Evidence for Tetrahedral Symmetry in ${}^{16}\mathrm{O}$

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.

Figure 1

Schematic spectrum of a spherical top with tetrahedral symmetry and ${\omega }_1={\omega }_2={\omega }_3$. The rotational bands are labeled by ($v_1$, $v_2$, $v_3$) (bottom). All states are symmetric under $S_4$.

Figure 2

The observed spectrum of ${}^{16}\mathrm{O}$ [17]. The levels are organized in columns corresponding to the ground-state band and the three vibrational bands with $A$, $E$, and $F$ symmetry of a spherical top with tetrahedral symmetry. The last column shows the lowest noncluster levels.

Figure 3

The excitation energies of cluster states in ${}^{16}\mathrm{O}$ plotted as a function of $L(L+1)$: closed circles for the ground-state band, closed squares for the $A$ vibration, open circles for the $E$ vibration, and open triangles for the $F$ vibration.