The spectral distribution methods are applied to calculate non-energy-weighted and linear-energy-weighted sum rules for electric and magnetic multipole excitations in the $\mathrm{ds}$-shell nuclei ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$. We see the inadequacy of $\mathrm{ds}$-shell model space to explain the observed isoscalar quadrupole transition strengths. Isospin admixing of $1^{+}$ levels in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ are also confirmed. For isovector $M1$, a detailed study of the Kurath sum rule is made. The strength sums for the higher order multipoles where experimental data are not accurate enough are also evaluated.

NUCLEAR STRUCTURE ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$; sum rules for $E2$, $E4$, $M1$, $M3$, $M5$ transitions; Brown-Kuo Hamiltonian; spectral distribution methods used for calculation; Kurath sum rule extended.

• Received 6 July 1981

DOI:https://doi.org/10.1103/PhysRevC.25.2029