Equilibrium Properties of a System of Charged Particles

Motivated by the formal identification that can be made between the electronic charge $e$ and a range parameter $\gamma$ that we have previously studied, we have developed high‐temperature, high‐density expansions of the Helmholtz free energy and potentials of average force for systems of ions with repulsive cores. It appears that the natural ordering parameter for our free energy expansion is $\mathrm{\kappa R}$ , where $\kappa$ is the inverse Debye length and $R$ an effective core diameter, and as a result the expansion is useful for either sufficiently high temperatures at any density or sufficiently low densities at any temperature. We find the terms in this expansion through order ${\mathrm{(\kappa R)}}^7$ . We have also found effects that will serve to modify the shielding length at high densities so that it is no longer just ${\kappa }^{\text{−1}}$ . One such effect depends upon the disparity in the core sizes of the positive and negative ions, and it vanishes only when the disparity does. A higher‐order modification of the shielding length that remains in this symmetric case is also discussed.