Shape of ${}^{12}$C

We have examined the hypothesis by Bijker and Iachello who asserted that ${}^{12}$C has an internal structure with three α particles arranged in a triangular shape, leading to the formation of the ground rotational band consisting of 0${}^{+}$, 2${}^{+}$, 3${}^{-}$, 4${}^{\pm }$ and 5${}^{-}$ states. Following this idea, we reconstructed the intrinsic shape of ${}^{12}$C using experimental electron scattering data with minimal theoretical assumption. Our sole assumption was that the observed 0${}_1^{+}$, 2${}_1^{+}$, 3${}_1^{-}$, and 4${}_2^{+}$ states share a common internal structure, forming a rotational spectrum. The reconstructed intrinsic density showed a beautiful triangular shape with three peaks implying α cluster formation in the ground band.