Extended Exponential Model with Pairing Attenuation and Investigation of Energy Staggering and Identical Bands Effects in Superdeformed Thallium Nuclei

A proposed extended exponential model with pairing attenuation (EEMPA) is applied to inspect and exhibit the $$\Delta I=2$$ , $$\Delta I=1$$ staggering effects and the identical bands in transition energies $$E_{\gamma}(I)$$ of twelve superdeformed rotational bands (SDRB $${}^{\mathrm{,}}$$ s) in Thallium nuclei. A computer simulated fitting search program has been written to determine the unknown spins and the values of the model parameters of the considered SDRB $${}^{\mathrm{,}}$$ s so as to get a minimum root-mean-square deviation of the calculated $$E_{\gamma}(I)$$ and the observed ones. The adopted parameters are used to study the rotational frequency $$\hbar\omega$$ , the dynamic $$J^{(2)}$$ and kinematic $$J^{(1)}$$ moments of inertia. The calculated results agree very well with the empirical ones. The behavior of $$J^{(1)}$$ and $$J^{(2)}$$ versus $$\hbar\omega$$ is discussed. To show the $$\Delta I=2$$ staggering in transition energies $$E_{\gamma}(I)$$ for $${}^{192}$$ Tl(SD2) and $${}^{194}$$ Tl(SD1, SD3, SD5), a staggering function which represents the finite difference approximation to the fourth-order derivative is used (Cederwall five-point formula). The $$\Delta I=1$$ staggering in signature partners of Tl nuclei: $${}^{191}$$ Tl(SD1, SD2), $${}^{192}$$ Tl(SD1, SD2), $${}^{193}$$ Tl(SD1, SD2), $${}^{194}$$ Tl(SD1, SD2), and $${}^{195}$$ Tl(SD1, SD2) are investigated by using a staggering function representing the differences between the average transitions $$E_{\gamma}(I+2\to I)$$ , $$E_{\gamma}(I\to I-2)$$ in one band and the transition $$E_{\gamma}(I+1\to I-1)$$ in its signature partner. The difference in $$E_{\gamma}(I)$$ between transitions in SDRB $${}^{\mathrm{,}}$$ s of the odd–odd $${}^{194}$$ Tl nucleus and its neighbors odd- $$A$$ nuclei $${}^{193,195}$$ Tl were small to large range of $$\hbar\omega$$ , which indicates that these SDRB $${}^{\mathrm{,}}$$ s have been considered as identical bands (IB $${}^{\mathrm{,}}$$ s).