Calculation of nuclear structure in N = 90 isotones

The behavior of nuclear structures with an increase in atomic number from 150 Nd to 158 Er was investigated in this study. 152 Sm and 154 Gd 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 150 Nd can be explained using X(5) symmetry. However, because the 156 Dy and 158 Er 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 152 Sm and 154 Gd 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 E 2 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 E 2 transitions in isotones.