Electric hexadecupole transition strength in ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ and shell-model predictions for E4 systematics in the sd shell

The E4 form factor for inelastic electron scattering to the first $4^{+}$ state of ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ predicted from a systematic shell-model treatment of $0^{+}$→$4^{+}$ transitions in the A=18–38 region is found to be in excellent agreement with experiment. This shell-model prediction is quite different from recent deformed Hartree-Fock predictions for the same transition. Corresponding predictions for other doubly-even nuclei in the 0d,1s shell are also presented and discussed.