Do analogs of the Hoyle state exist in 16O?

Abstract

The root-mean-square radii of short-lived 0⁺-states in ¹⁶O were obtained for the first time from an analysis of α+¹⁶O diffraction scattering. Data on elastic and inelastic α+¹⁶O scattering were analyzed on the basis of the modified diffraction model in the range of projectile energies between a few tens of MeV units to 400 MeV. No case of a significant enhancement of the radius with respect to its ground-state value was observed. In particular, this concerns the 15.1-MeV 0₆⁺ state, which lies near the threshold for breakup to four alpha particles and for which we did not confirm a giant radius predicted by the alpha-particle-condensate model. This result disproves the hypothesis that the ¹⁶O nucleus in the 0₆⁺ state has a rarefied structure and appears to be an analog of the known Hoyle state at 7.65 MeV (0₂⁺) in ¹²C.