Effective Spectral Function for Quasielastic Scattering on Nuclei from Deuterium to Lead

TL;DR

This paper introduces an effective spectral function (ESF) that improves the modeling of quasielastic scattering on nuclei by accounting for final state interactions, providing better predictions of electron scattering data across a range of nuclei.

Contribution

The paper presents a modified effective spectral function that accurately describes quasielastic scattering, incorporating final state interactions and improving upon traditional models.

Findings

ESF models match kinematic distributions well

ESF combined with transverse enhancement predicts electron QE data

Binding energy parameter Δ is smaller than traditional estimates

Abstract

Spectral functions do not fully describe quasielastic electron and neutrino scattering from nuclei because they only model the initial state. Final state interactions distort the shape of the differential cross section at the peak and increase the cross section at the tails of the distribution. We show that the kinematic distributions predicted by the $\psi'$ superscaling formalism can be well described with a modified {\it {effective spectral function}} (ESF). By construction, models using ESF in combination with the transverse enhancement contribution correctly predict electron QE scattering data. Our values for the binding energy parameter $\Delta$ are smaller than $\overline{\epsilon}$ extracted within the Fermi gas model from pre 1971 data by Moniz, probably because these early cross sections were not corrected for coulomb effects.