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

Abstract

The theory of the capture of muons by nuclei (${\mu }^{-}+N_a\to {\nu }_{\mu }+N_b$) is developed, the nuclei $N_a$ and $N_b$ being treated as "elementary" particles. Form factors are introduced to describe the $N_a\to N_b$ 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 ${\mu }^{-}+{}_2{}^{}{}_{}{}^{}\mathrm{He}_1^{}{}_{}{}^3\to {\nu }_{\mu }+{}_1{}^{}{}_{}{}^{}\mathrm{H}_2^{}{}_{}{}^3$, ${\mu }^{-}+{}_6{}^{}{}_{}{}^{}\mathrm{C}_6^{}{}_{}{}^{12}\to {\nu }_{\mu }+{}_5{}^{}{}_{}{}^{}\mathrm{B}_7^{}{}_{}{}^{12}$, and ${\mu }^{-}+{}_3{}^{}{}_{}{}^{}\mathrm{Li}_3^{}{}_{}{}^6\to {\nu }_{\mu }+{}_2{}^{}{}_{}{}^{}\mathrm{He}_4^{}{}_{}{}^6$ are discussed explicitly and the calculated rates are compared with available measured values.