Attempt at describing triaxiality of ${}^{108,110,112}\mathrm{Ru}$ by the generalized triaxial rotor model with independent, variable moments of inertia

The generalized triaxial rotor model with independent variable moments of inertia is applied to describe the transitional behavior of staggering patterns observed in the $\gamma$ bands of ${}^{108,110,112}\mathrm{Ru}$. An oscillating behavior is introduced in the variations of the moments of inertia ${\mathcal{I}}_1$ and ${\mathcal{I}}_2$ to describe the $\gamma$-soft pattern in ${}^{108}\mathrm{Ru}$. Then the amplitude of the oscillating term is exponentially reduced as a function of spin in ${}^{110}\mathrm{Ru}$. The oscillating term is taken away completely in ${}^{112}\mathrm{Ru}$. A good agreement is obtained between the model calculation and the experimental data both in the phase and amplitude of the staggering pattern. Using the obtained eigenfunctions, effective $\gamma$ values are so determined to reproduce best the branching ratios of $\gamma$ decays from the $\gamma$ bands. The stable values of ${\gamma }_{\mathrm{eff}}\approx {20}^{\circ }$ are obtained for the lower-spin states in any of ${}^{108,110,112}\mathrm{Ru}$.

Figure 1

Theoretical energies are compared with the experimental ones for the ground-state and $\gamma$ bands. Variations of moments of inertia are displayed as a function of spin at the top. The staggering pattern in the $\gamma$ band is shown at the bottom. The staggering parameter $S\left(I\right)$ is defined in the text.

Figure 2

The evolution of the spin components and the spin direction for the ground-state and $\gamma$ bands in ${}^{108}\mathrm{Ru}$. The spin direction is depicted by the polar angle $\theta$ and azimuth angle $\varphi$, which are defined in the text.

Figure 3

Same as Fig. 2, but for ${}^{110}\mathrm{Ru}$.

Figure 4

Same as Fig. 2, but for ${}^{112}\mathrm{Ru}$.