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JETP Letters

, Volume 98, Issue 1, pp 33–37 | Cite as

Ground-state energy of quantum liquids

  • A. M. Dyugaev
  • P. D. Grigoriev
  • E. V. LebedevaEmail author
Condensed Matter
  • 61 Downloads

Abstract

The kinetic (K 4 0 (n) and K 3 0 (n)) and potential (V 4 0 (n) and V 3 0 (n)) energies of 4He and 3He atoms have been found from the law of corresponding states and the experimental data on the dependence of the ground-state energies E 4 0 (n) and E 3 0 (n) on the density of the isotopes 4He and 3He. In the approximation of structureless quantum liquid, the potential energies are equal, V 4 0 V 3 0 (n) = (n), and the kinetic energies are inversely proportional to the atomic mass, \(K_4^0 (n) = \frac{3} {4}K_3^0 (n)\). The potential energy given by the expression V 0 = 4E 4 0 − 3E 3 0 to a high accuracy is linear in the density n, which is associated with nearly an absence of short-range order in liquid helium. The kinetic energy of liquid 4He is given by the expression K 4 0 = 3(E 3 0 E 4 0 ), which agrees with the experimental data on neutron scattering in liquid 4He. The quantities K 4 0 (n) and K 3 0 (n) determine the scale of all thermodynamic characteristics in the temperature range where the effects of the particle statistics can be neglected.

Keywords

JETP Letter Ground State Energy Liquid Helium Atomic Mass Potential Energy Versus 
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.
    P. C. Hohenberg and P. M. Platzman, Phys. Rev. 152, 198 (1966).ADSCrossRefGoogle Scholar
  2. 2.
    V. F. Sears, Can. J. Phys. 59, 555 (1981).ADSCrossRefGoogle Scholar
  3. 3.
    J. de Boer, Physica 14, 139 (1948).ADSCrossRefGoogle Scholar
  4. 4.
    S. T. Belyaev, Sov. Phys. JETP 7, 299 (1958).zbMATHGoogle Scholar
  5. 5.
    V. A. Belyakov, Sov. Phys. JETP 13, 850 (1961).Google Scholar
  6. 6.
    C. Andreani, D. Colognesi, J. Mayers, et al., Adv. Phys. 54, 377 (2005).ADSCrossRefGoogle Scholar
  7. 7.
    H. R. Glyde, S. O. Diallo, R. T. Azuah, et al., Phys. Rev. B 84, 184506 (2011).ADSCrossRefGoogle Scholar
  8. 8.
    V. A. Khodel, J. W. Clark, V. R. Shaginyan, and M. V. Zverev, JETP Lett. 92, 532 (2010).ADSCrossRefGoogle Scholar
  9. 9.
    V. A. Khodel, J. W. Clark, and M. V. Zverev, Phys. At. Nucl. 74, 1237 (2011).CrossRefGoogle Scholar
  10. 10.
    J. W. Clark, V. A. Khodel, and M. V. Zverev, Phys. Rev. B 71, 012401 (2005).ADSCrossRefGoogle Scholar
  11. 11.
    V. A. Khodel, J. W. Clark, and M. V. Zverev, Phys. Rev. B 78, 075120 (2008).ADSCrossRefGoogle Scholar
  12. 12.
    C. Bauerle, Yu. V. Bunkov, A. S. Chen, et al., J. Low Temp. Phys. 110, 333 (1998).ADSCrossRefGoogle Scholar
  13. 13.
    C. Bauerle, J. Bossy, Yu. M. Bunkov, et al., J. Low Temp. Phys. 110, 345 (1998).ADSCrossRefGoogle Scholar
  14. 14.
    A. Casey, H. Patel, J. Nyeki, et al., Phys. Rev. Lett. 90, 115301 (2003).ADSCrossRefGoogle Scholar
  15. 15.
    A. M. Dyugaev, Sov. Phys. JETP 62, 703 (1985).Google Scholar
  16. 16.
    A. M. Dyugaev, JETP Lett. 42, 545 (1985); Sov. Phys. JETP 68, 480 (1989).ADSGoogle Scholar
  17. 17.
    A. M. Dyugaev, J. Low Temp. Phys. 78, 79 (1990).ADSCrossRefGoogle Scholar
  18. 18.
    F. K. Achter and L. Meyer, Phys. Rev. 188, 291 (1969).ADSCrossRefGoogle Scholar
  19. 19.
    W. E. Massey, Phys. Rev. 151, 153 (1966).ADSCrossRefGoogle Scholar
  20. 20.
    C. W. Woo, Phys. Rev. 151, 138 (1966).ADSCrossRefGoogle Scholar
  21. 21.
    R. de Bruynouboter and C. N. Yang, Physica B 144, 127 (1987).CrossRefGoogle Scholar
  22. 22.
    R. A. Aziz and R. K. Pathria, Phys. Rev. A 7, 809 (1973).ADSCrossRefGoogle Scholar
  23. 23.
    B. M. Abraham, Y. Eckstein, J. B. Ketterson, et al., Phys. Rev. A 1, 250 (1970).ADSCrossRefGoogle Scholar
  24. 24.
    R. W. Hill and O. V. Lounasmaa, Phil. Trans. R. Soc. London A 252, 357 (1960).ADSCrossRefGoogle Scholar
  25. 25.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1976; Pergamon, Oxford, 1980), p. 67.Google Scholar
  26. 26.
    H. R. Glyde, R. T. Azuah, and W. G. Stirling, Phys. Rev. B 62, 14337 (2000).ADSCrossRefGoogle Scholar
  27. 27.
    R. Senesi, C. Andreani, A. L. Fielding, et al., Phys. Rev. B 68, 214522 (2003).ADSCrossRefGoogle Scholar
  28. 28.
    R. Senesi, C. Andreani, D. Colognesi, et al., Phys. Rev. Lett. 86, 4584 (2001).ADSCrossRefGoogle Scholar
  29. 29.
    R. Dimeo, P. E. Sokol, R. T. Azuah, et al., Physica B 241, 497 (1976).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2013

Authors and Affiliations

  • A. M. Dyugaev
    • 1
    • 2
  • P. D. Grigoriev
    • 1
  • E. V. Lebedeva
    • 3
    Email author
  1. 1.Landau Institute of Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Max-Planck-Institut für Physik komplexer SystemeDresdenGermany
  3. 3.Institute of Solid State PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia

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