Abstract
ABSTRACT This paper presents a detailed study of the stopping power of a homogeneous electron gas in moderate and strong coupling regimes using the self‐consistent version of the method of moments as the key theoretical approach capable of expressing the dynamic characteristics of the system in terms of the static ones, which are the moments. We develop a robust framework that relies on nine sum rules and other exact relationships to analyze electron–electron interactions and their impact on energy loss processes. We derive an expression for the stopping power that takes into account both quantum statistical effects and electron correlation phenomena. Our results demonstrate significant deviations from classical stopping power predictions, especially under the strong coupling conditions, where electron dynamics are highly dependent on the collective behavior. This work not only advances the theoretical understanding of the homogeneous electron gas but also has implications for practical applications in fields such as plasma physics and materials science.