Electromagnetic selection rules in the triangular alpha-cluster model of 12C

Abstract

After recapitulating the procedure to find the bands and the states occurring in the ${\mathcal{D}}_{3h}$ alpha-cluster model of ${}^{12}$C in which the clusters are placed at the vertexes of an equilateral triangle, we obtain the selection rules for electromagnetic transitions. While the alpha cluster structure leads to the cancellation of E1 transitions, the approximations carried out in deriving the roto-vibrational hamiltonian lead to the disappearance of M1 transitions. Furthermore, although in general the lowest active modes are E2, E3, $\cdots$ and M2, M3, $\cdots$, the cancellation of M2, M3 and M5 transitions between certain bands also occurs, as a result of the application of group theoretical techniques drawn from molecular physics. These implications can be very relevant for the spectroscopic analysis of $\gamma$-ray spectra of ${}^{12}$C.

References in corpus (3)

• Evidence for Triangular D_3h Symmetry in 12C
• Nonlocalized Clustering: A New Concept in Nuclear Cluster Structure Physics
• Evidence for tetrahedral symmetry in 16O

Cited by in corpus (7)

• Transition densities and form factors in the triangular $\alpha$-cluster model of ${}^{12}$C with application to ${}^{12}$C+$\alpha$ scattering
• Alpha-induced inelastic scattering and alpha-transfer reactions in ${}^{12}$C and ${}^{16}$O within the Algebraic Cluster Model
• Breaking and restoration of rotational symmetry in the low-energy spectrum of light alpha-conjugate nuclei on the lattice I: ${}^8\mathrm{Be}$ and ${}^{12}\mathrm{C}$
• Electromagnetic transition rates of Carbon-12 and Oxygen-16 in rotational-vibrational models
• The algebraic molecular model in ${}^{12}$C and its application to the $\alpha$+${}^{12}$C scattering: from densities and transition densities to optical potentials and nuclear formfactors
• Shape of 12C
• An overview of the scientific contribution of Andrea Vitturi to Nuclear Physics (being an account of the recent TNP19 meeting held in Padova)