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The European Physical Journal D

, Volume 61, Issue 1, pp 117–130 | Cite as

Static and dynamic structure factors with account of the ion structure for high-temperature alkali and alkaline earth plasmas*

  • S. P. SadykovaEmail author
  • W. Ebeling
  • I. M. Tkachenko
Article

Abstract.

The electron-electron, electron-ion, ion-ion and charge-charge static structure factors are calculated for alkali (at T = 30 000 K, 60 000 K, n e = 0.7 × 1021 ÷ 1.1 × 1022 cm-3) and Be2+ (at T = 20 eV, n e = 2.5 × 1023 cm-3) plasmas using the method described by Gregori et al. The dynamic structure factors for alkali plasmas are calculated at T = 30 000 K, n e = 1.74 × 1020, 1.11 × 1022 cm-3 using the method of moments developed by Adamjan et al. In both methods the screened Hellmann-Gurskii-Krasko potential, obtained on the basis of Bogolyubov's method, has been used taking into account not only the quantum-mechanical effects but also the repulsion due to the Pauli exclusion principle. The repulsive part of the Hellmann-Gurskii-Krasko (HGK) potential reflects important features of the ion structure. Our results on the static structure factors for Be2+ plasma deviate from the data obtained by Gregori et al., while our dynamic structure factors are in a reasonable agreement with those of Adamyan et al.: at higher values of k and with increasing k the curves damp down while at lower values of k, and especially at higher electron coupling, we observe sharp peaks also reported in the mentioned work. For lower electron coupling the dynamic structure factors of Li+, Na+, K+, Rb+ and Cs+ do not differ while at higher electron coupling these curves split. As the number of shell electrons increases from Li+ to Cs+ the curves shift in the direction of low absolute value of ω and their heights diminish. We conclude that the short range forces, which we take into account by means of the HGK model potential, which deviates from the Coulomb and Deutsch ones, influence the static and dynamic structure factors significantly.

