Beyond the harmonic approximation description of wobbling excitations in even-even nuclei with frozen alignments

The wobbling motion in even-even nuclei is investigated by means of a collective Hamiltonian constructed from a semiclassical treatment applied to a triaxial rotor with a rigidly aligned pair of quasiparticles. The limits of distinct wobbling regimes are discussed in connection to the dynamic evolution of the wobbling excitations and corresponding electromagnetic properties. Model calculations are performed for the description of transverse wobbling bands in ${}^{130}\mathrm{Ba}, {}^{134}\mathrm{Ce}$, and ${}^{136,138}\mathrm{Nd}$ nuclei.

Figure 1

Classical energy surfaces for $j=10$ and different values of total angular momentum, as a function of $\phi$ and $x$ when $\gamma ={90}^{\circ }, a=2$ (left column, pair alignment along short axis) and $\gamma ={30}^{\circ }, a=1$ (right column, pair alignment along medium axis). The single or double minima are indicated with crosses, while the difference between two contour lines is 7 units of $1/{\mathcal{J}}_0$ for the left column and 25 $1/{\mathcal{J}}_0$ units for the right column.

Figure 2

The evolution with triaxial deformation of the classical critical angular momentum which delimits the transverse wobbling regime from the tilted-axis regime with double minima in the classical energy function of the assumed FA geometry along first ($a=1$) and second ($a=2$) principal axes.

Figure 3

The quantum wobbling potential as a function of the projection variable $x$, for different values of the total angular momentum and the following alignment geometries: (a) $\gamma ={90}^{\circ }, j=10$, and $a=2$. The transition from a single minimum (transverse wobbling) to double minima (tilted-axis wobbling) is noted by change of color; (b) $\gamma ={30}^{\circ }, j=10$, and $a=1$.

Figure 4

Evolution with angular momentum of the transverse (a) and longitudinal (b) wobbling energy (3.2) normalized to a rotational excitation for few values of the triaxial deformation $\gamma$. The wobbling energy is calculated using only the diagonalization results for alignment $j=10$ along axis 2($s$), respectively, axis 1($m$).

Figure 5

Calculated energies (minus a common rigid-rotor reference) of the yrast and excited bands for ${}^{130}\mathrm{Ba}, {}^{134}\mathrm{Ce}$, and ${}^{136,138}\mathrm{Nd}$, are compared to experimental data in the left column. Open symbols designate data points which were not considered in the fitting procedure. The corresponding theoretical and experimental wobbling energies are compared in the right column.

Figure 6

Comparison between experimental [50] and predicted energies of the yrast band (L6) and excited band (L7) of ${}^{138}\mathrm{Nd}$.