Dispersive Corrections to the Born Approximation in Elastic Electron-Nucleus Scattering in the Intermediate Energy Regime

TL;DR

This paper investigates dispersive corrections to the Born approximation in elastic electron scattering on carbon-12, revealing significant effects that depend on energy and could impact nuclear radius measurements and response quenching.

Contribution

It provides experimental evidence of large dispersive effects near the diffraction minimum in 12C, with a detailed analysis of their energy dependence and implications for nuclear physics.

Findings

Dispersive effects contribute approximately 30.6% to the cross section at 1 GeV.

The effects are strongly energy-dependent and larger than previously estimated.

Results align with previous data but with reduced precision.

Abstract

Measurements of elastic electron scattering data within the past decade have highlighted two-photon exchange contributions as a necessary ingredient in theoretical calculations to precisely evaluate hydrogen elastic scattering cross sections. This correction can modify the cross section at the few percent level. In contrast, dispersive effects can cause significantly larger changes from the Born approximation. The purpose of this experiment is to extract the carbon-12 elastic cross section around the first diffraction minimum, where the Born term contributions to the cross section are small to maximize the sensitivity to dispersive effects. The analysis uses the LEDEX data from the high resolution Jefferson Lab Hall A spectrometers to extract the cross sections near the first diffraction minimum of 12C at beam energies of 362 MeV and 685 MeV. The results are in very good agreement with previous world data, although with less precision. The average deviation from a static nuclear charge distribution expected from linear and quadratic fits indicate a 30.6% contribution of dispersive effects to the cross section at 1 GeV. The magnitude of the dispersive effects near the first diffraction minimum of 12C has been confirmed to be large with a strong energy dependence and could account for a large fraction of the magnitude for the observed quenching of the longitudinal nuclear response. These effects could also be important for nuclei radii extracted from parity-violating asymmetries measured near a diffraction minimum.