Theory of static correlations in rare gases for realistic model-interactions: Triple-point region and critical point

The crossover modified-hypernetted-chain equation, extended to take into account three-body forces, is tested against recent simulation results for realistic models of krypton and xenon which include also the three-body Axilrod-Teller interaction $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$. The effect of $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$ on g(r) is reproduced so well that this equation can also be used in the framework of inversion of structural data to separate the true two-body contribution out of the extracted effective potential. We also study the way $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$ influences the critical point of the liquid-vapor phase transition for Ar, Kr, and Xe. We find that both ${\rho }_c$ and $T_c$ are lowered by $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$ and that the small deviations from the law of corresponding states are as much due to $v_{\mathrm{AT}{}^{\mathrm{}\left(3\right)\mathrm{}}}$ as to the different shape of the pair interaction.