Skip to main content
SpringerLink
Log in

Statistical theory of rarified gases in the coulomb model of substance: Adiabatic approximation and initial atoms

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

In the framework of the adiabatic approximation for a subsystem of nuclei with the average distance between them significantly exceeding the dimensions of the initial atom, we consider a nonrelativistic Coulomb system consisting of electrons and nuclei of one type for the temperature range where we can restrict ourself to using the ground state to describe the electron subsystem. We show that the equilibrium properties of such a system are equivalent to the thermodynamic properties of the one-component system of initial atoms interacting between themselves via a short-range potential that is the effective potential of the nucleus-nucleus interaction. In the framework of the applicability of Boltzmann statistics, we present quantum group expansions for the thermodynamic properties of a chemically reacting rarified gas that correspond to the method of initial atoms.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. Ebeling, W. D. Kraeft, and D. Kremp, Theory of Bound States and Ionization Equilibrium in Plasmas and Solids, Academie, Berlin (1976).

    Google Scholar 

  2. A. B. Kudryavtsev, R. F. Jameson, and W. Linert, The Law of Mass Action, Springer, Berlin (2001).

    Book  Google Scholar 

  3. V. E. Fortov, A. G. Khrapak, and I. T. Yakubov, Physics of Nonideal Plasma [in Russian], Fizmatlit, Moscow (2010).

    Google Scholar 

  4. W. D. Kraeft, D. Kremp, W. Ebeling, and G. Ropke, Quantum Statistics of Charged Particle Systems, Plenum, New York (1986).

    Book  Google Scholar 

  5. E. H. Lieb and R. Seiringer, The Stability of Matter in Quantum Mechanics, Camridge Univ. Press, Cambridge (2009).

    Book  MATH  Google Scholar 

  6. V. K. Gryaznov, I. L. Iosilevskiy, V. E. Fortov, A. N. Starostin, V. K. Roerich, V. A. Baturin, and S. V. Ayukov, Contrib. Plasma Phys., 53, 392–396 (2013).

    Article  ADS  Google Scholar 

  7. R. Redmer and G. Ropke, Contrib. Plasma Phys., 50, 970–985 (2010).

    Article  ADS  Google Scholar 

  8. V. S. Bobrov and S. A. Trigger, High Temperature, 49, 495–505 (2011).

    Article  Google Scholar 

  9. A. N. Starostin and V. C. Roerich, JETP, 100, 165–198.

  10. A. Alastuey, V. Ballenegger, F. Cornu, and P. A. Martin, J. Stat. Phys., 130, 1119–1176 (2008).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. A. Alastuey and V. Ballenegger, Contrib. Plasma Phys., 50, 46–53 (2010).

    Article  ADS  Google Scholar 

  12. Y. A. Omarbakiyeva, C. Fortmann, T. S. Ramazanov, and G. Röpke, Phys. Rev. E, 82, 026407 (2010).

    Article  ADS  Google Scholar 

  13. V. B. Bobrov, S. A. Trigger, and W. Ebeling, Europhys. Lett., 95, 25001 (2011).

    Article  ADS  Google Scholar 

  14. A. Alastuey and V. Ballenegger, Contrib. Plasma Phys., 52, 95–99 (2012).

    Article  ADS  Google Scholar 

  15. J. M. McMahon, M. A. Morales, C. Pierleoni, and D. M. Ceperley, Rev. Modern Phys., 84, 1607–1653 (2012).

    Article  ADS  Google Scholar 

  16. M. A. Morales, J. M. McMahon, C. Pierleoni, and D. M. Ceperley, Phys. Rev. Lett., 110, 065702 (2013); arXiv: 1303.6671v1 [cond-mat.mtrl-sci] (2013).

    Article  ADS  Google Scholar 

  17. C. A. Jiménez-Hoyos, T. M. Henderson, T. Tsuchimochi, and G. E. Scuseria, J. Chem. Phys., 136, 164109 (2012).

    Article  ADS  Google Scholar 

  18. P. Hohenberg and W. Kohn, Phys. Rev., 136, B864–B871 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  19. R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules, Oxford Univ. Press, New York (1989).

