Onsager-Thomas-Fermi “Atoms” and “Molecules”: “Chemistry” of Correlations in Dense Plasmas

Abstract

Following Widom,¹ the m-body correlation function g^(m) (r₁,r₂….r_m) of a fluid can be expressed through the free energy change upon fixing the positions of m fluid particles in the appropriate configuration to form an m-interaction-site molecule. As a special case, the zero-separation theorem² relates the r=0 value of the plasma pair-screening potential, H(r) = ℓn(g(r)exp(βɸ (r)), to the thermodynamics of plasma mixtures.³ This relation is the starting point for calculating enhancement factors of nuclear reaction rates⁴. It played a key role in the study of the short range behavior of the bridge function, notably their universal characteristics.⁵ The application of Widom’s relation for calculating the complete pair correlation function g(r), not to mention higher order correlation functions, has been out of reach for existing theories⁶ for the thermodynamics of molecular fluids. A new theory for the statistical thermodynamics of interacting charged particles^7–10 is, however, of the required accuracy and simplicity to enable such a calculation. This physically transparent theory is applied here to a molecular fluid composed of clusters of positive ions in a uniform neutralizing background charge density. We calculate the m-particle screening potentials in classical plasmas. The results reported below represent the first accurate calculation of fluid many body correlation functions from a theory for the thermodynamics of molecular fluids.