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 ${}^{12}\mathrm{C}$.

Quasifree one-proton knockout reactions have been employed in inverse kinematics for a systematic study of the structure of stable and exotic oxygen isotopes at the ${\mathrm{R}}^3\mathrm{B}/\mathrm{LAND}$ setup with incident beam energies in the range of $300–450\mathrm{MeV}/\mathrm{u}$. The oxygen isotopic chain offers a large variation of separation energies that allows for a quantitative understanding of single-particle strength with changing isospin asymmetry. Quasifree knockout reactions provide a complementary approach to intermediate-energy one-nucleon removal reactions. Inclusive cross sections for quasifree knockout reactions of the type ${}^A\mathrm{O}(p,2p){}^{A-1}\mathrm{N}$ have been determined and compared to calculations based on the eikonal reaction theory. The reduction factors for the single-particle strength with respect to the independent-particle model were obtained and compared to state-of-the-art ab initio predictions. The results do not show any significant dependence on proton-neutron asymmetry.

Excited states in certain atomic nuclei possess an unusual structure, where the dominant degrees of freedom are those of $\alpha$ clusters rather than individual nucleons. It has been proposed that the diffuse $3\alpha$ system of the ${}^{12}\mathrm{C}$ Hoyle state may behave like a Bose-Einstein condensate, where the $\alpha$ clusters maintain their bosonic identities. By measuring the decay of the Hoyle state into three $\alpha$ particles, we obtained an upper limit for the rare direct $3\alpha$ decay branch of 0.047%. This value is now at a level comparable with theoretical predictions and could be a sensitive probe of the structure of this state.

The $\alpha ({}^{10}\mathrm{Be},\alpha ){}^{10}\mathrm{Be}$ resonant scattering reaction has been measured at nine ${}^{10}\mathrm{Be}$ beam energies from 25 to 48 MeV, scanning out resonances in ${}^{14}\mathrm{C}$ from excitation energies of 13 to 24 MeV. Angular distribution measurements were used to assign the spin and parity of $5^{-}$ to resonances at $E_x=18.82\left(2\right)$ and 19.67(2) MeV and $6^{+}$ at $E_x=20.80\left(2\right)$ MeV. The data also strongly indicate a $3^{-}$ resonance at 17.32(2) MeV. The systematic uncertainty on the excitation energies is 175 keV. An $R$-matrix analysis has been performed for the excitation energy range 16.5 to 22 MeV. The data are discussed in terms of cluster bands in ${}^{14}\mathrm{C}$.

Background: Near-threshold $\alpha$-clustered states in light nuclei have been postulated to have a structure consisting of a diffuse gas of $\alpha$ particles which condense into the $0s$ orbital. Experimental evidence for such a dramatic phase change in the structure of the nucleus has not yet been observed.