Symplectic symmetry approach to clustering in atomic nuclei: The case of $^{24}$Mg

TL;DR

This paper advances the symplectic symmetry approach to nuclear clustering, applying it to $^{24}$Mg to accurately describe its rotational bands and transition probabilities without effective charges.

Contribution

It refines the SSAC method and demonstrates its effectiveness in modeling low-energy rotational bands in $^{24}$Mg using an algebraic Hamiltonian.

Findings

Accurately describes excitation energies of $^{24}$Mg rotational bands.

Reproduces $B(E2)$ transition probabilities without effective charges.

Validates the symplectic symmetry approach for nuclear clustering studies.

Abstract

Symplectic symmetry approach to clustering (SSAC) in atomic nuclei, recently proposed, is modified and further developed in more detail. It is firstly applied to the light two-cluster $^{20}$Ne + $\alpha$ system of $^{24}$Mg, the latter exhibiting well developed low-energy $K^{\pi} = 0^{+}_{1}$, $K^{\pi} = 2^{+}_{1}$ and $K^{\pi} = 0^{-}_{1}$ rotational bands in its spectrum. A simple algebraic Hamiltonian, consisting of dynamical symmetry, residual and vertical mixing parts is used to describe these three lowest rotational bands of positive and negative parity in $^{24}$Mg. A good description of the excitation energies is obtain by considering only the $SU(3)$ cluster states restricted to the stretched many-particle Hilbert subspace, built on the leading Pauli allowed $SU(3)$ multiplet for the positive- and negative-parity states, respectively. The coupling to the higher cluster-model configurations allows to describe the known low-lying experimentally observed $B(E2)$ transition probabilities within and between the cluster states of the three bands under consideration without the use of an effective charge.