Thermodynamics of Metallic Helium

  • V. T. Shvets Odessa National Academy of Food Technologies
  • S. V. Kozytskiy Odessa National Maritime Academy
Keywords: liquid metallic helium, thermodynamic parameters, giant planets


The internal and free energies of liquid metallic helium are calculated for wide ranges of density and temperature, and the corresponding equation of state is obtained in the framework of perturbation theory. The electron-ion interaction potential is selected as a small parameter, and the calculations are carried out to the third order of smallness inclusive. Conduction electrons are considered in the random phase approximation with regard for the exchange interaction and correlations in the local field approximation. The hard-sphere model is used for the nuclear subsystem, the sphere diameter being the only parameter of the theory. The sphere diameter and the system density, at which helium transforms from the single- into double-ionized state are evaluated by analyzing the effective pair interaction between helium nuclei also in the third order of perturbation theory. The case of double-ionized helium atoms is considered. The third-order correction turns out substantial in all examined cases. The values obtained for thermodynamic parameters such as the density, temperature, and pressure fall within the ranges typical of the central regions of giant planets, which allows us to suppose the existence of metallic helium in the solar system.


  1. E.G. Maximov and Yu.T. Shilov, Usp. Fiz. Nauk 169, 1223 (1999).

  2. V.E. Fortov, Usp. Fiz. Nauk 177, 347 (2007).

  3. S.T. Weir, A.C. Mitchell, and W.J. Nellis, Phys. Rev. Lett. 76, 1860 (1996).

  4. V.E. Fortov, V.Ya. Ternovoi, S.V. Kvitov, V.B. Mintsev, D.N. Nikolaev, A.A. Pyaling, and A.S. Filimonov, Pis'ma Zh. Eksp. Teor. Fiz. 69, 874 (1999).

  5. V.Ya. Ternovoi, A.S. Filimonov, V.E. Fortov, S.V. Kvitov, D.N. Nikolaev, and A.A. Pyaling, Physica B 265, 6 (1999).

  6. M. Bastea, A.C. Mitchell, and W.J. Nellis, Phys. Rev. Lett. 86, 3108 (2001).

  7. R. Chau, A.C. Mitchell, R.W. Minich, and W.J. Nellis, Phys. Rev. Lett. 90, 245501 (2003).

  8. D.A. Young, A.K. McMahan, and M. Ross, Phys. Rev. B 24, 5119 (1981).

  9. A. Kietzmann, B. Holst, R. Redmer, M.P. Desjarfais, and T.R. Mattsson, Phys. Rev. Lett. 98, 190602 (2007).

  10. S.A. Kharallah and B. Militzer, Phys. Rev. Lett. 101, 106407 (2008).

  11. L. Stixrude and R. Jeanloz, Proc. Nat. Acad. Sci. USA 105, 11071 (2008).

  12. E.G. Brovman, Yu.M. Kagan, and A. Kholas, Zh. Eksp. `Teor. Fiz. 61, 2429 (1971).

  13. E.G. Brovman and Yu.M. Kagan, Usp. Fiz. Nauk 112, 369 (1974).

  14. D.J. Stevenson and N.W. Ashcroft, Phys. Rev. A 9, 782 (1974).

  15. V.T. Shvets, Zh. Eksp. Teor. Fiz. ` 131, 743 (2007).

  16. W.A. Harrison, Pseudopotentials in the Theory of Metals (Benjamin, New York, 1966).

  17. V.T. Shvets, Green's Function Method in the Theory of Metals (Latstar, Odessa, 2002) (in Ukrainian).

  18. I.A. Vakarchuk, Introduction to Many-Body Problem (I. Franko Lviv Nat. Univ., Lviv, 1999) (in Russian).

  19. W.H. Shih and D. Stroud, Phys. Rev. B 31, 3715 (1985).

  20. P. Lloyd and C.A. Shall, J. Phys. C 1, 1620 (1968).

  21. E.G. Brovman and Yu. Kagan, Zh. Eksp. Teor. Fiz. ` 63, 1937 (1972).

  22. E.G. Brovman and A. Kholas, Zh. Eksp. Teor. Fiz. ` 66, 1877 (1974).

  23. J. Hammerberg and N.W. Ashcroft, Phys. Rev. B 9, 3999 (1974).

  24. L. Ballentine and V. Heine, Philos. Mag. 9, 617 (1964).

  25. D.J.M. Geldart and S.H. Vosko, Can. J. Phys. 44, 2137 (1966).

  26. V.T. Shvets and E.V. Belov, Acta Phys. Pol. A 96, 741 (1999).

  27. V.T. Shvets, Phys. Metal. Metallogr. 89, 211 (2000).

  28. I.R. Yukhnovskii and M.F. Golovko, Statistical Theory of Classical Equilibrium Systems (Naukova Dumka, Kyiv, 1987) (in Russian).

  29. V.T. Shvets, S.V. Savenko, and Ye.K. Malinovskiy, Cond. Matter Phys. 9, 1 (2006).

  30. S.D. Kaim, N.P. Kovalenko, and E.V. Vasiliu, J. Phys. Stud. 1, 589 (1997).

  31. V.T. Shvets, Pis'ma Zh. Eksp. Teor. Fiz. 95, 34 (2012).

  32. V.T. Shvets, T.V. Shvets, and Ya.Ye. Rachynskiy, Ukr. J. Phys. 55, 251 (2010).

How to Cite
Shvets, V., & Kozytskiy, S. (2018). Thermodynamics of Metallic Helium. Ukrainian Journal of Physics, 58(5), 458.
Soft matter