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 $R_{\gamma },$ the partial branching ratios of radiative muon capture for photon energies $>57\mathrm{}$ MeV, for ${}^{58,60,62}\mathrm{Ni}$ were found to be (in units of ${10}^{-5})$ $1.48\pm 0.08,$ $1.39\pm 0.09,$ and $1.05\pm 0.06,$ 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 $R_{\gamma }$ data with neutron excess. Furthermore, the observed atomic mass and neutron excess dependence of the entire nuclear $R_{\gamma }$ data set is well reproduced by a relativistic Fermi-gas calculation. The ability of the model to reproduce the variation of the $R_{\gamma }$ data using the Goldberger-Treiman formula for $g_p$ suggests there is no compelling reason to invoke a more exotic $A$-dependent renormalization of $g_p.$

• Received 20 January 1998

DOI:https://doi.org/10.1103/PhysRevC.58.1767