Measurement and theoretical analysis of some reaction rates of interest in silicon burning

Total cross-sections for the 27Al(a, n)30P, 35Cl(a, n)38K, 46Ti(a, n)49Cr, 40Ca(a, p)43 Sc, and 45Sc(p, n)45Ti reactions have been measured in the energy range of importance for nucleosynthesis in stellar silicon burning. For comparison, reaction cross-sections have been calculated from the statistical theory of nuclear reactions, using an "equivalent square well" in the evaluation of the transmission functions. The calculated cross-sections are in general within a factor of 2 of the experimental values over the measured energy range. Stellar reaction rates, N aV , have been deduced from the observed reaction cross-sections and have been represented approximately by theoretically reasonable analytic functions of the temperature. It is shown that estimates for such analytic functions for reactions which have not been measured must take into account the competition between the dominant open reaction channels. The effect of excited states in target and residual nuclei is treated, and an effective overall cross-section is defined and discussed. Subject heading: nuclear reactions