A novel method to determine the 4th moment of the 208Pb charge density from low-momentum-transfer electron scattering

Abstract We propose a new method to determine the 4th moment of the nuclear charge-density distribution of 208Pb, 〈r4〉c, with high precision from low-momentum-transfer elastic electron scattering. The key feature of this approach is that Coulomb distortion effects, which are pronounced for heavy nuclei, are evaluated numerically and incorporated into the formalism of the Plane Wave Born Approximation as a correction factor. The 4th and higher-order charge-density moments are of particular interest because they are sensitive not only to the moments of the point-proton density distribution but also to those of the point-neutron density distribution in nuclei. Their precise determination is therefore essential for constraining the moments of the point-neutron density distribution. It is demonstrated that 〈r4〉c can be determined with an uncertainty of about 0.8% using the proposed approach, improving upon the present uncertainty of about 1.5% obtained from empirically determined charge-density distributions. Measurements of 〈r4〉c in 208Pb using this method are currently in progress at the Ultra-Low momentum transfer Q2 (ULQ2) facility at Research Center for Accelerator and Radioisotope Science (RARiS), Tohoku University.