Isotope dependence of radiative muon capture on the58,60,62Ni isotopes

Abstract

We report measurements of the photon rates and energy spectra from inclusive radiative muon capture on three nickel isotopes using a photon pair spectrometer at the TRIUMF cyclotron. The values of ${R}_{\ensuremath{\gamma}},$ the partial branching ratios of radiative muon capture for photon energies $>57$ MeV, for ${}^{58,60,62}\mathrm{Ni}$ were found to be (in units of ${10}^{\ensuremath{-}5})$ $1.48\ifmmode\pm\else\textpm\fi{}0.08,$ $1.39\ifmmode\pm\else\textpm\fi{}0.09,$ and $1.05\ifmmode\pm\else\textpm\fi{}0.06,$ assuming a Fermi-gas photon spectral shape. The results reveal a significant isotope effect in the nickel branching ratios and a simple empirical scaling of the present nickel and earlier nuclear ${R}_{\ensuremath{\gamma}}$ data with neutron excess. Furthermore, the observed atomic mass and neutron excess dependence of the entire nuclear ${R}_{\ensuremath{\gamma}}$ data set is well reproduced by a relativistic Fermi-gas calculation. The ability of the model to reproduce the variation of the ${R}_{\ensuremath{\gamma}}$ data using the Goldberger-Treiman formula for ${g}_{p}$ suggests there is no compelling reason to invoke a more exotic $A$-dependent renormalization of ${g}_{p}.$