    Google Scholar 

  20. M. W. C. Dharma-Wardana and F. Perrot, Phys. Rev. A, 26, 2096–2104 (1982).

    Article  ADS  Google Scholar 

  21. F. Perrot and M. W. C. Dharma-Wardana, Phys. Rev. A, 29, 1378–1390 (1984).

    Article  ADS  Google Scholar 

  22. M. W. C. Dharma-Wardana, Phys. Rev. Lett., 101, 035002 (2008); arXiv:0804.2083v1 [physics.plasm-ph] (2008).

    Article  ADS  Google Scholar 

  23. G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti, Rev. Modern Phys., 78, 865–951 (2006).

    Article  ADS  Google Scholar 

  24. W. Nelson, P. Bokes, P. Rinke, and R. W. Godby, Phys. Rev. A, 75, 032505 (2007).

    Article  ADS  Google Scholar 

  25. K. Burke, J. Chem. Phys., 136, 150901 (2012); arXiv:1201.3679v1 [physics.chem-ph] (2012).

    Article  ADS  Google Scholar 

  26. V. B. Bobrov and S. A. Trigger, Europhys. Lett., 94, 33001 (2011); arXiv:1012.3241v1 [cond-mat.stat-mech] (2010).

    Article  ADS  Google Scholar 

  27. V. B. Bobrov, S. A. Trigger, and Yu. P. Vlasov, Europhys. Lett., 98, 53002 (2012).

    Article  ADS  Google Scholar 

  28. V. B. Bobrov and S. A. Trigger, JETP, 116, 635–640 (2013).

    Article  ADS  Google Scholar 

  29. K. Pernal, Phys. Rev. Lett., 94, 233002 (2005).

    Article  ADS  Google Scholar 

  30. K. Pernal, Phys. Rev. A, 81, 052511 (2010).

    Article  ADS  Google Scholar 

  31. N. N. Lathiotakis, N. I. Gidopoulos, and N. Helbig, J. Chem. Phys., 132, 084105 (2010).

    Article  ADS  Google Scholar 

  32. V. B. Bobrov, S. A. Trigger, and Yu. P. Vlasov, Phys. Rev. A, 83, 034501 (2011).

    Article  ADS  Google Scholar 

  33. D. A. Kirzhnits, Field Theoretical Methods in Many-Body Theory [in Russian], Gosatomizdat, Moscow (1963); English transl. (Intl. Ser. Monogr. Nat. Philos., Vol. 8), Pergamon, Oxford (1967).

    Google Scholar 

  34. V. B. Bobrov and S. A. Trigger, Phys. Lett. A, 374, 4188–4192 (2010).

    Article  MATH  ADS  Google Scholar 

  35. A. M. Semenov, “Method of initial atoms in the statistical thermodynamics of chemically reacting gases [in Russian],” in: Mathematical Methods of Chemical Thermodynamics, Nauka, Novosibirsk (1982), pp. 88–99.

    Google Scholar 

  36. E. G. Maksimov and A. E. Karakozov, Phys. Usp., 51, 535–549 (2008).

    Article  ADS  Google Scholar 

  37. V. L. Bonch-Bruevich, I. P. Zvyagin, R. Keiper, A. G. Mironov, R. Enderlein, and B. Esser, Electronic Theory of Disordered Semiconductors [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  38. V. B. Bobrov and S. A. Trigger, Solid State Commun., 56, 29–34 (1985).

    Article  ADS  Google Scholar 

  39. L. D. Landau and E. M. Lifshitz, Statistical Physics [in Russian] (Vol. 5 in Course of Theoretical Physics), Nauka, Moscow (1976); English transl. prev. ed., Pergamon, Oxford (1968).

    Google Scholar 

  40. A. Messiah, Quantum Mechanics, Vol. 2, Wiley, New York (1961).

    Google Scholar 

  41. B. Kahn and G. E. Uhlenbeck, Phys., 5, 399–416 (1938).

    ADS  Google Scholar 

  42. K. Huang, Statistical Mechanics, Wiley, New York (1963).

    Google Scholar 

  43. T. L. Hill, Statistical Mechanics, McGraw-Hill, New York (1956).

    MATH  Google Scholar 

  44. B. V. Zelener, V. I. Mika, A. M. Semenov, and V. S. Filinov, Sov. Phys. Dokl., 22, 20 (1977).

    ADS  Google Scholar 

  45. W. Cencek, M. Przybytek, J. Komasa, J. B. Mehl, B. Jeziorski, and K. Szalewicz, J. Chem. Phys., 136, 224303 (2012).

    Article  ADS  Google Scholar 

  46. E. S. Yakub, “Numerical methods of the statistical thermodynamics of reacting liquids [in Russian],” in: Reviews of the Thermophysical Properties of Substances, Vol. 5(43), IVTAN, Moscow (1983), pp. 38–99.

    Google Scholar 

  47. E. Beth and G. E. Uhlenbeck, Phys., 4, 915–924 (1937).

    MATH  ADS  Google Scholar 

  48. G. Garheroglio, M. R. Moldover, and A. H. Harvey, J. Res. Natl. Inst. Stand. Technol., 116, 729–742 (2011).

    Article  Google Scholar 

  49. R. T. Jacobsen, J. W. Leachman, S. G. Penoncello, and E. W. Lemmon, Internat. J. Thermophys., 28, 758–772 (2007).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Joint Institute for High Temperatures, RAS, Moscow, Russia

    V. B. Bobrov

  2. Moscow Power Engineering Institute, Moscow, Russia

    V. B. Bobrov

Authors
  1. V. B. Bobrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. B. Bobrov.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 178, No. 3, pp. 433–448, March, 2014.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bobrov, V.B. Statistical theory of rarified gases in the coulomb model of substance: Adiabatic approximation and initial atoms. Theor Math Phys 178, 374–386 (2014). https://doi.org/10.1007/s11232-014-0149-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-014-0149-y

Keywords

Search

Navigation