better correlated with the full King model collision rate than is the cluster
luminosity. The two galaxies where results of King model fitting have been
reported in detail show a dearth of core-collapsed clusters relative to that
seen in the Milky Way, indicating that the core radii of the most concentrated
clusters are probably slightly overestimated. Recent work has suggested that
shallower than linear relations exist between proxies for Gamma and the
probability that a cluster will contain an X-ray source; we show that there is
a similarly shallow relationship between Gamma and Gamma_h; we also show that
measurement errors are likely to produce a shallower than linear relationship
even when Gamma itself is used. The evidence is thus consistent with the idea
that X-ray binary formation rates are linearly proportional to cluster
collision rates. We also find, through comparison with multimass models,
suggestive evidence that the retention fractions of neutron stars in globular
clusters may be related to the present day concentration parameters, which
would imply that the most concentrated clusters today were the most
concentrated clusters at the time of their supernovae.
