Empirical evidence of a superrigid structure of “flat” superdeformed bands

For the first time, we present the empirical evidence of superrigid character of the “flat” superdeformed bands in the Tl and Pb isotopes. For this purpose, we have used various rotational energy formulas. The free parameters of superdeformed (SD) bands in the Tl and Pb isotopes have been extracted and systematically studied to obtain the proposed empirical evidence. In particular, the intraband transition energies of the SD bands have been split into rotational and shape fluctuation energies. The role of the vibrational factor in the evolution of dynamic moment of inertia, softness parameter, alignment, and effective pairing gap parameter of the flat SD bands has been studied. Using these models, two distinct natures have been identified for the SD bands in the Tl and Pb isotopes. Our study establishes the role of shape fluctuations, vibrational effect, deformation, and pairing correlations for the unusual behavior of the dynamic moment of inertia in the flat SD bands of the $A\approx 190$ mass region.

Figure 1

The RMS deviation plot at various spin assignments for the flat bands ${}^{193}\mathrm{Pb}(1,2,9), {}^{195}\mathrm{Pb}(1,2)$, and ${}^{197}\mathrm{Pb}(1,2,3,4)$ using the exponential model and NS formula. $I_0$ correspond to the spin value of the lowest level observed. The circles/squares correspond to the values obtained from the NS formula/exponential model.

Figure 2

The variation of the shape fluctuation energy ($E_{\gamma }^{\mathrm{ROT}}$) for SD bands in the Tl isotopes.

Figure 3

The variation of the shape fluctuation energy ($E_{\gamma }^{\mathrm{SF}}$) for SD bands in the Tl isotopes.

Figure 4

The variation of the shape fluctuation energy ($E_{\gamma }^{\mathrm{ROT}}$) for SD bands in the Pb isotopes.

Figure 5

The variation of the shape fluctuation energy ($E_{\gamma }^{\mathrm{SF}}$) for SD bands in the Pb isotopes.

Figure 6

(a) The fitted values of alignment $i$ obtained from the semiclassical PRM for the SD bands in the Pb isotopes. (b) The fitted values of alignment $i$ obtained from the semiclassical PRM for the SD bands in the Tl isotopes.

Figure 7

The variation of experimental dynamic moment of inertia [40] with rotational frequency for flat bands in ${}^{193}\mathrm{Pb}, {}^{195}\mathrm{Pb}, {}^{197}\mathrm{Pb}$, and ${}^{192}\mathrm{Tl}$.

Figure 8

The variation of calculated kinematic and dynamic moment of inertia with rotational frequency for the flat bands ${}^{193}\mathrm{Pb}\left(2\right), {}^{195}\mathrm{Pb}\left(2\right)$, and ${}^{197}\mathrm{Pb}\left(2\right)$ using the exponential model and comparison with experimental data [40]. The solid/hollow circles correspond to the dynamic/kinematic MoI and solid squares with error (yellow region) correspond to experimental data of dynamic MoI.