Simple Relation between Cross Sections for Neutrino Scattering and Total Muon-Capture Rates by Nuclei

Abstract
Using the closure approximation, we derive a simple relation between the total forward cross section for elastic scattering of neutrinos by nuclei and the corresponding total muon-capture rates. This relation is in good agreement with previous estimates of neutrino scattering cross sections, but still in disagreement with recent experimental data.