• Ingvar LindgrenEmail author
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 63)


The quantum-mechanical treatment of many-electron systems, based on the Schrödinger equation and the Coulomb interaction between the electrons, was developed shortly after the advent of quantum mechanics, particularly by John Slater in the late 1920s and early 1930s [58]. Self-consistent-field (SCF) schemes were early developed by Slater, Hartree, Fock, and others.


Electron Correlation Helium Atom Relativistic Quantum Mechanic Dirac Theory Nonrelativistic Quantum Mechanic 
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.


  1. 1.
    Adkins, G.S., Fell, R.N.: Bound-state formalism for positronium. Phys. Rev. A 60, 4461–75 (1999)Google Scholar
  2. 2.
    Adkins, G.S., Fell, R.N., Mitrikov, P.M.: Calculation of the positronium hyperfine interval using the Bethe-Salpeter formalism. Phys. Rev. A 65, 042,103 (2002)Google Scholar
  3. 3.
    Araki, H.: Quantum-Electrodynamical Corrections to Energy-levels of Helium. Prog. Theor. Phys. (Japan) 17, 619–42 (1957)Google Scholar
  4. 4.
    Artemyev, A.N., Shabaev, V.M., Yerokhin, V.A., Plunien, G., Soff, G.: QED calculations of then = 1 andn = 2 energy levels in He-like ions. Phys. Rev. A 71, 062,104 (2005)Google Scholar
  5. 5.
    Bethe, H.A.: The Electromagnetic Shift of Energy Levels. Phys. Rev. 72, 339–41 (1947)Google Scholar
  6. 6.
    Bethe, H.A., Salpeter, E.E.: An Introduction to Relativistic Quantum Field Theory. Quantum Mechanics of Two-Electron Atoms. Springer, Berlin (1957)Google Scholar
  7. 7.
    Bjorken, J.D., Drell, S.D.: Relativistic Quantum Fields. Mc-Graw-Hill Pbl. Co, N.Y. (196)Google Scholar
  8. 8.
    Bjorken, J.D., Drell, S.D.: Relativistic Quantum Mechanics. Mc-Graw-Hill Pbl. Co, N.Y. (1964)Google Scholar
  9. 9.
    Boldwin, G.T., Yennie, D.R., Gregorio, M.A.: Recoil effects in the hyperfine structure of QED bound states. Rev. Mod. Phys. 57, 723–82 (1985)Google Scholar
  10. 10.
    Brandow, B.H.: Linked-Cluster Expansions for the Nuclear Many-Body Problem. Rev. Mod. Phys. 39, 771–828 (1967)Google Scholar
  11. 11.
    Breit, G.: Dirac’s equation and the spin-spin interaction of two electrons. Phys. Rev. 39, 616–24 (1932)Google Scholar
  12. 12.
    Brown, G.E., Ravenhall, D.G.: On the Interaction of Two electrons. Proc. R. Soc. London, Ser. A 208, 552–59 (1951)Google Scholar
  13. 13.
    Brueckner, K.A.: Many-Body Problems for Strongly Interacting Particles. II. Linked Cluster Expansion. Phys. Rev. 100, 36–45 (1955)Google Scholar
  14. 14.
    Caswell, W.E., Lepage, G.P.: Reduction of the Bethe-Salpeter equation to an equivalent Schrödinger equation, with applications. Phys. Rev. A 18, 810–19 (1978)Google Scholar
  15. 15.
    Connell, J.H.: QED test of a Bethe-Salpeter solution method. Phys. Rev. D 43, 1393–1402 (1991)Google Scholar
  16. 16.
    Cutkosky, R.E.: Solutions of the Bethe-Salpeter equation. Phys. Rev. 96, 1135–41 (1954)Google Scholar
  17. 17.
    Dirac, P.A.M.:. Roy. Soc. (London) 117, 610 (1928)Google Scholar
  18. 18.
    Dirac, P.A.M.: The Principles of Quantum Mechanics. Oxford Univ. Press, Oxford (1930, 1933, 1947, 1958)Google Scholar
  19. 19.
    Douglas, M.H., Kroll, N.M.: Quantum Electrodynamical Corrections to the Fine Structure of Helium. Ann. Phys. (N.Y.) 82, 89–155 (1974)Google Scholar
  20. 20.
