Study of Mixed Symmetry States in Even-Even Thorium Isotopes (220-230) by IBM-2 Framework

Abstract

The study of mixed-symmetry states in thorium isotopes within the IBM-2 framework is essential for achieving a comprehensive understanding of nuclear structure, characterizing collective excitations, and validating theoretical models. In this work, the proton–neutron interacting boson model (IBM-2) was employed to calculate the low-lying energy levels of even–even thorium isotopes in the mass range 220 ≤ A ≤ 230. The computations were performed using an improved version of the neutron–proton boson code (NPBOS). The Hamiltonian was constructed with parameter values optimized to provide the best fit to experimental energy levels. The model reproduced the energy spectra of isotopes with high accuracy, yielding root mean square error (RMSE) values of 0.014 MeV, 0.006 MeV, 0.002 MeV, 0.012 MeV, 0.503 MeV, and 0.401 MeV for each isotope, respectively, when compared with experimental data. Energy states were classified into fully symmetric (FS) and mixed-symmetry (MS) states by evaluating the F-spin of each calculated level. To investigate the role of the Majorana interaction, the parameters  , , and  in the Majorana term  were allowed to vary independently, enabling the study of their differential effects. Within the U(5) limit for  the MS states ( , , ) were found to be highly sensitive to changes in the parameter  confirming a key property of mixed-symmetry states. Furthermore, MS states with  ( ) can be categorized into three groups according to their distinct dependence on the excitation energies associated with , , and .