A simple collective rotational model has been constructed to investigate the identical bands in odd-odd nucleus ¹⁹⁴Tl and its neighbor odd-A nuclei ¹⁹³Tl and ¹⁹⁵Tl, to describe the ∆I = 1 staggering effect in signature partner pairs of odd-A superdeformed bands ¹⁹³Tl (SD1, SD2) and ¹⁹⁵Tl (SD1, SD2) and to describe also the ∆I = 2 staggering observed in ¹⁹⁴Tl (SD3).
The model parameters and the bandhead spin ware obtained by adopted best fit method. The systematic variation of the kinematic and dynamic moments of inertia are studied as a function of the rotational frequency, it is found that the blocking effect of the high-j intruder orbital plays an important role. To describe the ∆I = 1 staggering we extracted the differences between the average transitions I + 2 → I → I - 2 energies in one band and the transition     I + 1 → I - 1 energies in its signature partner. To describe ∆I = 2 staggering we calculated the deviation of transition energies from a smooth reference representing the finite difference approximation to the fourth derivative of the transition energies. We noticed transition energies in the nucleus ¹⁹³Tl is identical to their N + 1, N + 2 neighbors. Also the analysis done allows us to confirm ∆I = 1 staggering in signature partners of ¹⁹³Tl, ¹⁹⁵Tl and    ∆I = 2 staggering in SD3 band in ¹⁹⁴Tl by performing a staggering parameter analysis.