  It has been shown that the behaviour of primordial gas collapsing in a dark
matter minihalo can depend on the adopted choice of 3-body H$_2$ formation
rate. The uncertainties in this rate span two orders of magnitude in the
current literature, and so it remains a source of uncertainty in our knowledge
of population III star formation. Here we investigate how the amount of
fragmentation in primordial gas depends on the adopted 3-body rate. We present
the results of calculations that follow the chemical and thermal evolution of
primordial gas as it collapses in two dark matter minihalos. Our results on the
effect of 3-body rate on the evolution until the first protostar forms agree
well with previous studies. However, our modified version of GADGET-2 SPH also
includes sink particles, which allows us to follow the initial evolution of the
accretion disc that builds up on the centre of each halo, and capture the
fragmentation in gas as well as its dependence on the adopted 3-body H$_2$
formation rate. We find that the fragmentation behaviour of the gas is only
marginally effected by the choice of 3-body rate co-efficient, and that
halo-to-halo differences are of equal importance in affecting the final mass
distribution of stars.
