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On the asymptotic behavior of the pair correlation function for liquid4He

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Zeitschrift für Physik B Condensed Matter

Abstract

A new expression for the asymptotic pair correlation function of He II is proposed. Unlike the standard expressions, this contains explicitly the condensate fraction and leans heavily on the corresponding function for He I. The consequences for the long-wavelength liquid structure factor and the asymptotic effective interaction in the system are explored. In passing, the triplet and higher-order correlations are discussed briefly. Whenever possible, the connection with other treatments is pointed out.

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References

  1. Hansen, J.-P., McDonald, I.R.: Theory of simple liquids. London: Academic Press 1976

    Google Scholar 

  2. March, N.H., Tosi, M.: Atomic dynamics in liquids. New York: Wiley 1976

    Google Scholar 

  3. Enderby, J.E., Gaskell, T., March, N.H.: Proc. Phys. Soc. London85, 217 (1965)

    Google Scholar 

  4. Feynman, R.P.: Phys. Rev.94, 262 (1954); Feynman, R.P., Cohen, M.: Phys. Rev.102, 1189 (1956)

    Google Scholar 

  5. Reatto, L., Chester, G.V.: Phys. Rev.155, 88 (1967)

    Google Scholar 

  6. Feenberg, E.: Ann. Phys. (NY)70, 133 (1972)

    Google Scholar 

  7. Sears, V.F., Svensson, E.C., Martel, P., Woods, A.D.B.: Phys. Rev. Lett.49, 279 (1982); Svensson, E.C.: In: 75th Jubilee Conference on Helium-4. Armitage, J.G.M. (ed.), pp. 10–15. Singapore. World Scientific 1983

    Google Scholar 

  8. Griffin, A.: Phys. Rev. B (to be published)

  9. Fetter, A.L.: Phys. Rev. B23, 2425 (1981)

    Google Scholar 

  10. Ornstein, L.S., Zernike, F.: Proc. K. Ned. Akad. Wetschap. Ser. B17, 793 (1914). [Reprinted in: Frisch, H.L., Lebowitz, J.L.: The equilibrium theory of classical fluids. pp. III2–16. New York: Benjamin 1964]

    Google Scholar 

  11. Price, P.J.: Phys. Rev.94, 257 (1954); Feenberg, E.: Theory of quantum fluids. New York: Academic Press 1969

    Google Scholar 

  12. Egelstaff, P.A., London, H.: Proc. R. Soc. London242, 374 (1957)

    Google Scholar 

  13. Tan, H.T.: Phys. Rev. A4, 256 (1971)

    Google Scholar 

  14. March, N.H., Galasiewicz, Z.M.: Phys. Chem. Liq.5, 103 (1976)

    Google Scholar 

  15. Lighthill, M.J.: Introduction to fourier analysis and generalized functions. Eq. (30), p. 56. Cambridge: The University Press 1959

    Google Scholar 

  16. Huang, K.: In: The many body problem. Les Houches Lectures. pp. 601–649. London: Methuen 1958

    Google Scholar 

  17. Bogoliubov, N.N., Zubarev, D.N.: Sov. Phys. JETP1, 83 (1955)

    Google Scholar 

  18. Penrose, O.: In: Proceedings of the International Conference in Low Temperature Physics. Dillinger, J.R. (ed.), p. 117. Madison: University of Wisconsin Press 1958

    Google Scholar 

  19. Battaini, S., Reatto, L.: Phys. Rev. B28, 1263 (1983)

    Google Scholar 

  20. Isihara, A.: Physica106 B, 161 (1981)

    Google Scholar 

  21. Raveché, H.J., Kayser, R.F.: Phys. Rev. A29, 1003 (1984)

    Google Scholar 

  22. Kayser, R.F., Raveché, H.J.: Phys. Rev. A29, 1013 (1984)

    Google Scholar 

  23. As emphasized in Ref. 22, a rigorous proof of Eq. (15) is still lacking, although the result is widely believed to be true and its validity has been demonstrated for special cases

