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.
Categories: nucl-th