Collective Representation of Lower Lying States in ${\mathrm{Ne}}^{21}$, ${\mathrm{Na}}^{21}$, and ${\mathrm{Na}}^{23}$

Employing model parameters deduced from the observed static properties of the nuclear systems ${\mathrm{Ne}}^{21}$, ${\mathrm{Na}}^{21}$, and ${\mathrm{Na}}^{23}$, both total and partial gamma-ray transition probabilities involving relevant states in the ground-state rotational bands are computed within the Nilsson strong-coupling collective-model framework and compared with the respective observed values; agreement within a factor of 2 is noted for all cases with the exception of the first-excited to ground-state ${\mathrm{Ne}}^{21}$ transition. Similar comparisons of relative total gamma-ray transition probabilities involving postulated ${\frac{9}{2}}^{+}$ members of these same rotational bands are also presented. The relative phases of coherently interfering magnetic-dipole and electric-quadrupole radiation amplitudes are predicted for the pertinent intraband transitions; agreement with the observed relative phases is found in three of the four cases available for unambiguous comparison. Model-predicted values for beta-ray transition probabilities involving the ground states of these three nuclei are in good agreement with observations. These comparisons provide striking support for the model validity for the description of these nuclei; prolate deformations corresponding to $\eta \sim +4.0\mathrm{}$ are indicated by these comparisons and in addition by examination of the total nuclear binding energy calculated as a function of deformation.