Nuclear Structure Effects in "Elastic" Neutrino-Induced Reactions

The effects of nuclear structure on "elastic" neutrino-induced reactions: ${\nu }_{\mu }+[Z, A]\to {\mu }^{-}+[Z+1, A]$, ${\overline{\nu }}_{\mu }+[Z, A]\to {\mu }^{+}+[Z-1, A]$, 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 ${\nu }_{\mu }+n\to {\mu }^{-}+p$ and ${\overline{\nu }}_{\mu }+p\to {\mu }^{+}+n$ from the observed cross sections for ${\nu }_{\mu }+{[Z, A]}_0\to {\mu }^{-}+{[Z+1, A]}_{\mathrm{all}}$ and ${\overline{\nu }}_{\mu }+{[Z, A]}_0\to {\mu }^{+}+{[Z-1, A]}_{\mathrm{all}}$, 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 $E_{\nu }$ are given.