Keywords

Soft Core Pauli Exclusion Principle Dynamic Structure Factor Static Structure Factor Short Range Force 
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.
    G. Gregori, O.L. Landen, S.H. Glenzer, Phys. Rev. E 74, 026402 (2006) CrossRefADSGoogle Scholar
  2. 2.
    G. Gregori, A. Ravasio, A. Höll, S.H. Glenzer, S.J. Rose, High Energy Density Physics 3, 99 (2007) CrossRefADSGoogle Scholar
  3. 3.
    V.M. Adamyan, I.M. Tkachenko, Teplofiz. Vys. Temp. 21, 417 (1983) [High Temp. (USA) 21, 307 (1983)] ADSGoogle Scholar
  4. 4.
    V.M. Adamyan, T. Meyer, I.M. Tkachenko, Fiz. Plazmy 11, 826 (1985) [Sov. J. Plasma Phys. 11, 481 (1985)] Google Scholar
  5. 5.
    S.V. Adamjan, I.M. Tkachenko, J.L. Muñoz-Cobo, G. Verdú Martín, Phys. Rev. E 48, 2067 (1993) CrossRefADSGoogle Scholar
  6. 6.
    V.M. Adamyan, I.M. Tkachenko, Contrib. Plasma Phys. 43, 252 (2003) CrossRefADSGoogle Scholar
  7. 7.
    S. Sadykova, W. Ebeling, I. Valuev, I. Sokolov, Contrib. Plasma Phys. 49, 76 (2009) CrossRefADSGoogle Scholar
  8. 8.
    M.J. Rosseinsky, K. Prassides, Nature 464, 39 (2010) CrossRefADSGoogle Scholar
  9. 9.
    Physics and Chemistry of Alkali Metal Adsorption, edited by H.P. Bonzel, A.M. Bradshaw, G. Ertl (Elsevier, Amsterdam, 1989), Materials Science Monographs, Vol. 57 Google Scholar
  10. 10.
    A.N. Klyucharev, N.N. Bezuglov, A.A. Matveev, A.A. Mihajlov, Lj.M. Ignjatović, M.S. Dimitrijević, New Astron. Rev. 51, 547 (2007) CrossRefADSGoogle Scholar
  11. 11.
    F. Hensel, Liquid Metals, edited by R. Evans, D.A. Greenwood, IOP Conf. Ser. No. 30 (IPPS, London, 1977) Google Scholar
  12. 12.
    F. Hensel, S. Juengst, F. Noll, R. Winter, In Localisation and Metal Insulator Transitions, edited by D. Adler, H. Fritsche (Plenum Press, New York, 1985) Google Scholar
  13. 13.
    N.F. Mott, Metal-Insulator Transitions (Taylor and Francis, London, 1974) Google Scholar
  14. 14.
    H. Hess, Physics of nonideal plasmas, edited by W. Ebeling, A. Foerster, R. Radtke, B.G. Teubner (Leipzig, 1992) Google Scholar
  15. 15.
    V. Sizyuk, A. Hassanein, T. Sizyuk, J. Appl. Phys. 100, 103106 (2006) CrossRefADSGoogle Scholar
  16. 16.
    S. Sadykova, W. Ebeling, I. Valuev, I. Sokolov, Contrib. Plasma Phys. 49, 388 (2009) CrossRefADSGoogle Scholar
  17. 17.
    H. Ebert, Physikalisches Taschenbuch (F. Vieweg & Sohn, Braunschweig, 1967) Google Scholar
  18. 18.
    S.H. Glenzer, G. Gregori, R.W. Lee, F.J. Rogers, S.W. Pollaine, O.L. Landen, Phys. Rev. Lett. 90, 175002 (2003) CrossRefADSGoogle Scholar
  19. 19.
    G. Gregori, S.H. Glenzer, H.-K. Chung, D.H. Froula, R.W. Lee, N.B. Meezan, J.D. Moody, C. Niemann, O.L. Landen, B. Holst, R. Redmer, S.P. Regan, H. Sawada, J. Quant. Spectrosc. Radiat. Transfer 99, 225237 (2006) CrossRefGoogle Scholar
  20. 20.
    D. Riley, N.C. Woolsey, D. McSherry, I. Weaver, A. Djaoui, E. Nardi, Phys. Rev. Lett. 84, 1704 (2000) CrossRefADSGoogle Scholar
  21. 21.
    S.H. Glenzer, Phys. Rev. Lett. 98, 065002 (2007) CrossRefADSGoogle Scholar
  22. 22.
    J. Sheffield, Plasma Scattering of Electromagnetic Radiation (Academic Press, New York, 1975) Google Scholar
