RELATIVISTIC CORRECTIONS FOR A CLASSICAL ONE-COMPONENT PLASMA WITH DARWIN INTERACTIONS

We study the thermodynamic properties of a weakly relativistic one-com ponent plasma described by the Darwin hamiltonian. In this model, the charges are classical (non-quantum) and interact via the Coulomb poten tial plus the two-body momentum-dependent Darwin potential with amplit ude proportional to 1/c(2), where c is the speed of light. The low-den sity forms of the first non-ideal relativistic corrections to the Coul omb equilibrium quantities are explicitly computed from resummed diagr ammatical representations derived elsewhere. The canonical density is first studied and its momentum dependence is calculated at the lowest orders in the density rho and in 1/c. The two-body correlations are co nsidered at the level of the mean-field approximation, and beyond. The non-ideal relativistic contributions decay algebraically with oscilla tions, because of the bad screening of the Darwin potential. Similar a lgebraic tails are also found in the charge correlations and might inh ibit the screening of external charges. In the space of velocities, th e first deviations from the familiar non-relativistic Maxwellian are o btained. Moreover, we show that if unscreened current correlations app ear, they do not induce any diamagnetic properties. The first relativi stic correction to the equation of state is of order 1/c(4) and involv es fluctuations beyond the mean-field approximation. Eventually, we br iefly compare all these results with those obtained for related models , and we give their physical regimes of validity for the description o f real plasmas. (C) 1998 Elsevier Science B.V. All rights reserved.