Skip to main content
SpringerLink
Log in

The Influence of Pauli Blocking Effects on the Mott Transition in Dense Hydrogen

  • Chapter
  • First Online:
Metal-to-Nonmetal Transitions

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 132))

Abstract

We investigate the effects of Pauli blocking on the properties of hydrogen at high pressures. In this region recent experiments have shown a transition from insulating behavior to metal-like conductivity. To describe this transition, several effects have to be taken into account, an important one is the quantum character of the electrons. As electron states can only be occupied once (Pauli blocking), atomic states need more phase space than available at high densities, and bound states disintegrate subsequently (Mott effect). We calculate the energy shifts due to Pauli blocking and discuss the Mott effect solving an effective Schrödinger equation for strongly correlated systems. Additionally, we include corrections due to polarization effects. The ionization equilibrium is treated on the basis of an advanced chemical approach based on the assumption that the system is a gas-like mixture of chemical species. We calculate the Pauli shifts by variational methods and discuss corrections due to polarization. Results for the ionization equilibrium in the region 5,000 < T[K] < 15,000, 0. 1 < ρ[g cm−3] < 1 are presented, where the transition from a neutral hydrogen gas to a highly ionized plasma occurs. We show that the transition to a highly conducting state is softer than predicted in earlier work.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. P. Wigner, H.B. Huntington, J. Chem. Phys. 3, 764 (1935)

    Article  ADS  Google Scholar 

  2. A.A Abrikosov, L.P. Gorkov, L.P. Dsyaloshinsky, Methods of Quantum Field Theory in Statistical Physics (in Russian, Moscow, 1962)

    Google Scholar 

  3. G.I. Kerley, Los Alamos Scientific Laboratory Report, LA–4776, January 1972

    Google Scholar 

  4. E.G. Brovman, Yu. Kagan, A. Kholas, Fiz. Tverd. Tela 12, 1001 (1970); E.G. Brovman, Yu. Kagan, Usp. Fiz. Nauk 112, 369 (1974)

    Google Scholar 

  5. W. Ebeling, W.D. Kraeft, D. Kremp, Theory of Bound States and Ionization Equilibrium (Akademie Verlag, Berlin, 1976)

    Google Scholar 

  6. W. Ebeling, Physica 130 A, 587 (1985)

    ADS  Google Scholar 

  7. W. Ebeling, W. Richert, Phys. Stat. Sol. B 128, 467 (1985); Phys. Lett. A 108, 80 (1985); Contrib. Plasma Phys. 25, 1 (1985)

    Article  ADS  Google Scholar 

  8. W.D. Kraeft, D. Kremp, W. Ebeling, G. Röpke, Quantum Statistics of Charged Particle Systems (Plenum Press, New York, 1986)

    Google Scholar 

  9. D. Saumon, G. Chabrier, Phys. Rev. Lett. 62, 2397 (1989); Phys. Rev A 46, 2084 (1992)

    Article  ADS  Google Scholar 

  10. D. Kremp, M. Schlanges, W.D. Kraeft, Quantum statistics of nonideal plasmas (Springer, Berlin, 2005)

    Google Scholar 

  11. L.B. Da Silva, P. Celliers, G.W. Collins, K.S. Budil, N.C. Holmes, T.W. Barbee Jr., B.A. Hammel, J.D. Kilkenny, R.J. Wallace, M. Ross, R. Cauble, A. Ng, G. Chiu, Phys. Rev. Lett. 78, 483 (1997)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. G.W. Collins, L.B. Da Silva, P. Celliers, D.M. Gold, M.E. Foord, R.J. Wallace, A. Ng, S.V. Weber, K.S. Budil, R. Cauble, Science 281, 1178 (1998)

    Article  ADS  Google Scholar 

  14. M. Mochalov, Conf. Strongly Coupled Coulomb Systems, Moscow, 2005; V. Fortov, M. Mochalov et al., Phys. Rev. Lett. 99, 185001 (2007)

