Longitudinal and transverse response functions for quasielastic electron scattering

Abstract

We consider the longitudinal and transverse response functions for quasielastic electron scattering from $^{56}\mathrm{Fe}$. In a previous work we showed that the longitudinal response is overestimated by about forty percent in the impulse approximation. We argued that shortrange correlations, among other effects, could shift transition strength to higher energies. To account for these features we multiplied the cross sections by a factor ${Z}^{2}$, where $Z$ is a measure of the strength of the quasiparticle pole. The model we proposed then led to a significant underestimate of the transverse response. In this work we concentrate on the analysis of the transverse response and consider the electromagnetic properties of an interacting system of nucleons and deltas. Specific assumptions concerning the transition amplitudes $N{N}^{\ensuremath{-}1}\ensuremath{\rightarrow}N{N}^{\ensuremath{-}1}$ and $N{N}^{\ensuremath{-}1}\ensuremath{\rightarrow}\ensuremath{\Delta}{N}^{\ensuremath{-}1}$ allow for a simultaneous fit to both the longitudinal and transverse response functions. In our model the amplitude $N{N}^{\ensuremath{-}1}\ensuremath{\rightarrow}\ensuremath{\Delta}{N}^{\ensuremath{-}1}$ is governed by rho exchange with no additional correlation corrections. The model further requires that the $N{N}^{\ensuremath{-}1}\ensuremath{\rightarrow}N{N}^{\ensuremath{-}1}$ amplitude be small for the momentum transfers considered here: $210 \mathrm{MeV}/c\ensuremath{\le}|\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}|\ensuremath{\le}410 \mathrm{MeV}/c$. Some theoretical support is offered for these small values of the latter amplitude.NUCLEAR REACTIONS Quasielastic electron scattering; transverse and longitudinal response functions; effective forces in nuclei at intermediate momentum transfer.