Electromagnetic sum rules by spectral distribution methods

Abstract

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.