  The transformation of atomic hydrogen to molecular hydrogen through
three-body reactions is a crucial stage in the collapse of primordial,
metal-free halos, where the first generation of stars (Population III stars) in
the Universe are formed. However, in the published literature, the rate
coefficient for this reaction is uncertain by nearly an order of magnitude. We
report on the results of both adaptive mesh refinement (AMR) and smoothed
particle hydrodynamics (SPH) simulations of the collapse of metal-free halos as
a function of the value of this rate coefficient. For each simulation method,
we have simulated a single halo three times, using three different values of
the rate coefficient. We find that while variation between halo realizations
may be greater than that caused by the three-body rate coefficient being used,
both the accretion physics onto Population III protostars as well as the
long-term stability of the disk and any potential fragmentation may depend
strongly on this rate coefficient.
