Phenomenological description of the states $0^+$ and $2^+$ in some even-even nuclei

TL;DR

This paper models the $0^+$ and $2^+$ states in even-even nuclei using a sixth-order quadrupole boson Hamiltonian, comparing semi-classical and exact eigenvalue approaches, both fitting experimental data well.

Contribution

It introduces two alternative methods for describing nuclear energy levels with a sixth-order boson Hamiltonian, providing close energy formulas and fitting experimental data across multiple nuclei.

Findings

Both methods accurately reproduce experimental energy levels.

The semi-classical approach uses four parameters; the exact method uses five.

Predicted transition probabilities await experimental validation.

Abstract

A sixth-order quadrupole boson Hamiltonian is used to describe the states $0^+$ and $2^+$ identified in several nuclei by various types of experiments. Two alternative descriptions of energy levels are proposed. One corresponds to a semi-classical approach of the model Hamiltonian while the other one provides the exact eigenvalues. Both procedures yield close formulas for energies. The first procedure involves four parameters, while the second involves a compact formula with five parameters. In each case the parameters are fixed by a least-square fit procedure. Applications are performed for eight even-even nuclei. Both methods yield results which are in a surprisingly good agreement with the experimental data. We give also our predicted reduced transition probabilities within the two approaches, although the corresponding experimental data are not yet available.