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

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.

13 pages, 4 figures, 2 tables

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