Theory of Natural Line Shape

  • Luiz Davidovich
  • H. M. Nussenzveig
Conference paper


The treatment of the emission of light by an atom in quantum electrodynamics has been strongly influenced by Weisskopf and Wigner’s early contribution [1] to this subject. While their work was highly successful in accounting for the observed line shape, several disturbing questions about the underlying assumptions remained unsettled:
  1. (i)

    The initial state assumed for the system (atom in excited state with no photons present) seems quite unphysical. The state preparation and the dependence of the decay on the excitation should be discussed.

  2. (ii)

    The Weisskopf-Wigner exponential decay “Ansatz” cannot be valid for all times. Deviations from it are expected to be extremely small for long-lived decaying states such as the atomic ones. However, the range of validity of the exponential decay law should be determined.

  3. (iii)

    The state space was restricted to a two-level atom and to the vacuum and one-photon sectors, without any indication of how to proceed in order to improve the approximation. For such a basic problem, a clear-cut formulation should be provided, as well as a systematic procedure for deriving corrections to the Weisskopf-Wigner approximation.



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  1. 1.
    V. Weisskopf and E.P. Wigner, Z. Phys. 63, 54 (1930).ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    W. Lamb, Phys. Rev. 85, 259 (1952).ADSCrossRefGoogle Scholar
  3. 3.
    W. Heitler and S.T. Ma, Proc. Roy. Ir. Acad. 52, 109 (1949); E. Arnous and S. Zienau, Heiv. Phys. Acta 24, 279 (1951); E. Arnous and K. Bleuler, Hely. Phys. Acta 25, 581, 631 (1952).Google Scholar
  4. 4.
    E. Arnous and W. Heitler, Proc. Roy. Soc. (London) A 220, 290 (1953).ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    W. Heitler, The Quantum Theory of Radiation, 3rd ed. ( Oxford University Press, London, 1954 ).zbMATHGoogle Scholar
  6. 6.
    F.E. Low, Phys. Rev. 88, 53 (1952).ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    H.M. Nussenzveig, Causality and Dispersion Relations ( Academic Press, New York, 1972 ), Chapter 4.Google Scholar
  8. 8.
    L. Davidovich, Ph.D. thesis, University of Rochester (1975); L. Davidovich and H.M. Nussenzveig, to be published.Google Scholar
  9. 9.
    M.E. Rose, Elementary Theory of Angular Momentum ( Wiley, New York, 1957 ).zbMATHGoogle Scholar
  10. 10.
    H.E. Moses, Phys. Rev. A 8, 1710 (1973).ADSCrossRefMathSciNetGoogle Scholar
  11. 11.
    L. Van Hove, Physica 21, 901 (1955).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    F.J. Dyson, Phys. Rev. 75, 486, 1736 (1949).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    E. Grimm and V. Ernst, J. Phys. A 7, 1664 (1974); Z. Phys. A 274, 293 (1975).Google Scholar
  14. 14.
    E.B. Davies, J. Math. Phys. 15, 2036 (1974).ADSCrossRefGoogle Scholar
  15. 15.
    Cf. E. Grimm and V. Ernst, Ref. 13, for an example where this condition is not fulfilled.Google Scholar
  16. 16.
    E.C.G. Stueckelberg and D. Rivier, Hely. Phys. Acta 23, 215 (1950); M. Fierz, Heiv. Phys. Acta 23, 731 (1950).Google Scholar
  17. 17.
    L.D. Faddeev, Soy. Phys. Doklady 8, 881 (1964).Google Scholar
  18. 18.
    H.A. Bethe, Phys. Rev. 72, 339 (1947).ADSCrossRefzbMATHGoogle Scholar
  19. 19.
    E.A. Power and S. Zienau, Nuovo Cimento 6, 7 (1957), Phil. Trans. Roy. Soc. (London) A 251, 427 (1959); M. Babiker, E.A. Power and T. Thirunamachandran, Proc. Roy. Soc. (London) A 338, 235 (1974).Google Scholar
  20. 20.
    R.G. Woolley, Molec. Phys. 22, 1013 (1971).ADSCrossRefGoogle Scholar
  21. 21.
    A cutoff in momentum space is required in order for (9.1) to define a proper unitary transformation. One can adopt the same cutoff as in (8.3).Google Scholar
  22. 22.
    P.A.M. Dirac, The Principles of Quantum Mechanics, 4th ed. ( Oxford University Press, London, 1958 ).zbMATHGoogle Scholar
  23. 23.
    M. Gavrila, Phys. Rev. 163, 147 (1967).ADSCrossRefGoogle Scholar
  24. 24.
    S.R. Lundeen and F.M. Pipkin, Phys. Rev. Lett. 34, 1368 (1975).ADSCrossRefGoogle Scholar
  25. 25.
    If this degeneracy is not removed, the first-order contribution of the minimal-coupling interaction to the 2sz - 2pß, + one photon transition vanishes, and one must compute higher-order contributions, leading essentially to the same results (cf. E.J. Kelsey, Phys. Rev. A 15,647 (1977)).Google Scholar
  26. 26.
    J.J. Sakurai, Advanced Quantum Mechanics ( Addison-Wesley, Reading, Mass., 1967 ).Google Scholar
  27. 27.
    Z. Fried, Phys. Rev. A 8, 2835 (1973).ADSCrossRefGoogle Scholar
  28. 28.
    S. Klarsfeld, Lett. N. Cim. 1, 682 (1969).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • Luiz Davidovich
    • 1
  • H. M. Nussenzveig
    • 2
  1. 1.Institut für Theoretische PhysikETHZürichSwitzerland
  2. 2.Universidade de São PauloSão PauloBrasil

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