Symplectic symmetry approach to clustering in atomic nuclei: the case of ²⁴Mg

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 + α system of 24 Mg, the latter exhibiting well developed low-energy <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> </mml:msup> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> 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 obtained 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 us to describe the known low-lying experimentally observed B ( E 2) transition probabilities within and between the cluster states of the three bands under consideration without the use of an effective charge.