The impact of nuclear physics uncertainties on nucleosynthesis in thermonuclear supernovae has not been fully explored using comprehensive and systematic studies with multiple models. To better constrain predictions of yields from these phenomena, we have performed a sensitivity study by post-processing thermodynamic histories from two different hydrodynamic, Chandrasekhar-mass explosion models. We have individually varied all input reaction and, for the first time, weak interaction rates by a factor of ten and compared the yields in each case to yields using standard rates. Of the 2305 nuclear reactions in our network, we find that the rates of only 53 reactions affect the yield of any species with an abundance of at least 10^-8 M_sun by at least a factor of two, in either model. The rates of the 12C(a,g), 12C+12C, 20Ne(a,p), 20Ne(a,g) and 30Si(p,g) reactions are among those that modify the most yields when varied by a factor of ten. From the individual variation of 658 weak interaction rates in our network by a factor of ten, only the stellar 28Si(b+)28Al, 32S(b+)32P and 36Ar(b+)36Cl rates significantly affect the yields of species in a model. Additional tests reveal that reaction rate changes over temperatures T > 1.5 GK have the greatest impact, and that ratios of radionuclides that may be used as explosion diagnostics change by a factor of less than two from the variation of individual rates by a factor of 10. Nucleosynthesis in the two adopted models is relatively robust to variations in individual nuclear reaction and weak interaction rates. Laboratory measurements of a limited number of reactions would help to further constrain predictions. As well, we confirm the need for a consistent treatment for relevant stellar weak interaction rates since simultaneous variation of these rates (as opposed to individual variation) has a significant effect on yields in our models.
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