It is shown that the dilute density distribution of $\alpha$ particles in nuclei can be observed in the Airy structure in nuclear rainbow scattering. We have analyzed $\alpha +{}^{12}\mathrm{C}$ rainbow scattering to the $0_2^{+}\left(7.65\mathrm{MeV}\right)$ state of ${}^{12}\mathrm{C}$ in a coupled-channel method with the precise wave functions for ${}^{12}\mathrm{C}$. It is found that the enhanced Airy oscillations in the experimental angular distributions for the $0_2^{+}$ state is caused by the dilute density distribution of this state in agreement for the idea of Bose-Einstein condensation of the three alpha particles.

• Received 4 December 2003

DOI:https://doi.org/10.1103/PhysRevC.70.041602