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

Abstract

All available $B(E2)$ values in the mass region $8\ensuremath{\le}Z$, $N\ensuremath{\le}20$ relevant to the isovector electric quadrupole operator are compared to the theoretical $B(E2)$ values based on Chung-Wildenthal $0{d}_{\frac{5}{2}}\ensuremath{-}1{s}_{\frac{1}{2}}\ensuremath{-}0{d}_{\frac{3}{2}}$ 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 ${e}_{p}\ensuremath{-}{e}_{n}$ 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.NUCLEAR STRUCTURE $17\ensuremath{\le}A\ensuremath{\le}39$ nuclei: comparison of experimental $E2$ isovector matrix elements with shell-model predictions; extraction of the isovector effective charge; full basis $0{d}_{\frac{5}{2}}\ensuremath{-}1{s}_{\frac{1}{2}}\ensuremath{-}0{d}_{\frac{3}{2}}$ shell-model wave functions; Chung-Wildenthal Hamiltonians.