IsovectorE2matrix elements from electromagnetic transitions in thes−dshell: Experiment and shell-model calculations

All available $B\left(E2\mathrm{}\right)\mathrm{}$ values in the mass region $8\le Z$, $N\le 20$ relevant to the isovector electric quadrupole operator are compared to the theoretical $B\left(E2\mathrm{}\right)\mathrm{}$ values based on Chung-Wildenthal $0d_{\frac{5}{2}}-1\mathrm{}{s}_{\frac{1}{2}}-0\mathrm{}{d}_{\frac{3}{2}}$ shell-model wave functions with harmonic oscillator radial wave functions, and some selected cases are compared with local and energy dependent Woods-Saxon potential wave functions. The empirical effective charges deduced from these comparisons are insensitive to differences in mass, state, and dominant single-nucleon orbit. The value for the effective charge parameter $e_p-e_n$ extracted in the harmonic oscillator approximation is consistent with $1.0e$. The values extracted with local and energy-dependent Woods-Saxon potentials, which are more meaningfully related to the underlying structure of the isovector polarizability, are consistent with $0.7e$ and $0.6e$, respectively. Some inadequacies in the experimental data and theoretical models are discussed and improvements are suggested.