The present study investigates the dynamical symmetries of even-even Se⁷4-78, Ru¹04-106 and Mo¹06-108 isotopes within the framework of the Interacting Boson Model-1 (IBM-1). The analysis explores the three fundamental symmetry groups: SU (5) (vibrational), O (6) (gamma-soft), and SU (3) (rotational). Energy levels were calculated using newly optimized Hamiltonian parameterizations based on the U (6) unitary group structure in six dimensions, and the results were compared with experimental data, demonstrating excellent agreement. A key finding of this study is that for each nucleus, the predominant Hamiltonian parameter can be selectively adjusted to achieve an optimal theoretical-experimental match, particularly in relation to the E4/E2 energy ratio. This approach provides a systematic and efficient method for refining Hamiltonian parameterization, offering a standardized technique to enhance the accuracy of nuclear structure studies. The findings contribute to a deeper understanding of nuclear collective motion and may serve as a foundation for further advancements in theoretical nuclear physics.
Berun N. Ghafoor (Mon,) studied this question.