Theory of Muon Capture with Initial and Final Nuclei Treated as "Elementary" Particles

Abstract

The theory of the capture of muons by nuclei (${\ensuremath{\mu}}^{\ensuremath{-}}+{N}_{a}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}+{N}_{b}$) is developed, the nuclei ${N}_{a}$ and ${N}_{b}$ being treated as "elementary" particles. Form factors are introduced to describe the ${N}_{a}\ensuremath{\rightarrow}{N}_{b}$ transition matrix elements of the hadron weak currents; these form factors are then evaluated on the basis of the conserved-vector-current and partially-conserved-axial-vector-current hypotheses and with use of appropriate experimental data regarding the corresponding electromagnetic and beta-decay transitions. The reactions ${\ensuremath{\mu}}^{\ensuremath{-}}+_{2}\mathrm{He}_{1}^{3}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}+_{1}\mathrm{H}_{2}^{3}$, ${\ensuremath{\mu}}^{\ensuremath{-}}+_{6}\mathrm{C}_{6}^{12}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}+_{5}\mathrm{B}_{7}^{12}$, and ${\ensuremath{\mu}}^{\ensuremath{-}}+_{3}\mathrm{Li}_{3}^{6}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\mu}}+_{2}\mathrm{He}_{4}^{6}$ are discussed explicitly and the calculated rates are compared with available measured values.