Electric quadrupole and magnetic dipole transition probabilities within the ground configuration ofF+

Abstract

The radiative lifetime of the ${2s}^{2}{2p}^{4}$ ${}^{1}{S}_{0}$ level in ${\mathrm{F}}^{+}$ has been measured by time-resolved observations of both strong (though electric-dipole forbidden) decay branches: the electric quadrupole $(E2)$ transition $(\ensuremath{\approx}80%$ branch) to the ${2s}^{2}{2p}^{4}$ ${}^{1}{D}_{2}$ level and the magnetic dipole $(M1)$ transition $(\ensuremath{\approx}20%$ branch) to the ${2s}^{2}{2p}^{4}$ ${}^{3}{P}_{1}$ level. We observed the fluorescence associated with both transitions from a population of ${\mathrm{F}}^{+}$ ions circulating in a heavy-ion storage ring. Our result for the ${\mathrm{F}}^{+}$ ${2s}^{2}{2p}^{4}$ ${}^{1}{S}_{0}$ level lifetime of $420\ifmmode\pm\else\textpm\fi{}12$ ms provides a benchmark for theory. Moreover, although the calculated lifetimes vary by more than 20%, the calculated branching fractions vary by less than 4% and 7% for the ${}^{1}{\stackrel{\ensuremath{\rightarrow}}{{S}_{0}}}^{1}{D}_{2}$ $E2$ and ${}^{1}{\stackrel{\ensuremath{\rightarrow}}{{S}_{0}}}^{3}{P}_{1}$ $M1$ transitions, respectively. Using our measured lifetime and the calculated branching fractions, we report semiempirical transition probabilities for the ${}^{1}{\stackrel{\ensuremath{\rightarrow}}{{S}_{0}}}^{1}{D}_{2}$ $E2$ and ${}^{1}{\stackrel{\ensuremath{\rightarrow}}{{S}_{0}}}^{3}{P}_{1}$ M1 transitions of 1.90 ${\mathrm{s}}^{\ensuremath{-}1}\ifmmode\pm\else\textpm\fi{}7%$ and 0.50 ${\mathrm{s}}^{\ensuremath{-}1}\ifmmode\pm\else\textpm\fi{}9%,$ respectively.