We introduce an algebraic framework for the description of baryons. Within this framework we study a collective string-like model and show that this model gives a good overall description of the presently available data. We discuss in particular masses and electromagnetic couplings, including the transition form factors that can be measured at new electron facilities.Comment: to be published in Annals of Physics (N.Y.), 44 pages of LaTex, 11 postscript figure files on request, UU-94-0

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

We derive the rotation-vibration spectrum of a $4\alpha$ configuration with tetrahedral symmetry ${\mathcal{T}}_d$ and show evidence for the occurrence of this symmetry in the low-lying spectrum of ${}^{16}\mathrm{O}$. All vibrational states with $A$, $E$, and $F$ symmetry appear to have been observed as well as the rotational bands with $L^P=0^{+}$, $3^{-}$, $4^{+}$, $6^{+}$ on the $A$ states and part of the rotational bands built on the $E$, $F$ states. We derive analytic expressions for the form factors and $B(EL)$ values of the ground-state rotational band and show that the measured values support the tetrahedral symmetry of this band.