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

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.