Il Nuovo Cimento D

, Volume 14, Issue 9, pp 873–880 | Cite as

A nonlinear sum rule for atomic hydrogen

  • S. Scandolo
  • F. Bassani


A sum rule for the nonlinear absorption of a probe beam induced by an external light beam is derived for the H atom. Numerical calculations are carried out using the pseudostate summation method and the consistency of the calculation is verified by comparing the length and the velocity gauge. The results confirm the validity of the pseudostate summation method in perturbation theory and give a measure of the strength of nonlinear effects in atomic hydrogen. They are shown to increase by orders of magnitude with increasing the frequency of the external beam. Asymmetries in the nonlinear absorption are expected, with larger negative contributions on the high-frequency side of the spectrum.

PACS 42.65.Bp

General theory 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F. Bassani andM. Altarelli:Interaction of radiation with condensed matter, inHandbook of Synchrotron Radiation, edited byE. E. Koch, Vol. 1a (North-Holland, Amsterdam, 1983); see alsoJ. D. Jackson,Classical Electrodynamics (J. Wiley & Sons, New York, N.Y., 1975), Chapt. 7.Google Scholar
  2. [2]
    F. Bassani andS. Scandolo:Phys. Rev. B,44, 8446 (1991).CrossRefADSGoogle Scholar
  3. [3]
    See for instance:H. A. Bethe andE. E. Salpeter:Quantum Mechanics of One and Two Electron Atoms (Springer-Verlag, Berlin, 1957), sect. 61.Google Scholar
  4. [4]
    S. Scandolo andF. Bassani:Phys. Rev. B, to be published (1992).Google Scholar
  5. [5]
    F. Bassani, M. Inguscio andT. W. Hänsch (Editors):The Hydrogen Atom (Springer-Verlag, Berlin, 1989).Google Scholar
  6. [6]
    See for instance:F. Bassani andG. Pastori-Parravicini:Electronic States and Optical Transitions in Solids (Pergamon Press, Oxford, 1974, Chapt. 6.Google Scholar
  7. [7]
    C. Flytzanis:Theory of nonlinear optical sysceptibilities, inQuantum Electronics, edited byH. Rabin andC. L. Tang, Vol. I, Part A (Academic Press, New York, N.Y., 1975).Google Scholar
  8. [8]
    F. Bassani, J. J. Forney andA. Quattropani:Phys. Rev. Lett.,39, 1070 (1977)A. Quattropani, F. Bassani andS. Carrillo:Phys. Rev. A,25, 3079 (1982);V. Florescu, P. Patrascu andO. Stoican:Phys. Rev. A,36, 2155 (1987), and references therein.CrossRefADSGoogle Scholar
  9. [9]
    R. Kubo:J. Phys. Soc. Jpn.,12, 570 (1957).MATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    J. F. Ward:Rev. Mod. Phys.,11, 323 (1969).Google Scholar
  11. [11]
    B. J. Orr andJ. F. Ward:Molec. Phys.,20, 513 (1971).CrossRefADSGoogle Scholar
  12. [12]
    D. W. Martin andP. A. Fraser:J. Phys. B,13, 3383 (1980).CrossRefADSGoogle Scholar
  13. [13]
    A. Quattropani andN. Binggeli: inThe Hydrogen Atom, edited byF. Bassani, M. Inguscio andT. W. Hänsch (Springer-Verlag, Berlin, 1989).Google Scholar
  14. [14]
    R. J. Drachmann, A. K. Bathia andA. A. Shabazz:Phys. Rev. A,42, 6333 (1990).CrossRefADSGoogle Scholar
  15. [15]
    A. Pasquarello, L. C. Andreani, N. Binggeli andA. Quattropani:Europhys. Lett.,17, 387 (1992).ADSGoogle Scholar
  16. [16]
    See Ref.[3],, sect. 63.Google Scholar

Copyright information

© Società Italiana di Fisica 1992

Authors and Affiliations

  • S. Scandolo
    • 1
    • 2
  • F. Bassani
    • 1
  1. 1.Scuola Normale SuperiorePisaItalia
  2. 2.Institut Romand de Recherche Numerique en Physique des Materiaux (IRRMA) PHB-EcublensLausanneSwitzerland

Personalised recommendations