Onsager-Thomas-Fermi “Atoms” and “Molecules”: “Chemistry” of Correlations in Dense Plasmas
Following Widom,1 the m-body correlation function g(m) (r1,r2….rm) 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 particles7–10 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.
KeywordsExcess Free Energy Mean Spherical Approximation Bridge Function Screen Potential Nuclear Reaction Rate
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