  23. 23.
    A. Höll, Th. Bornath, L. Cao, T. Döppner, S. Düsterer, E. Föster, C. Fortmann, S.H. Glenzer, G. Gregori, T. Laarmann, K.-H. Meiwes-Broer, A. Przystawik, P. Radcliffe, R. Redmer, H. Reinholz, G. Röpke, R. Thiele, J. Tiggesbäumker, S. Toleikis, N.X. Truong, T. Tschentscher, I. Ushmann, U. Zastrau, High Energy Density Phys. 3, 120 (2007) CrossRefADSGoogle Scholar
  24. 24.
    Yu.V. Arkhipov, A. Askaruly, D. Ballester, A.E. Davletov, G.M. Meirkhanova, I.M. Tkachenko, Phys. Rev. E 76, 026403 (2007) CrossRefADSGoogle Scholar
  25. 25.
    Yu.V. Arkhipov, A. Askaruly, D. Ballester, A.E. Davletov, I.M. Tkachenko, G. Zwicknagel, Phys. Rev. E 81, 026402 (2010) CrossRefADSGoogle Scholar
  26. 26.
    J.P. Hansen, I.R. Mc. Donald, Phys. Rev. A 23, 2041 (1981) CrossRefADSGoogle Scholar
  27. 27.
    J.P. Hansen, E.L. Polock, I.R. McDonald, Phys. Rev. Lett. 32, 277 (1974) CrossRefADSGoogle Scholar
  28. 28.
    V. Schwarz, B. Holst, T. Bornath, C. Fortmann, W-D. Kraeft, R. Thiele, R. Redmer, G. Gregori, H. Ja Leed, T. Döppner, S.H. Glenzer, High Energy Density Phys. 5, 1 (2009) CrossRefGoogle Scholar
  29. 29.
    D.O. Gericke, K. Wünsch, J. Vorberger, Nucl. Instrum. Methods Phys. Res. A 606, 142 (2009) CrossRefADSGoogle Scholar
  30. 30.
    B. Bernu, D. Ceperley, Quantum Monte Carlo Methods in Physics and Chemistry, edited by M.P. Nightingale, C. Umrigar (Kluwer Academic Publishers, Boston, 1999), NATO ASI Series, Series C, Mathematical and Physical Sciences, Vol. C-525 Google Scholar
  31. 31.
    G. Kelbg, Ann. Physik 13 354 (1964) Google Scholar
  32. 32.
    C. Deutsch, Phys. Lett. A 60, 317 (1977) CrossRefADSGoogle Scholar
  33. 33.
    H. Minoo, M.M. Gombert, C. Deutsch, Phys. Rev. A 23, 924 (1981) CrossRefADSGoogle Scholar
  34. 34.
    W. Ebeling, G.E. Norman, A.A. Valuev, I. Valuev, Contrib. Plasma Phys. 39, 61 (1999) CrossRefADSGoogle Scholar
  35. 35.
    A.V. Filinov, M. Bonitz, W. Ebeling, J. Phys. A. 36, 5957 (2003) zbMATHCrossRefADSGoogle Scholar
  36. 36.
    H. Hellmann, J. Chem. Phys. 3, 61 (1935) CrossRefADSGoogle Scholar
  37. 37.
    H. Hellmann, Acta Fizicochem. USSR 1, 913 (1935) Google Scholar
  38. 38.
    H. Hellmann, Acta Fizicochem. USSR 4, 225 (1936) Google Scholar
  39. 39.
    H. Hellmann, W. Kassatotschkin, Acta Fizicochem. USSR 5, 23 (1936) Google Scholar
  40. 40.
    W.A. Harrison, Pseudopotentials in the Theory of Metals (Benjamin, New York, 1966) Google Scholar
  41. 41.
    V. Heine, M.L. Cohen, D. Weaire, Psevdopotenzcial'naya Teoriya (Mir, Moskva, 1973) Google Scholar
  42. 42.
    V. Heine, The pseudopotential concept, edited by H. Ehrenreich, F. Seitz, D. Turnbull, Solid State Physics 24, 1 (Academic, New York 1970) Google Scholar
  43. 43.
    G.L. Krasko, Z.A. Gurskii, JETP Lett. 9, 363 (1969) ADSGoogle Scholar
  44. 44.
    W. Ebeling, W.-D. Kraeft, D. Kremp, Theory of Bound State and Ionization Equilibrium in Plasmas and Solids (Akademie-Verlag, Berlin, 1976) Google Scholar
  45. 45.
    W. Zimdahl, W. Ebeling, Ann. Phys. (Leipzig) 34, 9 (1977) ADSGoogle Scholar
  46. 46.
