An investigation into the granular temperature distributions of a binary vibrofluidized granular bed has been conducted using positron emission particle tracking. By repeating each experiment with the tracer selected in turn from the two size components, the granular temperature and packing fraction distributions for each phase were determined. It was found that, for a range of size fractions, the granular temperature of the larger particles was higher than that of the smaller diameter grains, a result which was supported by a simple theoretical analysis based on the steady state energy equation.

We report a measurement of a new high spin $J^{\pi }=5^{-}$ state at 22.4(2) MeV in ${}^{12}\mathrm{C}$ which fits very well to the predicted (ground state) rotational band of an oblate equilateral triangular spinning top with a ${\mathcal{D}}_{3h}$ symmetry characterized by the sequence $0^{+}$, $2^{+}$, $3^{-}$, $4^{\pm }$, $5^{-}$ with almost degenerate $4^{+}$ and $4^{-}$ (parity doublet) states. Such a ${\mathcal{D}}_{3h}$ symmetry was observed in triatomic molecules, and it is observed here for the first time in nuclear physics. We discuss a classification of other rotation-vibration bands in ${}^{12}\mathrm{C}$ such as the ($0^{+}$) Hoyle band and the ($1^{-}$) bending mode band and suggest measurements in search of the predicted (“missing”) states that may shed new light on clustering in ${}^{12}\mathrm{C}$ and light nuclei. In particular, the observation (or nonobservation) of the predicted (“missing”) states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.654 MeV in ${}^{12}\mathrm{C}$.