Temperature-dependent Coulomb interactions in hydrogenic systems

In a hydrogenic plasma, the effective potentials Vᵢⱼ(r) of electron-proton, electron-positron, and electron-electron systems are considered. The inclusion of quantum-mechanical effects leads to a finite value of Vᵢⱼ(0) at the origin. For each system simple and analytical expressions are obtained at high temperature and small interparticle distance. Barker's numerical computations are extended to the high-temperature domain, small-r region, and electron-positron system. The symmetry effects are included for the electron-electron system. Various simple approximate formulas are obtained which describe Vᵢⱼ(r) at all distances. Some of them are in excellent agreement with the numerical results.