Abstract
An investigation has been made of the behaviour of nuclear structure as a function of an increase in neutron number from 224 Th to 234 Th. Thorium of mass number 234 is a typical rotor nucleus that can be explained by the SU(3) limit of the interacting boson model(IBM) in the algebraic nuclear model. Furthermore, 224−232 Th lie on the path of the symmetry-breaking phase transition. Moreover, the nuclear structure of 224 Th can be explained using X(5) symmetry. However, as 226−230 Th nuclei are not fully symmetrical nuclei, they can be represented by adding a perturbed term to express symmetry breaking. Through the following three calculation steps, we identified the tendency of change in nuclear structure. Firstly, the structure of 232 Th is described using the matrix elements of the Hamiltonian and the electric quadrupole operator between basis states of the SU(3) limit in IBM. Secondly, the low-lying energy levels and E2 transition ratios corresponding to the observable physical values are calculated by adding a perturbed term with the first-order Casimir operator of the U(5) limit to the SU(3) Hamiltonian in IBM. We compared the results with experimental data of 224−234 Th. Lastly, the potential of the Bohr Hamiltonian is represented by a harmonic oscillator, as a result of which the structure of 224−234 Th could be expressed in closed form by an approximate separation of variables. The results of these theoretical predictions clarify nuclear structure changes in Thorium nuclei over mass numbers of practical significance.
Highlights
The interacting boson model (IBM) [1] is one of the representative models for the study of nuclear structure
The critical point symmetries are based on the special solutions of the Bohr Hamiltonian [8] with potentials of the special form instead of the algebraic descriptions of three limits of the IBM
The E(5) critical point symmetry corresponds to the phase transition between U(5) and O(6) while the X(5)
Summary
The interacting boson model (IBM) [1] is one of the representative models for the study of nuclear structure. We have studied the collective properties of even Th nuclei based on the SU(3) limit of the IBM and the X(5) critical point symmetry. The structure of 226−232Th exhibits a slight breaking of the SU(3) symmetry in the direction of U(5), so we have added the d-boson number operator nd , which is the main term of the U(5) symmetric Hamiltonian, to the SU(3) Hamiltonian of the IBM[9]. Such small breaking of the low-lying energy levels and the E2 transition rates in 226−232Th can be explained by applying perturbation theory rather than direct diagonalization.
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