Muon capture by11Band the hyperfine effect

Abstract

This paper reports a precision measurement of the ratio of the exclusive capture rates from the two hyperfine levels of the muonic ${}^{11}\mathrm{B}$ atom leading to the excited level of ${}^{11}\mathrm{Be}$ at 320 keV: ${\ensuremath{\lambda}}^{+}/{\ensuremath{\lambda}}^{\ensuremath{-}}=0.028\ifmmode\pm\else\textpm\fi{}0.021(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}0.003$ (syst.). Using the most up-to-date halo wave functions of the nuclei involved, the induced pseudoscalar to axialvector form factor ratio is obtained as ${g}_{P}{/g}_{A}{=4.3}_{\ensuremath{-}4.3}^{+2.8}(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}0.5$ (syst.). This value agrees with the partial conservation of the axial current prediction and does not reproduce the anomaly observed in radiative muon capture on hydrogen. The hyperfine conversion rate between the two hyperfine levels is also determined, $R=[181\ifmmode\pm\else\textpm\fi{}16(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}1(\mathrm{syst}.)]\ifmmode\times\else\texttimes\fi{}{10}^{3} {\mathrm{s}}^{\ensuremath{-}1}.$ The total capture rate from the lower hyperfine level and its difference compared to the upper one were also determined: ${\ensuremath{\lambda}}_{C}^{\ensuremath{-}}=[23.53\ifmmode\pm\else\textpm\fi{}0.72(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}0.25(\mathrm{syst}.)]\ifmmode\times\else\texttimes\fi{}{10}^{3} {\mathrm{s}}^{\ensuremath{-}1}$ and $\ensuremath{\Delta}\ensuremath{\lambda}=[\ensuremath{-}13.2\ifmmode\pm\else\textpm\fi{}1.7(\mathrm{stat}.)\ifmmode\pm\else\textpm\fi{}0.7(\mathrm{syst}.)]\ifmmode\times\else\texttimes\fi{}{10}^{3} {\mathrm{s}}^{\ensuremath{-}1}.$