Effective proton-proton potential in hydrogen plasmas

The proton-proton pair potential for protons in a finite-temperature electron gas is calculated without making the usual approximations of second-order pseudopotential theory, linear response, etc., which are known to be untenable for protons. This is achieved by the inversion of the proton-proton pair distribution of an electron-proton plasma obtained by a full nonlinear finite-temperature density-functional calculation for the two-component system. As the latter is a spherically symmetric calculation, the method affords a means of obtaining ion-ion pair potentials in plasmas and liquid metals which go beyond second-order pseudopotential-type formulations without solving a two-center Schr\"odinger problem.