Tidal wave in ${}^{102}\mathrm{Pd}$: An extended five-dimensional collective Hamiltonian description

The five-dimensional collective Hamiltonian based on the covariant density functional theory is applied to investigate the observed tidal wave mode in the yrast band of ${}^{102}\mathrm{Pd}$. The energy spectra, the relations between the spin and the rotational frequency, and the ratios of $B\left(E2\right)/\mathcal{J}\left(I\right)$ in the yrast band are well reproduced by introducing the empirical $ab$ formula for the moments of inertia. This $ab$ formula is related to the fourth order effect of collective momentum in the collective Hamiltonian. It is also shown that the shape evolution in the tidal wave is determined microscopically by the competition between the rotational kinetic energy and the collective potential in the framework of the collective Hamiltonian.

Figure 1

The potential energy surface in the $\beta \text{−}\gamma$ plane $\left(0\le \gamma \le {60}^{\circ }\right)$ for ${}^{102}\mathrm{Pd}$ calculated by the constrained triaxial CDFT with PC-PK1 [46]. All energies are normalized with respect to the binding energy of the absolute minimum (in MeV). The energy between each contour line is 0.5 MeV.

Figure 2

The comparison of the yrast band energy between the experimental data and 5DCH calculations for ${}^{102}\mathrm{Pd}$. The blue circle with the dashed line (5DCH) and the red lozenge with the solid line (5DCH*) represent the calculations with the MOI corrected by renormalizing the IB effective MOI to the empirical values with a common factor and by the empirical $ab$ formula, respectively. The harmonic vibrational and rotational limits are shown in dashed and dashed-dotted lines.

Figure 3

The experimental and theoretical $I\text{−}\hslash \omega$ relation of the yrast band for ${}^{102}\mathrm{Pd}$. The light cyan band represents a region of $\hslash \omega =0.2$ to $0.6$ MeV.

Figure 4

The experimental and theoretical moments of inertia $\mathcal{J}$ as functions of the spin $I$ for ${}^{102}\mathrm{Pd}$. The harmonic vibrational and rotational limits are shown in dashed and dashed-dotted lines.

Figure 5

(a) The experimental and theoretical reduced electromagnetic transition probabilities $B\left(E2\right)$ of the yrast band as a function of the spin $I$ for ${}^{102}\mathrm{Pd}$. (b) The experimental and calculated ratios $B\left(E2\right)/\mathcal{J}$ as a function of the spin $I$.

Figure 6

The average values of the quadrupole deformation parameters (a) $\beta$ and (b) $\gamma$ calculated by the 5DCH as functions of spin $I$ for ${}^{102}\mathrm{Pd}$.

Figure 7

The probability distributions in the $\beta \text{−}\gamma$ plane for the $0_1^{+},4_1^{+},8_1^{+}$, and ${12}_1^{+}$ states of ${}^{102}\mathrm{Pd}$ calculated by the 5DCH and ${5\mathrm{DCH}}^{*}$.