Elementary-Particle Treatment of Muon Capture inO16

Abstract

The rate of the muon-capture process in ${\mathrm{O}}^{16}$ which leads to the ${2}^{\ensuremath{-}}$ ground state of ${\mathrm{N}}^{16}$ is calculated treating the initial and final nuclei as "elementary" particles. Nuclear form factors are evaluated on the basis of the conserved-vector-current and partially-conserved-axial-vector-current hypotheses using experimental data on the corresponding beta-decay and inelastic-electron-scattering processes. The resultant calculated rate ${[\ensuremath{\Gamma}({\ensuremath{\mu}}^{\ensuremath{-}}+{\mathrm{O}}^{16}({0}^{+})\ensuremath{\rightarrow}{\mathrm{N}}^{16}({2}^{\ensuremath{-}})+{\ensuremath{\nu}}_{\ensuremath{\mu}})]}_{\mathrm{theor}}=(5.8\ifmmode\pm\else\textpm\fi{}2.3)\ifmmode\times\else\texttimes\fi{}{10}^{3}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ is consistent with the measured value ${[\ensuremath{\Gamma}({\ensuremath{\mu}}^{\ensuremath{-}}+{\mathrm{O}}^{16}({0}^{+})\ensuremath{\rightarrow}{\mathrm{N}}^{16}({2}^{\ensuremath{-}})+{\ensuremath{\nu}}_{\ensuremath{\mu}})]}_{\mathrm{exper}}=(6.3\ifmmode\pm\else\textpm\fi{}0.7)\ifmmode\times\else\texttimes\fi{}{10}^{3}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ and is to be contrasted with a calculated rate of ${(12\ifmmode\pm\else\textpm\fi{}2)\ifmmode\times\else\texttimes\fi{}10}^{3}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ obtained on the basis of a nuclear-model impulse-approximation approach.