A Semi-Empirical Statistical Model for Thermonuclear Reaction Rates and its Application to Neutron Induced Reactions

A global statistical model for the calculation of laboratory cross sections and of ground and excited state thermonuclear reaction rates of importance to intermediate and heavy element nucleosynthesis in stars is constructed, and its application to neutron induced reactions is discussed. The model is based upon the statistical theory of nuclear reactions as embodied in the Hauser-Feshbach formula. It is applicable to reactions involving proton, neutron, alpha, and photon channels and compound nuclei from approximately Ne to Bi at energies from the resonance range (usually several keV) to approximately 10 MeV. Excited state effects are considered not only in all exit channels, but also in target nuclei for the calculation of stellar reaction rates. The adopted level density formulation and photon transmission function are both constructed from a combination of theoretical and experimental information. A discussion on the extension of the model to include isospin is given. The discussion of the neutron induced reactions develops simple analytical fitting formulae for the reaction rates and designed for use in nucleosynthesis codes. It also presents sample results of extensive calculations carried out using this model, and considers the systematics of 30 keV (n,γ) reaction rates which are important to s-process nucleosynthesis. The model developed is capable of calculating, typically to within a factor of 2, cross sections and reaction rates for a large number of reactions given only the charges, masses, binding energies, and excited state properties (if known) of the component nuclei, and to do so without the use of prohibitive amounts of computer time.