Application of Suggested Three Parameters Collective Rotational Model to Superdeformed Thallium Odd-Mass Nuclei

Abstract

The superdeformed rotational bands (SDRB’s) of axial symmetric Tl odd-A nuclei are described within the framework of the suggested model as an extended version of Bohr-Moltelson (BM) model. The suggested model has three parameters rather than the BM model’s two parameters. The model is employed to calculated the transition energies and therefore the unknown level spins within the three pairs of signature partners 191Tl (SD1, SD2), 193Tl (SD1, SD2) and 195Tl (SD1, SD2). The optimized model parameters and therefore the unknown spins for every band are adjusted by employing a computer simulated search program to induce a minimum root mean square deviation between the calculated theoretical and experimental transition energies Eγ (I). The most effective adopted model parameters and spins are wont to calculate the kinematic J (1) and dynamic J (2) moments of inertia, and rotational frequency ħω,. The calculated results agree excellently with the experimental ones. The behaviour of J (1) and J (2) with ħω is examined and discussed. Also, the calculated transition energies and spins are accustomed investigate and exhibit the ΔI = 1 staggering effects in transition energies between each pair of the signature partners. This can be done by considering three staggering indices looking on the dipole γ-transitions between the 2 bands of the signature partners and therefore the quadrupole γ-transitions within each band. All the studied three signature partner pairs showed an oversized amplitude staggering pattern. The ΔI = 1 energy staggering also appears within the transition energies after subtracting a rigid rotor reference when plotted versus spin. The phenomenon of identical bands (IB’s) is additionally investigated within the two pairs [193Tl (SD1), 195Tl (SD1)] and [193Tl (SD2), 195Tl (SD2)] by using the concept of incremental alignment.