We formulate criteria for identification of the nuclear tetrahedral and octahedral symmetries and illustrate for the first time their possible realization in a Rare Earth nucleus 152 Sm. We use realistic nuclear mean-field theory calculations with the phenomenological macroscopic-microscopic method, the Gogny-Hartree-Fock-Bogoliubov approach and the general point-group theory considerations to guide the experimental identification method as illustrated on published experimental data. Following group-theory the examined symmetries imply the existence of exotic rotational bands on whose properties the spectroscopic identification criteria are based. These bands may contain simultaneously states of even and odd spins, of both parities and parity doublets at well defined spins. In the exact-symmetry limit those bands involve no E2-transitions. We show that coexistence of tetrahedral and octahedral deformations is essential when calculating the corresponding energy minima and surrounding barriers and that it has a characteristic impact on the rotational bands. The symmetries in question imply the existence of long-lived shape-isomers and, possibly, new waiting point nuclei -impacting the nucleosynthesis processes in astrophysics -and an existence of 16-fold degenerate particle-hole excitations. Specifically designed experiments which aim at strengthening the identification arguments are briefly discussed.

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The inclusive energy distributions of fragments with Z ≥ 3 emitted from the bombardment of 12 C by 20 Ne beams with incident energies between 145 and 200 MeV have been measured in the angular range θ lab ∼ 10 • -50 • . Damped fragment yields in all cases have been found to be characteristic of emission from fully energy equilibrated composites; for B, C fragments, average Q-values, < Q >, were independent of the centre of mass emission angle (θc.m.), and the angular distributions followed ∼1/sinθc.m. like variation, signifying long life times of the emitting di-nuclear systems. Estimation of total yields of these fragments have been found to be much larger compared to the standard statistical model predictions of the same. This may be indicative of the survival of orbiting like process in 12 C + 20 Ne system at these energies.