Determination of the Deformation in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ from Electron Scattering

The elastic and inelastic form factors for the $0^{+}$, $2^{+}$, and $4^{+}$ states in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ were measured. The data were analyzed by treatment of the rotational excitation in the framework of the Nilsson model. We have obtained a single intrinsic state which satisfies simultaneously the observed form factors for the intraband transitions. The deformations were extracted directly from the charge distribution of the intrinsic state.