Nuclear Data for Explosive Hydrogen Burning on A=30-50 Nuclei

We have provided an exhaustive compilation and documentation of parameters relevant to the 31P(p,?) and 31P(p,a) reactions, including where possible resonance energies, spins and parities, resonance strengths and proton, gamma, alpha and total widths. We have also compiled the uncertainties wherever possible, one of the primary goals of our compilation, for not only the resonance energies but also for the resonance strengths and widths. In calculating the final uncertainties for cross sections and reaction rates, a method for propagating those errors through the reaction rate calculations was developed, using both deterministic matrix techniques and Monte Carlo simulation methods. (Hix 1999, M. Smith 2002) Our conclusion was that the Monte Carlo simulations were the preferred method. (D. Smith 2002) It was also determined that using a lognormal probability function rather than the usual Gaussian distribution is appropriate in situations where the uncertainties in the resonance strengths are large. (Smith 1991) If not addressed in this manner, one could end up with the completely unphysical situation where some of the forward reaction rates are negative when using a sampling method such as the Monte Carlo simulations do. The large uncertainties, usually in resonance strength, occur quite frequently especially in the low excitation energy levels which are often the most important for astrophysical calculations, but are also the most difficult to measure. We have also laid the groundwork for a method which might be followed in further compilations, and have carefully addressed the assumptions that underlie such compilations and calculations as we have undertaken. The complete results will be published in Argonne Report ANL/NDM-155.