Nuclear Structure Effects in "Elastic" Neutrino-Induced Reactions

Abstract

The effects of nuclear structure on "elastic" neutrino-induced reactions: ${\ensuremath{\nu}}_{\ensuremath{\mu}}+[Z, A]\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+[Z+1, A]$, ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}+[Z, A]\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}+[Z\ensuremath{-}1, A]$, are considered by use of methods analogous to those developed in the theory of muon capture by complex nuclei. A "nuclear structure effect quantity" ("n.s.e.q."), which allows calculation of the cross sections for ${\ensuremath{\nu}}_{\ensuremath{\mu}}+n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+p$ and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}+p\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}+n$ from the observed cross sections for ${\ensuremath{\nu}}_{\ensuremath{\mu}}+{[Z, A]}_{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+{[Z+1, A]}_{\mathrm{all}}$ and ${\overline{\ensuremath{\nu}}}_{\ensuremath{\mu}}+{[Z, A]}_{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}+{[Z\ensuremath{-}1, A]}_{\mathrm{all}}$, is derived and discussed. This "n.s.e.q." is, to a reasonable approximation, independent of the nucleon form factors associated with the lepton-hadron weak interaction and essentially involves only the nucleon-nucleon correlation function of ${[Z, A]}_{0}$ as determined by the internucleon forces and the exclusion principle. Finally, it is shown how the nuclear parameters entering into the nucleon-nucleon correlation function can be found from existing empirical data on electron scattering and muon capture by complex nuclei and, with use of the so-determined values of these parameters, values of the "n.s.e.q." for various [$Z, A$] and ${E}_{\ensuremath{\nu}}$ are given.