Abstract
A new representation is obtained for the isothermal density derivative ofg(r). It explicitly exhibits the contributions of potential energy terms that are not pairwise additive. Consideration of a previously known result shows that one has to be rather cautious when using it to obtain information on the triplet correlation function from the well-known relation between this function andδg/δρ, due to large cancellations which take place at high density. By integrating with respect to density the new representation forδg/δρ, after a suitable closure has been introduced, we obtain an augmented Percus-Yevick equation for hard spheres which has full thermodynamic consistency. The equation of state and the cavity functiony(r) are very accurate at low density and considerably improve PY at medium density, so that this appears to be a useful new approach to the theory of fluids, but it is necessary to improve the closure in order to treat a dense fluid.
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References
H. van Beijeren,Phys. Lett. 105A:191 (1984); see also A. F. E. M. Haffmans, I. M. de Schepper, J. P. J. Michels, and H. van Beijeren,Phys. Rev. A 37:2698 (1988).
F. P. Buff and R. Brout,J. Chem. Phys. 33:1417 (1960).
P. Schofield,Proc. Phys. Soc. 88:149 (1966).
P. Hutchinson,Proc. Phys. Soc. 91:506 (1967).
H. J. Raveché and R. D. Mountain,J. Chem. Phys. 53:3101 (1970);57:3987 (1972).
G. Stell, inPhase Transitions and Critical Phenomena, Vol. 5B, C. Domb and M. S. Green, eds. (Academic Press, London, 1976).
J. K. Percus and G. J. Yevick,Phys. Rev. 110:1 (1958).
E. Thiele,J. Chem. Phys. 39:474 (1963); M. S. Wertheim,Phys. Rev. Lett. 10:321 (1963).
L. Verlet and J. J. Weis,Phys. Rev. A 5:939 (1972).
E. W. Grundke and D. Henderson,Mol. Phys. 24:269 (1972).
W. G. Hoover and J. C. Poirier,J. Chem. Phys. 37:1041 (1962).
E. Meeron and A. J. F. Siegert,J. Chem. Phys. 48:3139 (1968).
B. R. A. Nijboer and L. Van Hoven,Phys. Rev. 85:777 (1952); F. H. Ree, R. N. Keeler, and S. L. McCarthy,J. Chem. Phys. 44:3407 (1966).
J. J. Erpenbeck and W. W. Wood,J. Stat. Phys. 35:321 (1984).
N. F. Carnahan and K. E. Starling,J. Chem. Phys. 51:635 (1969).
P. A. Egelstaff, D. I. Page, and C. R. T. Heard,J. Phys. C 4:1453 (1971).
L. W. Johnson and R. Dean Riess,Numerical Analysis (Addison-Wesley, Reading, Massachusetts, 1982).
W. R. Smith and D. Henderson,Mol. Phys. 19:411 (1970).
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This paper is dedicated to Jerry Percus on the occasion of his 65th birthday.
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Reatto, L., Stell, G. & Tau, M. On the isothermal density derivative ofG(r) and a new theory of the pair correlation function of hard spheres. J Stat Phys 64, 481–500 (1991). https://doi.org/10.1007/BF01048303
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DOI: https://doi.org/10.1007/BF01048303