β- andγ-Vibrational Bands ofSm152andGd154

Employing radioactive sources of ${}_{}{}^{152}{}_{}{}^{}\mathrm{Eu}$ (12.4 yr) and ${}_{}{}^{154}{}_{}{}^{}\mathrm{Eu}$ (16 yr) in both $\gamma$-ray singles and $\gamma -\gamma$ coincidence experiments, we have determined the intensities of most of the weak $\gamma$-ray transitions depopulating the 0+, 2+, and 4+ members of the $\beta$-vibrational bands and the 2+, 3+, and 4+ members of the $\gamma$-vibrational bands in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}$. From these $\gamma$-ray intensities, ratios of reduced $E2\mathrm{}$ transition probabilities have been determined and a detailed analysis of band mixing in these nuclei has been accomplished. Mixing of the $\beta$ and $\gamma$ bands into the ground-state rotational band and into each other has been considered but is found to be grossly insufficient in explaining the $B\left(E2\mathrm{}\right)\mathrm{}$ ratios from members of the $\beta$ band. However, this treatment does seem to be adequate in explaining the ratios from members of the $\gamma$ band in each nucleus. From our $\gamma$-ray intensities and literature values for the internal-conversion electron intensities and the reduced $E2\mathrm{}$ transition probabilities, it has been possible to evaluate the reduced nuclear matrix element $\rho$ for the electric-monopole transitions between the $\beta$ and ground-state bands in each nucleus. For ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$, $\rho$ is determined to be 0.28±0.02, while only an estimate of 0.44 is possible for ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}$. Values of $X$, the dimensionless ratio of the squares of the $E0\mathrm{}$ to $E2\mathrm{}$ reduced matrix elements, are determined and compared to the model predictions. The experimental values are generally 2.5 to 5 times smaller than predicted. Furthermore, the effects of non-adiabatic perturbations on the ground-state rotational band are considered. The contributions of centrifugal stretching to the observed energy shifts and to changes in radius within the rotational spectra can be estimated from our experimental determination of the band-mixing amplitudes. The results indicate that centrifugal stretching of the nucleus cannot explain the energy shifts in ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$ and ${}_{}{}^{154}{}_{}{}^{}\mathrm{Gd}$ but probably can account for the observed changes in radius for