    Article  ADS  Google Scholar 

  15. N. Nettelmann, B. Holst, A. Kietzmann, M. French, R. Redmer, D. Blaschke, Astrophys. J. 683, 1217 (2008)

    Article  ADS  Google Scholar 

  16. D.G. Hummer, D. Mihalas, Astrophys. J. 331, 794 (1988); D. Mihalas, W. Däppen, D.G. Hummer, Astrophys. J. 331, 815 (1988)

    Article  ADS  Google Scholar 

  17. S. Atzeni, J. Meyer-ter-Vehn, The Physics of Inertial Fusion (Oxford Science Publication, Oxford, 2004)

    Book  Google Scholar 

  18. D. Beule, W. Ebeling, A. Förster, H. Juranek, S. Nagel, R. Redmer, G. Röpke, Phys. Rev. B 59, 14–177 (1999)

    Article  Google Scholar 

  19. D. Beule, W. Ebeling, A. Förster, H. Juranek, R. Redmer, G. Röpke, Contrib. Plasma Phys. 39, 21 (1999)

    Article  ADS  Google Scholar 

  20. W. Ebeling, H. Hache, H. Juranek, R. Redmer, G. Röpke, Contr. Plasma Phys. 45, 160 (2005)

    Article  ADS  Google Scholar 

  21. E. Beth, G.E. Uhlenbeck, Physica 3, 729 (1936); 4, 915 (1937)

    Article  MATH  Google Scholar 

  22. M. Schmidt, G. Röpke, H. Schulz, Ann. Phys. 202, 57 (1990)

    Article  ADS  Google Scholar 

  23. G. Röpke, K. Kilimann, D. Kremp, W.D. Kraeft, Phys. Lett. 68A, 329 (1978)

    ADS  Google Scholar 

  24. G. Röpke, K. Kilimann, D. Kremp, W.D. Kraeft, R. Zimmermann, phys. stat. sol. B 88, K59 (1978); R. Zimmermann, K. Kilimann, D. Kremp, W.D. Kraeft, G. Röpke, phys. stat. sol. B 90, 175 (1978)

    Article  ADS  Google Scholar 

  25. R. Redmer, Phys. Rep. 282, 35 (1997)

    Article  ADS  Google Scholar 

  26. V.E. Fortov, I.T. Yakubov, Physics of Nonideal Plasmas (Hemisphere Publications Corporation, New York, 1990)

    Google Scholar 

  27. H.C. Graboske, D.J. Harwood, F.J. Roges, Phys. Rev. 186, 210 (1969)

    Article  ADS  Google Scholar 

  28. G. Röpke, T. Seifert, H. Stolz, R. Zimmermann, Phys. Stat. Sol. B 100, 215 (1980); G. Röpke, M. Schmidt, L. Münchow, H. Schulz, Nucl. Phys. A 399, 587 (1983); G. Röpke, in Aggregation Phenomena in Complex Systems, ed. by J. Schmelzer et al., (Wiley-VCH, Weinheim, New York, 1999)

    Article  ADS  Google Scholar 

  29. W. Ebeling, K. Kilimann, Z. Naturforschung 44A, 519 (1989)

    Google Scholar 

  30. S. Arndt, W.D. Kraeft, J. Seidel, phys. stat. sol. B 194, 601 (1996)

    Article  ADS  Google Scholar 

  31. W. Stolzmann, W. Ebeling, Phys. Lett. A 248, 242 (1998)

    Article  ADS  Google Scholar 

  32. A. Bunker, S. Nagel, R. Redmer, G. Röpke, Phys. Rev. B 56, 3094 (1997); Contrib. Plasma Phys. 37, 115 (1997)

    Article  ADS  Google Scholar 

  33. H. Juranek, R. Redmer, J. Chem. Phys. 112, 3780 (2000)

    Article  ADS  Google Scholar 

  34. D. Beule, W. Ebeling, A. Förster, H. Juranek, R. Redmer, G. Röpke,Phys. Rev. E 63, 060202 (2001)

    Article  ADS  Google Scholar 

  35. N.F. Carnahan, K.E. Starling, J. Chem. Phys. 51, 635 (1969)

    Article  ADS  Google Scholar 

  36. W. Ebeling, A. Förster, V.E. Fortov, V.K. Gryaznov, A. Ya. Polishchuk, Thermophysical Properties of Hot Dense Plasmas (Teubner Verlag, Stuttgart and Leipzig, 1991)

