Establishing the geometry of $\alpha$ clusters in ${}^{12}\mathrm{C}$ through patterns of polarized $\gamma$ rays

Linearly polarized monocromatic beams of $\gamma$ rays, that will be available at the ELI-NP facility, will open up the way to nuclear fluorescence experiments aimed at measuring the depolarization ratio of the outcoming photons. This is the ideal tool to clearly discriminate among the various proposed geometric configurations for $\alpha$-cluster nuclei, such as ${}^{12}\mathrm{C}$ in a model-independent way. For this nucleus, all possible outcomes have been enumerated in this Rapid Communication, and the predicted theoretical patterns of intensities will serve as a guide for the conclusive experimental identification of its nuclear molecular structure.

Figure 1

This table enumerates the possible shapes of a nuclear molecule made out of three $\alpha$'s, their underlying point-group symmetry, and the characters of the normal modes of vibration (with totally symmetric modes highlighted). The last column shows the schematic predicted patterns for depolarization ratios (intensity vs energy, not to scale). The white and black histograms represent parallel and perpendicular intensities.

Figure 2

Schematic of the PES, depending on the relevant variables of the potentials $v_1,...$ (in general, multidimensional). More than one minimum, belonging to different symmetries, ${\mathcal{S}}_{1,2}$ might be present, with its own set of excited states (bandheads shown with dashed lines).

Figure 3

Group-subgroup chain relations.

Figure 4

Descent in symmetry restricted to representations of the groups that are relevant to all possible configurations of three identical particles.