Statistical theory of nuclear neutrino capture

Abstract

Abstract The statistical theory of nuclear neutrino capture is extended to include first-forbidden transitions. A comparison with the theory of Bahcall and Frautschi is made. It is found that the present theory predicts neutrino capture cross sections which are smaller than those of Bahcall and Frautschi by a factor 2–3 for neutrino energies less than 50 MeV when first-forbidden transitions are dominant. Calculation of the cross section is made for the process in which 37 Cl nuclei capture electron neutrinos that are emitted in muon decay. The present calculation gives a cross section which is around one half of that of Donnelly and Haxton. Finally the contributions of the highly excited states in 37 Ar to the neutrino capture cross section are evaluated. It is shown that the contributions from the highly excited states ( E > 6.02 MeV) to the neutrino capture cross section amount to 60% for E v = 50 MeV.