The classical $\alpha$-particle model has been consistently applied to all $4N$ nuclei in the $2s-1d$ shell. The ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ nucleus was found to be a $D_{2d}$ distorted tetrahedron in agreement with earlier investigations. Electron scattering form factors were predicted, but there are at present no experimental data for comparison. Most interesting results were obtained for ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, where the experimental matrix elements, energy spectrum, and electron scattering form factors were found to definitely favor a $D_{2h}$ bitetrahedron over the $D_{4h}$ square bipyramid used in other papers. Recent experiments on ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ also slightly favor an oblate $D_{3d}$ structure over the previously considered $D_{5h}$ pentagonal bipyramid. No definite structures could be established for ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ and ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, because of the large number of $\alpha$ particles involved. However, a unique structure was found for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$. It consists of six $\alpha$ clusters arranged in an octahedron outside of a tetrahedral ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ core.

• Received 18 June 1971

DOI:https://doi.org/10.1103/PhysRevC.4.1044