Differential cross section analysis for electron–hydrogen molecule collisions across various energies

This work reports comprehensive calculations of differential, elastic, and momentum transfer cross sections, as well as spin polarization, for elastic electron scattering from hydrogen molecules at incident energies of 10, 20, 40, 100, 400, and 700 eV. The analysis is carried out within a relativistic Dirac equation framework using partial-wave expansion and an optical model potential derived from a single-center Hartree–Fock method. The adopted model incorporates numerically evaluated static potentials and systematically accounts for exchange, correlation, and polarization effects through well-established quantum mechanical approximations. The results demonstrate that exchange and polarization interactions play a dominant role at low incident energies and small scattering angles. The calculated differential cross sections show close agreement with a broad set of experimental data reported in the literature. Overall, the study provides reliable relativistic predictions that enhance the understanding of electron–molecule interactions and confirm the robustness of relativistic quantum scattering models, with implications for applications in nuclear physics, atmospheric science, and plasma research.