Relativistic corrections for lepton-nucleus scattering in the short-time approximation

TL;DR

This paper develops a method to include relativistic effects in lepton-nucleus scattering calculations within the Short-Time Approximation, extending its validity to high momentum transfers and improving agreement with experimental data.

Contribution

It introduces an expansion scheme that treats initial nucleon momentum perturbatively while allowing arbitrary momentum transfer, enhancing the STA's applicability to high-$q$ regimes.

Findings

Achieved good agreement with experimental data for $^3$He and $^4$He scattering.

Extended the STA to high-$q$ regimes with relativistic corrections.

Improved accuracy over previous low-$q$ limited models.

Abstract

We present an approach for including relativistic corrections in lepton-nucleus scattering calculations within the Short-Time Approximation (STA). Previous ab-initio studies employed electromagnetic currents expanded in powers of $q/m$, where $q$ is the momentum transfer and $m$ is the nucleon mass, restricting their validity to low-$q$ kinematics. We adopt an expansion scheme that treats the initial nucleon momentum perturbatively while allowing for arbitrary momentum transfer, thereby extending the applicability of the STA to high-$q$ regimes. Additionally, we incorporate a relativistic treatment of the two-nucleon final-state energies. Calculations for $^3$He and $^4$He inclusive electron scattering cross sections show a substantial improvement over previous results, achieving good agreement with experimental data in the quasi-elastic region for both low- and high-momentum transfer.