Electromagnetic selection rules for ²⁴ Mg in a 6 <i>α</i> cluster model with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>h</mml:mi> </

Abstract In the framework of a macroscopic α -cluster model, the structural properties and the spectroscopy of the 24 Mg nucleus are investigated. Special attention is devoted to the electromagnetic selection rules imposed by the point-symmetry group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">D</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>h</mml:mi> </mml:mrow> </mml:msub> </mml:math> that leaves invariant the adopted 6 α equilibrium configuration, a square bipyramid. The analysis entails the application of group-theoretical identities and character tables, in a way familiar to quantum chemists. The results show that the occurrence of interband E0, E2, and M1, M2, M3 transitions is strictly regulated by the transformation properties of the excited vibrational modes to which the states in the process belong. Unlike the 12 C nucleus in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi class="MJX-tex-calligraphic" mathvariant="script">D</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> <mml:mi>h</mml:mi> </mml:mrow> </mml:msub> </mml:math> -symmetric 3 α arrangement, M1 transition channels are active between states corresponding to a single quantum of vibrational excitation. Conversely, the measured E1 strengths in the 24 Mg spectrum are attributable to the excitation of single-nucleon degrees of freedom, as E1 transitions are forbidden by the model. The implications can be relevant for the spectroscopic analysis of 24 Mg, namely for the γ -transitions between collective states ascribed to different rotational bands.