An accurate equation of state for the one-component plasma in the low coupling regime

An accurate equation of state of the one-component plasma is obtained in the low coupling regime 0 <= Gamma <= 1. The accuracy results from a smooth combination of the well-known hypernetted chain integral equation, Monte Carlo simulations and asymptotic analytical expressions of the excess internal energy u. In particular, special attention has been brought to describe and take advantage of finite size effects on Monte Carlo results to get the thermodynamic limit of u. This combined approach reproduces very accurately the different plasma correlation regimes encountered in this range of values of Gamma. This paper extends to low Gamma's, an earlier Monte Carlo simulation study devoted to strongly coupled systems for 1 <= Gamma <= 190 (J-M Caillol 1999 J. Chem. Phys. 111 6538). Analytical fits of u(Gamma) in the range 0 <= Gamma <= 1 are provided with a precision that we claim to be not smaller than p = 10(-5). The hypernetted chain equation and exact asymptotic expressions are shown to give reliable results for u(Gamma) only in narrow Gamma intervals, i.e. 0 <= Gamma less than or similar to 0.5 and 0 <= Gamma less than or similar to 0.3 respectively.