Electron scattering form factors of stretched transitions using Woods-Saxon wave functions

Abstract

Electron scattering form factors for stretched transitions are computed using radial wave functions from realistic nuclear potentials, including the unbound nature of final states above particle decay thresholds. The calculated form factors are compared to data for ${4}^{\mathrm{\ensuremath{-}}}$ states in $^{12}\mathrm{C}$, $^{14}\mathrm{C}$, and $^{16}\mathrm{O}$, ${6}^{\mathrm{\ensuremath{-}}}$ states in $^{24}\mathrm{Mg}$, $^{26}\mathrm{Mg}$, and $^{28}\mathrm{Si}$, ${8}^{\mathrm{\ensuremath{-}}}$ states in $^{48}\mathrm{Ca}$, $^{54}\mathrm{Fe}$, $^{58}\mathrm{Ni}$, and $^{60}\mathrm{Ni}$, the ${10}^{\mathrm{\ensuremath{-}}}$ state in $^{90}\mathrm{Zr}$, and the ${14}^{\mathrm{\ensuremath{-}}}$ state in $^{208}\mathrm{Pb}$. We assess the fraction of the single-particle sum rule strengths using these realistic nuclear potentials in place of the standard results using harmonic oscillator wave functions. Appreciably greater fractions are obtained for low mass nuclei in the present work, totalling 105% of the sum strength for $^{12}\mathrm{C}$ and 81% for $^{16}\mathrm{O}$. Much less damping of the magnetic strength is thus experimentally observed than is the case when oscillator wave functions are used for comparison. The results of including meson exchange currents in the analysis are also discussed.