Skip to main content
Log in

Three-phonon vertex corrections to the excitation spectrum and liquid-structure function of liquid4He

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

The energy spectrum of elementary excitations and the liquid-structure function of liquid4He are calculated by means of the method of correlated basis functions in the approximation of second-order perturbation theory. The procedure is based on (i) the construction of phonon functions in terms of collective coordinates and the optimum Bijl-Dingle-Jastrow type of ground-state wave function and (ii) the evaluation of leading correction terms to the Bijl-Feynman excitation spectrum, which are generated by two types of three-phonon vertices. Numerical results are obtained using the optimum liquid-structure function computed by Campbell and Feenberg in the paired-phonon analysis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Feenberg,Theory of Quantum Fluids (Academic Press, New York, 1969, Chaps. 5–7).

    Google Scholar 

  2. E. Feenberg,Am. J. Phys. 38, 684 (1970).

    Google Scholar 

  3. A. Bijl,Physica 7, 869 (1940).

    Google Scholar 

  4. R. B. Dingle,Phil. Mag. 40, 573 (1949).

    Google Scholar 

  5. R. Jastrow,Phys. Rev. 98, 1479 (1955).

    Google Scholar 

  6. F. Y. Wu and E. Feenberg,Phys. Rev. 122, 739 (1961); W. E. Massey,Phys. Rev. 151, 153 (1966).

    Google Scholar 

  7. W. L. McMillan,Phys. Rev. 138, A44s (1965).

  8. D. Schiff and L. Verlet,Phys. Rev. 160, 208 (1967).

    Google Scholar 

  9. M. A. Pokrant,Phys. Rev. A6, 1588 (1972).

    Google Scholar 

  10. H. W. Jackson and E. Feenberg,Ann. Phys. (N.Y.)15, 266 (1961).

    Google Scholar 

  11. C. E. Campbell and E. Feenberg,Phys. Rev. 188, 396 (1969).

    Google Scholar 

  12. T. B. Davison and E. Feenberg,Ann. Phys. (N.Y.)53, 559 (1969).

    Google Scholar 

  13. D. K. Lee,Phys. Rev. A4, 1670 (1971).

    Google Scholar 

  14. P. Berdahl and D. K. Lee,Phys. Rev. A7, 1376 (1973).

    Google Scholar 

  15. D. K. Lee,Phys. Rev. A7, 2162 (1973).

    Google Scholar 

  16. H. W. Jackson and E. Feenberg,Rev. Mod. Phys. 34, 686 (1962).

    Google Scholar 

  17. R. P. Feynman,Phys. Rev. 94, 262 (1954).

    Google Scholar 

  18. A. Bhattacharyya and C. W. Woo,Phys. Rev. Letters 28, 1320 (1972).

    Google Scholar 

  19. D. K. Lee,Phys. Letters 42A, 1 (1972).

    Google Scholar 

  20. N. N. Bogoliubov and D. N. Zubarev,Zh. Eksperim. i. Teor. Fiz. 28, 129 (1955) [English transl.,Soviet Phys.—JETP 1, 83 (1955)].

    Google Scholar 

  21. E. Meeron,Phys. Fluids 1, 139 (1958);J. Math. Phys. 1, 192 (1960).

    Google Scholar 

  22. T. Morita,Progr. Theoret. Phys. (Kyoto)20, 920 (1958);23, 829 (1960).

    Google Scholar 

  23. J. K. Percus and G. J. Yevick,Phys. Rev. 110, 1 (1958).

    Google Scholar 

  24. D. K. Lee and F. H. Ree,Phys. Rev. A7, 730 (1973).

    Google Scholar 

  25. D. K. Lee,Phys. Rev. A2, 278 (1970).

    Google Scholar 

  26. D. K. Lee,Phys. Rev. 187, 326 (1969).

    Google Scholar 

  27. R. P. Feynman and M. Cohen,Phys. Rev. 102, 1189 (1956).

    Google Scholar 

  28. D. G. Henshaw and A. D. B. Woods,Phys. Rev. 121, 1266 (1961).

    Google Scholar 

  29. R. A. Cowley and A. D. B. Woods,Can. J. Phys. 49, 177 (1971).

    Google Scholar 

  30. D. G. Henshaw,Phys. Rev. 119, 9 (1960).

    Google Scholar 

  31. W. L. Gordon, C. H. Shaw, and J. G. Daunt,Phys. Chem. Solids 5, 117 (1958).

    Google Scholar 

  32. E. K. Achter and L. Meyer,Phys. Rev. 188, 291 (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported in part by the University of Kansas General Research Fund under grant No. 3235-5038.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, D.K. Three-phonon vertex corrections to the excitation spectrum and liquid-structure function of liquid4He. J Low Temp Phys 12, 579–588 (1973). https://doi.org/10.1007/BF00654958

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00654958

Keywords

Navigation