  We consider the effects of uncertainties in nuclear reaction rates on the
cosmological constraints on the decays of unstable particles during or after
Big-Bang nucleosynthesis (BBN). We identify the nuclear reactions due to
non-thermal hadrons that are the most important in perturbing standard BBN,
then quantify the uncertainties in these reactions and in the resulting
light-element abundances. These results also indicate the key nuclear processes
for which improved cross section data would allow different light-element
abundances to be determined more accurately, thereby making possible more
precise probes of BBN and evaluations of the cosmological constraints on
unstable particles. Applying this analysis to models with unstable gravitinos
decaying into neutralinos, we calculate the likelihood function for the
light-element abundances measured currently, taking into account the current
experimental errors in the determinations of the relevant nuclear reaction
rates. We find a region of the gravitino mass and abundance in which the
abundances of deuterium, He4 and Li7 may be fit with chi^2 = 5.5, compared with
chi^2 = 31.7 if the effects of gravitino decays are unimportant. The best-fit
solution is improved to chi^2 ~ 2.0 when the lithium abundance is taken from
globular cluster data. Some such re-evaluation of the observed light-element
abundances and/or nuclear reaction rates would be needed if this region of
gravitino parameters is to provide a complete solution to the cosmological Li7
problem.
