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

  • Yaakov Rosenfeld
Part of the NATO ASI Series book series (volume 154)

Abstract

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.

Keywords

Excess Free Energy Mean Spherical Approximation Bridge Function Screen Potential Nuclear Reaction Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    B. Windom, J. Chem. Phys. 39:2808 (1963).ADSCrossRefGoogle Scholar
  2. 1a.
    See also J. S. Rowlinson and B. Windom, “Molecular Theory of Capilarity”, Clarendon-Press, Oxford 1982.Google Scholar
  3. 2.
    W. G. Hoover and J. C. Poirer, J. Chem. Phys. 37:1041 (1962).ADSCrossRefGoogle Scholar
  4. 3.
    B. Jancovici, J. Stat. Phys. 17:357 (1977).ADSCrossRefGoogle Scholar
  5. 4.
    See, e.g., the review by S. Ichimaru, Rev. Mod. Phys. 54:1017 (1982).ADSCrossRefGoogle Scholar
  6. 5.(a)
    Y. Rosenfeld and N. W. Ashcroft, Phys. Rev. A 20:1208 (1979)ADSCrossRefGoogle Scholar
  7. 5.(b)
    Y. Rosenfeld, J. Phys. (Paris), Collog. 41:c-77 (1980)Google Scholar
  8. 5.(c)
    Y. Rosenfeld, Phys. Rev. Lett. 44:146 (1980).ADSCrossRefGoogle Scholar
  9. 6.
    C. G. Gray and K. E. Gubbins, “Theory of Molecular Fluids”, Volume I,Clarendon Press, Oxford, 1984.MATHGoogle Scholar
  10. 7.
    Y. Rosenfeld, Phys. Rev. A 25:1206 (1982)ADSCrossRefGoogle Scholar
  11. 7a.
    Y. Rosenfeld, Phys. Rev. A A 26:3622 (1982).ADSCrossRefGoogle Scholar
  12. 8.
    Y. Rosenfeld and W. M. Gelbart, J. Chem. Phys. 81:4574 (1984).ADSCrossRefGoogle Scholar
  13. 9.
    Y. Rosenfeld and L. Blum, J. Phys. Chem. 89:5149 (1985)CrossRefGoogle Scholar
  14. 9a.
    Y. Rosenfeld and L. Blum, J. Chem. Phys. 85:1556 (1986).ADSCrossRefGoogle Scholar
  15. 10.
    Y. Rosenfeld, Phys. Rev. A 32:1834 (1985)ADSCrossRefGoogle Scholar
  16. 10a.
    Y. Rosenfeld, Phys. Rev. A A 33:2025 (1986).ADSCrossRefGoogle Scholar
  17. 11.
    M. Baus and J. P. Hansen, Phys. Rep. 59:1 (1980).MathSciNetADSCrossRefGoogle Scholar
  18. 12.
    H. E. DeWitt, in “Strongly Coupled Plasmas”, edited by G. Kalman, Plenum Press, New York, 1977.CrossRefGoogle Scholar
  19. 13.
    From direct application of Widom’s relation.Google Scholar
  20. 14.
    Y. Rosenfeld, J. Stat. Phys. 37:215 (1984).MathSciNetADSMATHCrossRefGoogle Scholar
  21. 15.
    L. Onsager, J. Phys. Chem. 43:189 (1939).CrossRefGoogle Scholar
  22. 16.
    E. H. Lieb and H. Narnhofer, J. Stat. Phys. 12:2916 (1975)MathSciNetCrossRefGoogle Scholar
  23. 16a.
    Ph. Choquard, in “Strongly Coupled Plasmas”, edited by G. Kalman, Plenum Press, New York, 1977.Google Scholar
  24. 17.
    Eq. (2) is derived in Ref. (10) above: Eq. (3) follows directly from the discussion in Ref. (9) above.Google Scholar
  25. 18.
    Direct application of Sec. III in Ref. (8) above.Google Scholar
  26. 19.
    See, e.g., N. Itoh, H. Totsuji, S. Ichimaru, and H. E. DeWitt, Astrophys. J. 234:1079 (1979), and compare with Ref. (5c) above.ADSCrossRefGoogle Scholar
  27. 20.
    K. C. Ng, J. Chem. Phys. 61:2680 (1974)ADSCrossRefGoogle Scholar
  28. 20a.
    F. J. Rogers and H. E. DeWitt (unpublished): see also Ref. (10) above.Google Scholar
  29. 21.
    J. G. Kirkwood, J. Chem. Phys. 3:300 (1935)ADSCrossRefGoogle Scholar
  30. 21a.
    compare with F. J. Pinski and C. E. Campbell, Phys. Rev. A 33:4232 (1986).ADSCrossRefGoogle Scholar
  31. 22.
    Appendix B in Ref. (5a) above, and references therein.Google Scholar
  32. 23.
    M. Friedman, A. Rabinovitch, Y. Rosenfeld and R. Thieberger “Thomas-Fermi Equation with Non-Spherical Boundary Conditions”, J. Comp. Phys., in print.Google Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Yaakov Rosenfeld
    • 1
  1. 1.Nuclear Research Center-NegevBeer-ShevaIsrael

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