    Dyson, F.J.: The radiation Theories of Tomonaga, Schwinger, and Feynman. Phys. Rev. 75, 486–502 (1949)Google Scholar
  21. 21.
    Dyson, F.J.: The Wave Function of a Relativistic System. Phys. Rev. 91, 1543–50 (1953)Google Scholar
  22. 22.
    Feynman, R.P.: Space-Time Approach to Quantum Electrodynamics. Phys. Rev. 76, 769–88 (1949)Google Scholar
  23. 23.
    Feynman, R.P.: The Theory of Positrons. Phys. Rev. 76, 749–59 (1949)Google Scholar
  24. 24.
    Froese-Fischer, C.: The Hartree-Fock method for atoms. John Wiley and Sons, New York, London, Sidney, Toronto (1977)Google Scholar
  25. 25.
    Gaunt, J.A.: The Triplets of Helium. Proc. R. Soc. London, Ser. A 122, 513–32 (1929)Google Scholar
  26. 26.
    Gell-Mann, M., Low, F.: Bound States in Quantum Field Theory. Phys. Rev. 84, 350–54 (1951)Google Scholar
  27. 27.
    Goldstein, J.S.: Properties of the Salpeter-Bethe Two-Nucleon Equation. Phys. Rev. 91, 1516–24 (1953)Google Scholar
  28. 28.
    Goldstone, J.: Derivation of the Brueckner many-body theory. Proc. R. Soc. London, Ser. A 239, 267–279 (1957)Google Scholar
  29. 29.
    Grotch, H., Owen, D.A.: Bound states in Quantum Electrodynamics: Theory and Applications. Fundamentals of Physics 32, 1419–57 (2002)Google Scholar
  30. 30.
    Grotch, H., Yennie, D.R.: Effective Potential Model for Calculating Nuclear Corrections to the Eenergy Levels of Hydrogen. Rev. Mod. Phys. 41, 350–74 (1969)Google Scholar
  31. 31.
    Kelly, H.P.: Application of many-body diagram techniques in atomic physics. Adv. Chem. Phys. 14, 129–190 (1969)Google Scholar
  32. 32.
    Kusch, P., Foley, H.M.: Precision Measurement of the Ratio of the Atomic ’g Values’ in the 2 P 3∕2 and 2 P 1∕2 States of Gallium. Phys. Rev. 72, 1256–57 (1947)Google Scholar
  33. 33.
    Kusch, P., Foley, H.M.: On the Intrinsic Moment of the Electron. Phys. Rev. 73, 412 (1948)Google Scholar
  34. 34.
    Lamb, W.W., Retherford, R.C.: Fine structure of the hydrogen atom by microwave method. Phys. Rev. 72, 241–43 (1947)Google Scholar
  35. 35.
    Lindgren, I.: The Rayleigh-Schrödinger perturbation and the linked-diagram theorem for a multi-configurational model space. J. Phys. B 7, 2441–70 (1974)Google Scholar
  36. 36.
    Lindgren, I., Salomonson, S., Åsén, B.: The covariant-evolution-operator method in bound-state QED. Physics Reports 389, 161–261 (2004)Google Scholar
  37. 37.
    Mahan, G.D.: Many-particle Physics, second edition. Springer Verlag, Heidelberg (1990)CrossRefGoogle Scholar
  38. 38.
    Mohr, P.J.: Numerical Evaluation of the 1s 1∕2 -State Radiative Level Shift. Ann. Phys. (N.Y.) 88, 52–87 (1974)Google Scholar
  39. 39.
    Mohr, P.J., Plunien, G., Soff, G.: QED corrections in heavy atoms. Physics Reports 293, 227–372 (1998)Google Scholar
  40. 40.
    Nakanishi, N.: Normalization condition and normal and abnormal solutions of Bethe-Salpeter equation. Phys. Rev. 138, B1182 (1965)Google Scholar
  41. 41.
    Namyslowski, J.M.: The Relativistic Bound State Wave Function. in Light-Front Quantization and Non-Perturbative QCD, J.P. Vary and F. Wolz, eds. (International Institute of Theoretical and Applied Physics, Ames) (1997)Google Scholar
  42. 42.
