Electron screening corrections in dense ionized matter

Thermodynamic perturbation theory is used to calculate the corrections to the free energy and equation of state of the one-component plasma, due to the polarization of the electron background. In a series of recent papers [1, 2, 3] the thermodynamic properties and correlation functions of the classical one-component plasma (OCP) in a uniform background have been computed accurately with the help of computer simulation techniques. The OCP is a reasonable model for the description of superdense, completely ionized matter typical of extreme astrophysical situations (e.g. white dwarfs and the interior of Jupiter) and possibly of metallic hydrogen. Under such conditions, the electrons are strongly degenerate and in the first approximation play the role of a rigid, uniform background. However, even a highly degenerate electron gas will be polarized by the ionic charge distribution; consequently the ion-ion interaction will be modified by the electron screening. Hubbard and Slattery [4] have shown how this effect can be accounted for through the dielectric function of the electron gas. In this letter electron screening corrections will be calculated with the help of thermodynamic perturbation theory. These screening corrections will be included in a simple equation of state for dense ionized matter. It should be noted that the electron screening lenght breaks the scale invariance of the OCP by which all equilibrium properties depend only on the single dimension less parameter where Ze is the charge of the ions, a = /4~pB-~3 ~ ions, ~ = ~ 20132013 j (*) Equipe associee au Centre National de la Recherche Scientifique (C.N.R.S.). is the ion-sphere radius (p = N/V is the number density) and # = 1/A~ T. Because of the large mass ratio between ions and electrons, the latter react practically instantanously to any variation of the ion charge density which plays the role of an external charge density : where the ri (1 i N) are the ion positions and Pe.,(r) has the following Fourier transform : Hence the induced charge density can be related to the external charge density through the stratic dielectric function e(k) of the electron gas [2, 4, 5] : From Poisson’s equation the corresponding total electrostatic potential is : where the first term stems from the external charge density and the second term from the induced charge density. Replacing peXt(k) by Pk for brevity, Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:01975003605013300