The first excited $0^{+}$ state in ${}^{12}\mathrm{C}$ (Hoyle state) has been predicted to be a dilute self-bound gas of bosonic $\alpha$ particles, similar to a Bose-Einstein condensate. To clarify this conjecture, precise electron scattering data on form factors of the ground state and the transition to the Hoyle state are compared with results of the fermionic molecular dynamics model, a microscopic $\alpha$-cluster model, and an $\alpha$-cluster model with reduced degrees of freedom (in the spirit of a Bose-Einstein condensed state). The data indicate clearly a dilute density with a large spatial extension of the Hoyle state. A closer inspection of the model calculations, which reproduce the experimental findings, reveals that the term Bose-Einstein condensation of three $\alpha$ particles must not be taken too literally.

• Received 15 September 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.032501