Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English   Periodicity: 4 times per year   Open access peer reviewed journal

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F. R. Abbas^*, A. K. Aobaid

Department of Physics, College of Education for Pure Science, University of Anbar, Ramadi, Iraq

^*Corresponding author. E-mail address: far23u3009@uoanbar.edu.iq

Abstract: In this study, three nuclear models - the Interacting Boson Model-1 (IBM-1), the Variable Moment of Inertia (VMI), and its generalized form (Generalized Variable Moment of Inertia - GVMI) - were employed to investigate the low-lying collective states of the even-even polonium isotopes ¹⁹⁰Po and ¹⁹²Po. The models were used to compute positive-parity energy levels E(L), transition energies Eγ, reduced electric quadrupole transition probabilities B(E2), and electric quadrupole moments Q_L, based on available experimental data and ideal level schemes. Characteristic energy ratios E(4⁺₁)/E(2⁺₁), E(6⁺₁)/E(2⁺₁), and E(8⁺₁)/E(2⁺₁) were evaluated to assess the dynamical symmetries of the nuclei and compared with theoretical limits of the SU(5), SU(3), and O(6) symmetry groups. Results indicate that ¹⁹⁰Po exhibits dominant O(6) γ-soft symmetry, while ¹⁹²Po displays transitional behavior between SU(5) and O(6). Comparative analysis revealed good agreement between experimental data and theoretical predictions, particularly from IBM-1 and GVMI, confirming their reliability in modeling structural evolution in medium-heavy nuclei. In addition, theoretical energy levels were extrapolated for high-spin states not yet experimentally observed. For ¹⁹⁰Po, IBM-1 predicts the 16⁺₁ state at 4.06 MeV, the 18⁺₁ state at 4.96 MeV, and the 20⁺₁ state at 6.01 MeV. For ¹⁹²Po, the predicted levels include 12⁺₁ at 3.12 MeV, 14⁺₁ at 4.11 MeV, and 16⁺₁ at 5.20 MeV. These predictions extend the known spectra up to spin 20⁺ and offer a theoretical framework for future experimental validation. These findings contribute to a deeper understanding of collective excitations and symmetry dynamics in the polonium isotopic chain.

Keywords: IBM-1, VMI, GVMI, ¹⁹⁰Po, ¹⁹²Po, energy levels, dynamical symmetry.

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