A Monte Carlo study has been made of a plasma of heavy ions immersed in a uniform neutralizing background. Systems containing from 32 to 500 particles, with periodic boundary conditions, were used. The results of the study are presented in terms of a dimensionless parameter Γ= (4π*n*/3) ^{⅓}[(Ze)^{2}/*kT*], where *n* is the ion density (particles per cubic centimeter), *T* is the temperature (degrees Kelvin), *k* is the Boltzmann constant, *e* is the electronic charge, and *Z* is the atomic number. Thermodynamic properties and pair distribution functions were obtained for values of Γ ranging from 0.05 to 100.0 from the canonical ensemble by the Monte Carlo (MC) method.

Two different methods were used to determine the potential energy of a configuration. The first is the ``minimum‐image convention'' employed in many previous MC calculations. Each particle is allowed to interact only with each other particle in the basic cell, or with the nearest periodic image of each other particle if the image is closer. In the second method, the interaction of a particle with all the images of the other particles, and with the uniform background is taken into account by a technique similar to the Ewald procedure used to calculate lattice sums. It is found that both methods of determining the potential energy yield essentially the same results for the pair distribution function *g* for Γ values of 10 or less. For larger values of Γ the results given by the two methods differ significantly, indicating that the minimum image convention is inadequate for plasma systems at high densities and low temperatures.

Energies and values of the pair distribution function are compared with predictions of various approximate theories for small Γ values. It is found that the nonlinear Debye—Hückel (DH) theory is in agreement with the MC results for values of Γ up to 0.1. At Γ=1.0, significant deviations from the DH theory are observed. For Γ=1.0, *g* is found to be in close agreement with Carley's calculations based on the Percus—Yevick equation. For values of Γ above 2, *g* is no longer a monotonic function of the interparticle distance *r,* but begins to show oscillations characteristic of latticelike structures. For large values of Γ these oscillations are quite pronounced. The system is observed to undergo a fluid—solid phase transition in the vicinity of Γ=125.

## REFERENCES

*The Collected Papers of Peter J. W. Debye*(Interscience Publishers, Inc., New York, 1954), pp. 217, 264.

*Statistical Mechanics*(John Wiley & Sons, Inc., New York, 1940).

*Ionic Solution Theory*(Interscience Publishers, Inc., New York, 1962).

*A General Kinetic Theory of Liquids*(Cambridge University Press, London, 1949);

*Studies in Statistical Mechanics*, J. De Boer and G. E. Uhlenbeck, Eds. (North‐Holland Publ. Co., Amsterdam, 1962), Vol. 1, Part A;

*Statistical Mechanics*(McGraw‐Hill Book Co., Inc., New York, 1956), Chap. 6.

*Principia*, Book 2, Sec. V;

*Kinetic Theory. The Nature of Gases and of Heat*, S. G. Brush, Ed. (Pergamon Press, Inc., Oxford, England, 1965), Vol. 1, pp. 52–56.

*i*th random number is $ri\u2009=\u2009515ri\u22121\u2009mod\u2009235,$ and $r0\u2009=\u2009247\u2009162\u2009405\u2009723\u2009(octal).$ See L. J. Gannon and L. A. Schmittroth, “Computer Generation and Testing of Random Numbers,” Phillips Petroleum Co., Idaho Falls, Ida., Rept. IDO‐16921, 1965, for discussion of this method of generating random numbers, and further references cited therein. We have carried out some tests for the particular parameters used in our calculations, and found that the numbers are sufficiently random for our purposes.

*Monte Carlo Methods*(John Wiley & Sons, Inc., New York, 1964.)

*Statistical Mechanics*(McGraw‐Hill Book Co., Inc., New York, 1956), Chap. 6.

*Statistical Theory of Liquids*(University of Chicago Press, Chicago, Ill., 1964), pp. 109–118 (originally published in Moscow in 1961);

*Statistical Physics*(Addison‐Wesley Publ. Co., Inc., Reading, Mass., 1958), p. 322.