Electroweak charge density distributions with parity-violating electron scattering

Abstract

Parity-violating electron scattering (PVS) is an accurate and model-independent way to investigate the weak-charge density distributions of nuclei. In this paper, we study parity-violating electron scattering with the Helm model where the effects of spin-orbit currents on nuclear weak skins are taken into account. The conditions of two PVS measurements to constrain the surface thickness ${\ensuremath{\sigma}}_{W}$ of Helm weak-charge densities are investigated. According to the plane wave Born approximation, ${A}_{\mathrm{pv}}$ is expressed in terms of parameters of the corresponding Helm charge and weak-charge densities. After fitting the results of ${A}_{\mathrm{pv}}$ calculated from the phase-shift analysis method where the Coulomb distortion effects are incorporated, an empirical formula in terms of Helm model parameters for calculating ${A}_{\mathrm{pv}}$ is obtained. If two PVS measurements with different scattering angles are carried out, the modeled weak-charge density distributions with two parameters could be extracted from this empirical formula.