Thermal and Polarization Influences on Electron–Hydrogen Scattering and Proton Exchange Membrane Fuel Cell Efficiency

Proton Exchange Membrane Fuel Cells (PEMFCs) are strongly influenced by electron–hydrogen scattering processes, especially under self-generated non-monochromatic polarized fields and thermal environments. The objective of this work is to examine the effect of such scattering on PEMFC performance. A thermal screening potential together with the thermal Volkov wavefunction was employed to formulate the interaction, from which the scattering matrix and transition matrix were derived. The transition matrix was then used within the differential cross-section (DCS) framework to analyze the scattering characteristics of electron–hydrogen interactions. The computed results shows that the DCS increases with the rise in self-generated PEMFC temperature, emphasizing the thermal contribution to scattering behavior. In contrast, scattering decreases with increasing scattering angle and momentum, indicating angular and momentum-dependent suppression. Screening effects were also observed, with higher scattering at low screening values and reduced scattering at higher values. Additionally, polarization of the self-generated field significantly modified the DCS, showing the combined influence of thermal and field conditions on the scattering process. These findings highlight that electron–hydrogen scattering plays a critical role in determining transport and energy transfer inside PEMFCs. The study suggests that optimizing thermal conditions and controlling polarization effects could improve PEMFC efficiency and operational stability. Beyond fuel cell applications, the results are relevant for understanding multiphoton processes, photon-assisted scattering, and energy transport in broader contexts, including laser–plasma interactions, condensed matter systems, and astrophysical environments. Thus, this work provides theoretical insights with practical implications for enhancing PEMFC performance and advancing scattering studies in complex fields.