Calculation of nuclear structure in N = 90 isotones

The behavior of nuclear structures with an increase in atomic number from ¹⁵⁰Nd to ¹⁵⁸Er was investigated in this study. ¹⁵²Sm and ¹⁵⁴Gd are typical nuclei lying between the rotational and vibrational states, which can be explained by a slight breaking of the SU(3) symmetry in the U(5)-direction via the interacting boson model (IBM). Furthermore, N=90 isotones lie in the path of this symmetry-breaking phase transition. Moreover, the nuclear structure of ¹⁵⁰Nd can be explained using X(5) symmetry. However, because the ¹⁵⁶Dy and 158Er nuclei are not fully symmetrical, they can be represented by adding a perturbed term to express symmetry breaking. We identified the tendency of change in the nuclear structure using the following three calculation steps. First, the structures of ¹⁵²Sm and ¹⁵⁴Gd were described using the matrix elements of the Hamiltonian and the electric quadrupole operator between the basis states of the SU(3) limit in the IBM. Second, the low-lying energy levels and E₂ transition ratios corresponding to the observable physical values were calculated by adding a perturbed term with the first-order Casimir operator of the U(5) limit to the SU(3) Hamiltonian in the IBM. We compared the calculation results with the experimental data of N=90 isotones. Finally, the potential of the Bohr Hamiltonian was represented by a harmonic oscillator; consequently, the structure of N=90 isotones could be expressed in the closed form by an approximate separation of variables. These nuclear structure prediction results were applied to elucidate the low-lying energy and E₂ transitions in isotones