$M1\mathrm{}$ Transition Probabilities in Odd-Mass Deformed Nuclei

The odd-mass deformed nuclei ${}_{}{}^{153}{}_{}{}^{}\mathrm{Eu}$, ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$, ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$, ${}_{}{}^{169}{}_{}{}^{}\mathrm{Tm}$, ${}_{}{}^{175}{}_{}{}^{}\mathrm{Lu}$, and ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$ have been studied by Coulomb excitation with 50-MeV oxygen ions. The branching ratios for the de-excitation of levels in the ground-state rotational bands were determined by measuring the $\gamma$-ray intensities in singles spectra observed with a Ge(Li) detector. $M1\mathrm{}$ transition rates were obtained from the branching ratios with the assumption that the rotational-model predictions for the $E2\mathrm{}$ transition rates are correct. For ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$, six $M1\mathrm{}$ transition rates are compared. In all cases the $M1\mathrm{}$ transition rates agree with rotational-model theory within experimental error. Absolute $E2\mathrm{}$ transition rates were also measured for some of the vibrational and intrinsic states observed.