  We consider the conditions required for a cluster core to shrink, by
adiabatic accretion of gas from the surrounding cluster, to densities such that
stellar collisions are a likely outcome. We show that the maximum densities
attained, and hence the viability of collisions, depends on a competition
between core shrinkage (driven by accretion) and core puffing up (driven by
relaxation effects). The expected number of collisions scales as
$N_{core}^{5/3} \tilde v^2$ where $N_{core}$ is the number of stars in the
cluster core and $\tilde v$ is the free fall velocity of the parent cluster
(gas reservoir). Thus whereas collisions are very unlikely in a relatively low
mass, low internal velocity system such as the Orion Nebula Cluster, they
become considerably more important at the mass and velocity scale
characteristic of globular clusters. Thus stellar collisions in response to
accretion induced core shrinkage remains a viable prospect in more massive
clusters, and may contribute to the production of intermediate mass black holes
in these systems.
