Hyperfine Structure and Nuclear Moments ofLu175

Abstract

The hyperfine structures of the $5d6{s}^{2}^{2}D_{\frac{3}{2}}$ ground state of ${\mathrm{Lu}}^{175}$ and its associated $^{2}D_{\frac{5}{2}}$ metastable state have been studied by means of the atomic beam magnetic resonance method. Radio-frequency transitions belonging to seven of the eight hfs intervals have been measured, as well as low-frequency ($\ensuremath{\Delta}F=0$) transitions at various magnetic fields in both states. The analysis of these data by means of an electronic computer yields not only precise values for the different interaction constants and the electronic $g$ factors, but also the first directly measured value for the nuclear $g$ factor of ${\mathrm{Lu}}^{175}$. The results are as follows $^{2}D_{\frac{3}{2}}$: $A=194.3316\ifmmode\pm\else\textpm\fi{}0.0004$ Mc/sec, $B=1511.4015\ifmmode\pm\else\textpm\fi{}0.0030$ Mc/sec, ${g}_{J}=\ensuremath{-}0.79921\ifmmode\pm\else\textpm\fi{}0.00008$, ${{g}_{I}}^{\ensuremath{'}}=+(3.50\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ (with ${\ensuremath{\mu}}_{I}$ expressed in Bohr magnetons), whence ${\ensuremath{\mu}}_{I}=+(2.25\ifmmode\pm\else\textpm\fi{}0.10)$ nm. $^{2}D_{\frac{5}{2}}$: $A=146.7790\ifmmode\pm\else\textpm\fi{}0.0008$ Mc/sec, $B=1860.6480\ifmmode\pm\else\textpm\fi{}0.0080$ Mc/sec, ${g}_{J}=\ensuremath{-}1.20040\ifmmode\pm\else\textpm\fi{}0.00016$, ${{g}_{I}}^{\ensuremath{'}}=+(3.13\ifmmode\pm\else\textpm\fi{}0.24)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ (with ${\ensuremath{\mu}}_{I}$ expressed in Bohr magnetons), whence ${\ensuremath{\mu}}_{I}=+(2.01\ifmmode\pm\else\textpm\fi{}0.15)$ nm.The values for the nuclear magnetic moment quoted for the two states are somewhat different from one another, even though their limits of error just overlap. The reason for this difference is not fully understood. For the present the mean of the two values, viz. ${\ensuremath{\mu}}_{I}=+(2.17\ifmmode\pm\else\textpm\fi{}0.19)$ nm (corrected for diamagnetic shielding effect) is taken as the best value. The nuclear electric quadrupole moment has been calculated from the $B$ factors to be $Q=+(5.68\ifmmode\pm\else\textpm\fi{}0.06)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$ (without Sternheimer correction). The accuracy of the present investigation was not sufficient to allow the derivation of an octupole moment.In the interpretation of the experimentally observed $A$ factors configuration mixing had to be considered.