    Google Scholar 

  37. W. Ebeling, H. Hache, M. Spahn, Eur. Phys. D 23, 265 (2003)

    Article  ADS  Google Scholar 

  38. D. Beule, W. Ebeling, A. Förster, Physica A 241, 719 (1997)

    Article  ADS  Google Scholar 

  39. W.J. Nellis, A.C. Mitchell, M. van Thiel, G.J. Devine, R.J. Trainor, N. Brown, J. Chem. Phys. 79, 1480 (1983)

    Article  ADS  Google Scholar 

  40. N.C. Holmes, M. Ross, W.J. Nellis, Phys. Rev. B 52, 15–835 (1995)

    Article  Google Scholar 

  41. M. Ross, Phys. Rev. B 58, 669 (1998)

    Article  ADS  Google Scholar 

  42. H. Shimizu, E.M. Brody, H.K. Mao, P.M. Bell, Phys. Rev. Lett. 47, 128 (1981)

    Article  ADS  Google Scholar 

  43. T.J. Lenosky, J.D. Kress, L.A. Collins, Phys. Rev. B 56, 5164 (1997)

    Article  ADS  Google Scholar 

  44. F.J. Rogers, D.A. Young, Phys. Rev. E 56, 5876 (1997)

    Article  ADS  Google Scholar 

  45. Z. Zinamon, Y. Rosenfeld, Phys. Rev. Lett. 81, 4668 (1998)

    Article  ADS  Google Scholar 

  46. J.D. Johnson, Phys. Rev. E 59, 3727 (1999)

    Article  ADS  Google Scholar 

  47. M. Ross, Phys. Rev. B 54, 9589 (1996)

    Article  ADS  Google Scholar 

  48. W.J. Nellis, S.T. Weir, A.C. Mitchell, Phys. Rev. B 59, 3434 (1999)

    Article  ADS  Google Scholar 

  49. L.D. Landau, E.M. Lifschitz, Lehrbuch der theoretischen Physik, Bd. VI: Hydrodynamik (Akademie Verlag, Berlin, 1991)

    Google Scholar 

  50. R. Redmer, G. Röpke, D. Beule, W. Ebeling, Contrib. Plasma Phys. 39, 25 (1999)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Physik, Humboldt-Universität Berlin, 12489, Berlin, Germany

    W. Ebeling

  2. Institute for Theoretical Physics, University of Wroclaw, 50-204, Wroclaw, Poland

    D. Blaschke

  3. Institut für Physik, Universität Rostock, 18051, Rostock, Germany

    R. Redmer, H. Reinholz & G. Röpke

Authors
  1. W. Ebeling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Blaschke
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Redmer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Reinholz
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. Röpke
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. Ebeling .

Editor information

Editors and Affiliations

  1. Inst. Physik, Universität Rostock, Rostock, 18051, Germany

    Ronald Redmer

  2. FB Physikalische Chemie, Universität Marburg, Hans-Meerwein-Str., Marburg, 35032, Germany

    Friedrich Hensel

  3. Inst. Physik, Universität Rostock, Rostock, 18051, Germany

    Bastian Holst

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ebeling, W., Blaschke, D., Redmer, R., Reinholz, H., Röpke, G. (2010). The Influence of Pauli Blocking Effects on the Mott Transition in Dense Hydrogen. In: Redmer, R., Hensel, F., Holst, B. (eds) Metal-to-Nonmetal Transitions. Springer Series in Materials Science, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03953-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03953-9_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03952-2

  • Online ISBN: 978-3-642-03953-9

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation