Large excesses of Ca44 in certain presolar graphite and silicon carbide grains give strong evidence for Ti44 production in supernovae. Furthermore, recent detection of the Ti44 gamma-line from the Cas A SNR by CGRO/COMPTEL shows that radioactive Ti44 is produced in supernovae. These make the Ti44 abundance an observable diagnostic of supernovae. Through use of a nuclear reaction network, we have systematically varied reaction rates and groups of reaction rates to experimentally identify those that govern Ti44 abundance in core-collapse supernova nucleosynthesis. We survey the nuclear-rate dependence by repeated calculations of the identical adiabatic expansion, with peak temperature and density chosen to be 5.5xE9 K and 1E7 g/cc, respectively, to approximate the conditions in detailed supernova models. We find that, for equal total numbers of neutrons and protons (eta=0), Ti44 production is most sensitive to the following reaction rates: Ti44(alpha,p)V47, alpha(2alpha,gamma)C12, Ti44(alpha,gamma)Cr48, V45(p,gamma)Cr46. We tabulate the most sensitive reactions in order of their importance to the Ti44 production near the standard values of currently accepted cross-sections, at both reduced reaction rate (0.01X) and at increased reaction rate (100X) relative to their standard values. Although most reactions retain their importance for eta > 0, that of V45(p,gamma)Cr46 drops rapidly for eta >= 0.0004. Other reactions assume greater significance at greater neutron excess: C12(alpha,gamma)O16, Ca40(alpha,gamma)Ti44, Al27(alpha,n)P30, Si30(alpha,n)S33. Because many of these rates are unknown experimentally, our results suggest the most important targets for future cross section measurements governing the value of this observable abundance.
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