  24. London, F.: J. Chem. Phys.11, 203 (1943)

    Google Scholar 

  25. Morita, T., Hara, H.: Prog. Theor. Phys.41, 60 (1969)

    Google Scholar 

  26. Fröhlich, H.: Phys. Kondens. Mater.9, 350 (1969); Riv. Nuovo Cimento3, 490 (1973)

    Google Scholar 

  27. Lal, P., Terreaux, C.: Phys. Kondens. Mater.12, 131 (1970); Terreaux, C., Lal, P.: Collective Phenomena1, 61 (1972)

    Google Scholar 

  28. Hyland, G.J., Rowlands, G., Cummings, F.W.: Phys. Lett.31 A, 465 (1970); Cummings, F.W., Hyland, G.J., Rowlands, G.: Phys. Kondens. Mater.12, 90 (1970); Phys. Lett.86 A, 370 (1981)

    Google Scholar 

  29. Raveché, H.J., Mountain, R.D.: Phys. Rev. A9, 435 (1974)

    Google Scholar 

  30. Ghassib, H.B., Sridhar, R.: Phys. Lett.100 A, 198 (1984)

    Google Scholar 

  31. Robkoff, H.N., Ewen, D.A., Hallock, R.B.: Phys. Rev. Lett.43, 2006 (1979); Robkoff, H.N., Hallock, R.B.: Phys. Rev. B24, 159 (1981)

    Google Scholar 

  32. Sears, V.F., Svensson, E.C.: Phys. Rev. Lett.43, 2009 (1979)

    Google Scholar 

  33. Wirth, F.W., Ewen, D.A., Hallock, R.B.: Phys. Rev. B27, 5530 (1983)

    Google Scholar 

  34. Another interpretation is that, as the liquid is heated toT λ from below, the population of thermal rotons increases — giving rise to a concomitant increase in short- and intermediate-range spatial order. See the relevant discussion in Ref. 33 and the references cited therein

  35. Mook, H.A.: Phys. Rev. Lett.51, 1454 (1983)

    Google Scholar 

  36. Sears, V.F.: Phys. Rev. B28, 5109 (1983)

    Google Scholar 

  37. Wilks, J.: Liquid and solid helium. pp. 17–21. Oxford: Clarendon Press 1967

    Google Scholar 

  38. Larsen, S.Y., Kilpatrick, J.E., Lieb, E.H., Jordan, H.F.: Phys. Rev.140, A 129 (1965); Boyd, M.E., Larsen, S.Y., Kilpatrick, J.E.: J. Chem. Phys.45, 499 (1966); Larsen, S.Y., Witte, K., Kilpatrick, J.E.: J. Chem. Phys.44, 213 (1966); Larsen, S.Y.: J. Chem. Phys.48, 1701 (1968)

    Google Scholar 

  39. A similar decomposition applies to the3He gas; but this does not concern us here

  40. Boer, J. de: Rep. Prog. Phys.12, 305 (1949). In particular, see p. 338et seq

    Google Scholar 

  41. Hirschfelder, J.O., Curtiss, C.F., Bird, R.B.: Molecular theory of gases and liquids. Chap. 3, p. 131. New York: Wiley 1954

    Google Scholar 

  42. Brush, S.G.: Rev. Mod. Phys.33, 79 (1961)

    Google Scholar 

  43. Fosdick, L.D., Jordan, H.F.: Phys. Rev.143, 58 (1966)

    Google Scholar 

  44. Maynard, J.: Phys. Rev. B14, 3868 (1976)

    Google Scholar 

  45. Bishop, R.F., Ghassib, H.B., Strayer, M.R.: J. Low Temp. Phys.26, 669 (1977)

    Google Scholar 

  46. Huang, K.: Statistical mechanics. Chap. 12, p. 253. New York: Wiley 1963

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Jordan, Amman, Jordan

    H. B. Ghassib

  2. Laboratory of Atomic and Solid State Physics, Cornell University, 14853, Ithaca, New York, USA

    G. V. Chester

Authors
  1. H. B. Ghassib
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  2. G. V. Chester
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Ghassib, H.B., Chester, G.V. On the asymptotic behavior of the pair correlation function for liquid4He. Z. Physik B - Condensed Matter 59, 371–378 (1985). https://doi.org/10.1007/BF01328844

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  • DOI: https://doi.org/10.1007/BF01328844

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