Systematic Calculation of Neutrino–Nucleus Cross Section Available for Astrophysical Applications

Abstract

Assuming the universality of weak interactions, we have studied the weak processes such as β-decay and electron capture using the nuclear gross theory of beta decay (GTBD). We evaluate the β^± and electron capture decay rates and the neutrino–nucleus cross sections as a function of the energy of the incident neutrino, for E_ν < 250 MeV. The evaluation performed some years ago for the electron neutrino–nucleus reactions in the mass region A < 70 is extended to the heavy one A < 220 for a set of 965 nuclear species of astrophysical interest. The nuclei are separated according to its parity in even–even, even–odd, odd–odd, and odd–even nuclei, both for β^±-decay and electron capture. The obtained cross sections are interpolated by means of a fourth-degree polynomial function in E_ν. The coefficients in these polynomials are obtained and later fitted as a function of A and Z. The fitting procedure is described in detail paying special attention to the root mean square deviations in the adjustment. These polynomial functions provide a tool for the systematic evaluation of the cross sections needed in astrophysical processes like the r-process during the nucleosynthesis of supernovae.