Nuclear magnetization distribution radii determined by hyperfine transitions in the1slevel of H-like ions185Re74+and187Re74+

Abstract

The $F=3$ to $F=2$ hyperfine transitions in the $1s$ ground state of the two isotopes ${}^{185}{\mathrm{Re}}^{74+}$ and ${}^{187}{\mathrm{Re}}^{74+}$ were measured to be $(4560.5\ifmmode\pm\else\textpm\fi{}3)\AA{}$ and $(4516.9\ifmmode\pm\else\textpm\fi{}3)\AA{},$ respectively, using emission spectroscopy in an electron beam ion trap. After applying appropriate corrections for the nuclear charge distribution and QED effects, a Bohr-Weisskopf effect of \ensuremath{\varepsilon}=2.23(9)% and 2.30(9)% are found for ${}^{185}\mathrm{Re}$ and ${}^{187}\mathrm{R}\mathrm{e},$ respectively. This value is almost twice that of a previous theoretical estimate, and indicates a distribution of the nuclear magnetization far more extended than that of the nuclear charge. A radius of the magnetization distribution of $〈{r}_{m}^{2}{〉}^{1/2}=7.57(32)$ fm and $〈{r}_{m}^{2}{〉}^{1/2}$=7.69(32) fm for ${}^{185}\mathrm{Re}$ and ${}^{187}\mathrm{R}\mathrm{e},$ respectively, is inferred from the data. These radii are larger than the nuclear charge distribution radius $[〈{r}_{c}^{2}{〉}^{1/2}=5.39(1)$ fm] for both isotopes by factors 1.40(6) and 1.43(6), respectively. We find that the Bohr-Weisskopf effect in H-like ions is a sensitive probe of nuclear magnetization distribution, especially for cases where the charge distribution and magnetic moments are accurately known.