Journal of Statistical Physics

, Volume 60, Issue 5–6, pp 619–637

Ionization equilibrium in the electron-proton gas

  • N. Macris
  • Ph. A. Martin
Articles

Abstract

Using Fefferman's analysis of the quantum electron-proton gas, we give a rigorous proof of ionization equilibrium in this system. Ionization equilibrium phases are obtained as low-density and low-temperature limits, letting the chemical potentialμ(T) approach the ground-state energy of the hydrogen atom as the temperatureT tends to zero. The rate of ionization is determined by the slope ofμ(T) atT=0 and is correctly given by the Saha formula. We also discuss a simpler model where a single quantum particle interacts with a classical gas of hard spheres.

Key words

Ionization equilibrium Saha formula Coulomb systems dilute gases 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. Fefferman,Rev. Math. Iberoam. 1:1 (1985).Google Scholar
  2. 2.
    C. Fefferman,Commun. Pure Appl. Math. 34:67 (1986).Google Scholar
  3. 3.
    J. L. Lebowitz and R. E. Penna,J. Chem. Phys. 59:1362 (1973).Google Scholar
  4. 4.
    W. Hughes,J. Stat. Phys. 41:975 (1985).Google Scholar
  5. 5.
    L. Landau and L. Lifschitz,Statistical Physics, 3rd ed., Part 1, (Pergamon Press, 1976).Google Scholar
  6. 6.
    E. H. Lieb and J. L. Lebowitz,Adv. Math. 9:316 (1972).Google Scholar
  7. 7.
    J. G. Conlon, E. H. Lieb, and H.-T. Yau,Commun. Math. Phys. 125:153 (1989).Google Scholar
  8. 8.
    N. Macris, Ph. A. Martin, and J. V. Pulé, A statistical mechanical model for equilibrium ionization, Preprint, Ecole Polytechnique de Lausanne (1989),Helv. Phys. Acta, to appear.Google Scholar
  9. 9.
    N. Macris, “Equilibre de ionisation en Mécanique Statistique,” Ph. D. dissertation, Ecole Polytechnique Fédérale de Lausanne (1990), unpublished.Google Scholar
  10. 10.
    H. P. Baltes and E. R. Hilf,Spectra of Finite Systems (Bibliographisches Institut Mannheim, 1976).Google Scholar
  11. 11.
    B. Simon,Functional Integration and Quantum Physics (Academic Press, 1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • N. Macris
    • 1
  • Ph. A. Martin
    • 1
  1. 1.Institut de Physique ThéoriqueEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

Personalised recommendations