    W. Ebeling, C.-V. Meister, R. Saendig, 13 ICPIG (Berlin, 1977) 725 Google Scholar
  47. 47.
    W. Ebeling, C.V. Meister, R. Saendig, W.-D. Kraeft, Ann. Phys. 491, 321 (1979) CrossRefGoogle Scholar
  48. 48.
    N.N. Bogolyubov, Dynamical Theory Problems in Statistical Physics (in Russian) (GITTL, Moscow, 1946) Google Scholar
  49. 49.
    N.N. Bogolyubov, Studies in Statistical Mechanics, Engl. Transl., edited by J. De Boer, G.E. Uhlenbeck (North-Holland, Amsterdam, 1962) Google Scholar
  50. 50.
    H. Falkenhagen, Theorie der Elektrolyte (S. Hirzel Verlag, Leipzig, 1971), p. 369 Google Scholar
  51. 51.
    Yu.V. Arkhipov, F.B. Baimbetov, A.E. Davletov, Eur. Phys. J. D 8, 299 (2000) CrossRefADSGoogle Scholar
  52. 52.
    P. Seuferling, J. Vogel, C. Toepffer, Phys. Rev. A 40, 323 (1989) CrossRefADSGoogle Scholar
  53. 53.
    L. Szasz, Pseudopotential Theory of Atoms and Molecules (Wiley-Intersc., New York, 1985) Google Scholar
  54. 54.
    W.H.E. Schwarz, Acta Phys. Hung. 27, 391 (1969) CrossRefGoogle Scholar
  55. 55.
    W.H.E. Schwarz, Theor. Chim. Acta 11, 307 (1968) CrossRefGoogle Scholar
  56. 56.
    N.P. Kovalenko, Yu.P. Krasnyj, U. Krey, Physics of Amorphous Metalls (Wiley-VCH, Weinheim, 2001) Google Scholar
  57. 57.
    Z.A. Gurski, G.L. Krasko, Doklady Akademii Nauk SSSR (in Russian) 197, 810 (1971) Google Scholar
  58. 58.
    C. Fiolhais, J.P. Perdew, S.Q. Armster, J.M. MacLaren, Phys. Rev. B 51, 14001 (1995) CrossRefADSGoogle Scholar
  59. 59.
    S.S. Dalgic, S. Dalgic, G. Tezgor, Phys. Chem. Liq. 40, 539, (2002) Google Scholar
  60. 60.
    E.M. Apfelbaum, Phys. Chem. Liq., 48, 534 (2010) Google Scholar
  61. 61.
    Yu.V. Arkhipov, A.E. Davletov, Phys. Lett. A 247, 339 (1998) CrossRefADSGoogle Scholar
  62. 62.
    W. Ebeling, J. Ortner, Physica Scripta T 75, 93 (1998) CrossRefADSGoogle Scholar
  63. 63.
    J. Ortner, F. Schautz, W. Ebeling, Phys. Rev. E 56, 4665 (1997) CrossRefADSGoogle Scholar
  64. 64.
    N.I. Akhieser, The classical Moment Problem (Oliver and Boyd, London, 1965) Google Scholar
  65. 65.
    M.G. Krein, A.A. Nudel'man, The Markov Moment Problem and External Problems (American Mathematical Society, Translations, New York, 1977) Google Scholar
  66. 66.
    M.J. Corbatón, I.M. Tkachenko, Int. Conference on Strongly Coupled Coulomb Systems (SCCS2008), Camerino, Italy, July-August, 2008, Book of Abstracts, p. 90 Google Scholar
  67. 67.
    V.M. Adamyan, A.A. Mihajlov, N.M. Sakan, V.A. Srećković, I.M. Tkachenko, J. Phys. A: Math. Theor. 42, 214005 (2009) CrossRefADSGoogle Scholar
  68. 68.
    S. Ichimaru, Statistical Plasma Physics, Vol. I: Basic Principles (Addison-Wesley, Redwood City, 1992) Google Scholar
  69. 69.
    W. Ebeling, A. Foerster, W. Richert, H. Hess, Physics A 150, 159 (1988) CrossRefADSGoogle Scholar
  70. 70.
    H. Wagenknecht, W. Ebeling, A. Förster, Contrib. Plasma Phys. 41, 15 (2001) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Institut für Physik, Humboldt Universitat zu BerlinBerlinGermany
  2. 2.Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de ValenciaValenciaSpain

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