β -delayed proton decays of the T z = 1 / 2 series nuclei, 81 Zr and 85 Mo

The decays of ${T}_{z}=1/2$ series nuclei ${}^{81}\\mathrm{Zr}$ and ${}^{85}\\mathrm{Mo}$ have been restudied via their $\\ensuremath{\\beta}$-delayed proton decay by using p-$\\ensuremath{\\gamma}$ coincidence measurements. The $\\ensuremath{\\beta}$-delayed proton spectra populating the first excited states of the final nuclei have been obtained. By using statistical model calculations with level densities calculated with a backshifted Fermi gas model, the spin and parity for the ground state of ${}^{81}\\mathrm{Zr}$ have been tentatively assigned to be ${3/2}^{\\ensuremath{-}}$ and those for ${}^{85}\\mathrm{Mo}$ to be ${1/2}^{\\ensuremath{-}}.$ Their ${Q}_{\\mathrm{e}.\\mathrm{c}.}\\ensuremath{-}{B}_{p}$ values are $4.7\\ifmmode\\pm\\else\\textpm\\fi{}0.2$ and $5.1\\ifmmode\\pm\\else\\textpm\\fi{}0.2 \\mathrm{MeV},$ which correspond to mass excesses of $\\ensuremath{-}58.3\\ifmmode\\pm\\else\\textpm\\fi{}0.2 \\mathrm{MeV}$ for ${}^{81}\\mathrm{Zr}$ and of $\\ensuremath{-}59.1\\ifmmode\\pm\\else\\textpm\\fi{}0.4 \\mathrm{MeV}$ for ${}^{85}\\mathrm{Mo},$ respectively. Combining the measured half-lives with the calculated partial ones yields branches of $\\ensuremath{\\beta}$-delayed proton decay for ${}^{81}\\mathrm{Zr}$ and ${}^{85}\\mathrm{Mo}$ of $(1.2\\ifmmode\\pm\\else\\textpm\\fi{}0.2)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}3}$ and $(1.4\\ifmmode\\pm\\else\\textpm\\fi{}0.2)\\ifmmode\\times\\else\\texttimes\\fi{}{10}^{\\ensuremath{-}3},$ respectively.