The Electric Microfield and Its Spatial Derivatives Distribution Functions through Kelbg Potential: An Application on Lyman-α Spectral Line Shape of Hydrogenoid Lithium Plasma and Deducing of the Electrical Permittivity

Abstract

The electric microfield distribution functions were computed using two approchs: Monte Carlo simulation and analytical calculation. To achieve this, the Kelbg interaction, which accounts for quantum effects at short distances, was employed. Although the focus is on a weak coupling regime where quantum effects are negligible at average interparticle distances, the Kelbg potential was still utilized. In the simulation, all interactions between plasma components were fully accounted for, while the analytical calculation relied on the independent particles model (emitter–perturber). The results were compared with other findings that either include or exclude quantum effects. Various behaviors of the microfield distribution functions were identified. Additionally, the spatial derivatives of the microfield distribution functions were analytically derived, considering all interactions. These functions and their spatial derivatives were then incorporated into the calculation of the spectral line shape Ly-α of the pure plasma Li⁺², which was subsequently used to determine the electrical permittivity of the plasma. The obtained results for the electrical permittivity of this plasma are quite similar to those found in the literature. These results are important for modern applications. It has been shown that quantum action at zero interparticles has an important role in the microfield distribution functions in strongly correlated plasmas, where the degree of quantification is relatively large.