SummaryA general method is presented for computation of radial distribution functions for plasmas over a wide range of temperatures and densities. The method uses the Monte Carlo technique applied by Wood and Parker, and extends this to long-range forces using results borrowed from crystal lattice theory. The approach is then used to calculate the radial distribution functions for a proton-electron plasma of density 1018 electrons/cm3 at a temperature of 104 OK. The results show the usefulness of the method if sufficient computing facilities are available.

Two-particle “effective potentials,” which incorporate the quantum mechanical effects into the pair interaction potential, are evaluated accurately. Tables and graphs of these potentials between electron–proton, parallel spin electron–electron, antiparallel spin electron–electron, and proton–proton are presented for a wide range of temperatures. The range of validity and analytic properties of the effective potentials in certain regions are given. Possible uses of these potentials to evaluate thermodynamic properties and percentage ionization of the plasma are discussed.

A quantum mechanical calculation of the radial distribution function g".m.(r) for unlike particles in a hydrogenous plasma is presented. Results for a neutral plasma over a range of temperatures show that gq.m.(r) differs significantly from the corresponding classical distribution function g.(r) = exp(fJel/r) when r is less than a chosen distance r" the value of which is temperature dependent. The effect of shielding, the relative contribution from scattered and bound states, and the relation to percentage ionization are discussed. I. lNTRODUOTIONIn solving a modified Perous-Yevick integral equation for a hydrogenous plasma to find the radial distribution function for unlike particles for temperatures near 10' OK, it was found (Barker 1966) that the efficiency of the numerical iterative procedure used was very sensitive to the initial form assumed for the radial distribution function. If a classical or Debye-Huckel form was used, the cutoff point as r became small was of critical importance to the solution. This reflects the fact that at these temperatures an appreciable number of particles of opposite charges are bound, and the classical theory does not adequately describe the bound states. To overcome this difficulty a quantum mechanical expression for the radial distribution function at low radii has been evaluated, the results of which are presented in this paper. II. QUANTUM MEOHANIOAL EXPRESSION FOR gab(r)The radial distribution function gab(r) is usually defined by Dab(r) = Db gab(r) , where Dab(r) is the number density of particles of type b at a distance r from a particle of type a, and Db is the average number density of type b particles throughout the fluid. It is proportional to the conditional probability of finding particle b in volume element dx(2) given particle a in volume element dx(I), and, for a neutral plasma of electron number density De, the distribution function between protons and electrons can be expressed aswhere the summation over n sums over the bound states of energy En of the hydrogen atom, and rpnlm are the wavefunctions normalized so that f rpnlm rp:lm d V = 1. The

171bulk liquid-and merit special attention on that account. It is hoped that the present results will clear the way for a more successful treatment of the phenomenon, along the lines, for example, suggested by Di Castro, 3 if, indeed, vortex rings are to provide the answer.

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