Inelastic scattering $E4$ transition probabilities in the $0d$, $1s$ shell

Theoretical $E4\mathrm{}$ transition matrix elements calculated in the full $d_{\frac{5}{2}}-s_{\frac{1}{2}}-d_{\frac{3}{2}}$ shell-model space are presented for excitations of some ground states of stable nuclei for $18\le A\le 38$. These matrix elements have been used to calculate inelastic transition probabilities for electromagnetic and hadronic probes. Available data on the relative magnitudes and energy distributions of $E4\mathrm{}$ excitation strengths are found to be well reproduced theoretically thereby. Based on several experimentally measured transition strengths, the empirical isoscalar $E4\mathrm{}$ effective charge is found to be $e_p+e_n=(2.0\mathrm{}\pm 0.2)e$. This is similar in magnitude to the analogous isoscalar $E2\mathrm{}$ effective charge, but is much larger than existing theoretical estimates.

NUCLEAR STRUCTURE ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{34}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$; calculations for the strengths of $E4\mathrm{}$ inelastic scattering transitions and their proton and neutron components; complete $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{5}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ shell-model wave functions; Chung-Wildenthal Hamiltonians.