    Onida, G., Reining, L., Rubio, A.: Electronic excitations: density-functional versus many-body Green’s-function approaches. Rev. Mod. Phys. 74, 601–59 (2002)Google Scholar
  43. 43.
    Pachucki, K.: Quantum electrodynamics effects on helium fine structure. J. Phys. B 32, 137–52 (1999)Google Scholar
  44. 44.
    Pachucki, K.: Improved Theory of Helium Fine Structure. Phys. Rev. Lett. 97, 013,002 (2006)Google Scholar
  45. 45.
    Pachucki, K., Sapirstein, J.: Contributions to helium fine structure of order mα 7. J. Phys. B 33, 5297–5305 (2000)ADSCrossRefGoogle Scholar
  46. 46.
    Pachucky, K., Yerokhin, V.A.: Reexamination of the helium fine structure (vol 79, 062516, 2009). Phys. Rev. Lett. 80, 19,902 (2009)Google Scholar
  47. 47.
    Pachucky, K., Yerokhin, V.A.: Reexamination of the helium fine structure (vol 79, 062516, 2009). Phys. Rev. A 81, 39,903 (2010)Google Scholar
  48. 48.
    Persson, H., Salomonson, S., Sunnergren, P., Lindgren, I.: Two-electron Lamb-Shift Calculations on Heliumlike Ions. Phys. Rev. Lett. 76, 204–07 (1996)Google Scholar
  49. 49.
    Plante, D.R., Johnson, W.R., Sapirstein, J.: Relativistic all-order many-body calculations of then = 1 andn = 2 states of heliumlike ions. Phys. Rev. A 49, 3519–30 (1994)Google Scholar
  50. 50.
    Rosenberg, L.: Virtual-pair effects in atomic structure theory. Phys. Rev. A 39, 4377–86 (1989)Google Scholar
  51. 51.
    Salpeter, E.E.: Mass Correction to the Fine Structure of Hydrogen-like Atoms. Phys. Rev. 87, 328–43 (1952)Google Scholar
  52. 52.
    Salpeter, E.E., Bethe, H.A.: A Relativistic Equation for Bound-State Problems. Phys. Rev. 84, 1232–42 (1951)Google Scholar
  53. 53.
    Sazdjian, H.: Relativistiv wave equations for the dynamics of two interacting particles. Phys. Rev. D 33, 3401–24 (1987)Google Scholar
  54. 54.
    Sazdjian, H.: The connection of two-particle relativistic quantum mechanics with the Bethe-Salpeter equation. J. Math. Phys. 28, 2618–38 (1987)Google Scholar
  55. 55.
    Schweber, S.S.: The men who madt it: Dyson, Feynman, Schwinger and Tomonaga. Princeton University Press, Princeton (1994)Google Scholar
  56. 56.
    Schwinger, J.: Quantum electrodynamics I. A covariant formulation. Phys. Rev. 74, 1439 (1948)Google Scholar
  57. 57.
    Shabaev, V.M.: Two-times Green’s function method in quantum electrodynamics of high-Z few-electron atoms. Physics Reports 356, 119–228 (2002)Google Scholar
  58. 58.
    Slater, J.: Quantum Theory of Atomic Spectra. McGraw-Hill, N.Y. (1960)Google Scholar
  59. 59.
    Sucher, J.: Energy Levels of the Two-Electron Atom to Order α 3 Ry; Ionization Energy of Helium. Phys. Rev. 109, 1010–11 (1957)Google Scholar
  60. 60.
    Sucher, J.: S-Matrix Formalism for Level-Shift Calculations. Phys. Rev. 107, 1448–54 (1957)Google Scholar
  61. 61.
    Sucher, J.: Ph.D. thesis, Columbia University (1958). Univ. Microfilm Internat., Ann Arbor, MichiganGoogle Scholar
  62. 62.
    Sucher, J.: Foundations of the Relativistic Theory of Many Electron Atoms. Phys. Rev. A 22, 348–62 (1980)Google Scholar
  63. 63.
    Todorov, I.T.: Quasipotential Equation Corresponding to the relativistic Eikonal Approximation. Phys. Rev. D 3, 2351–56 (1971)Google Scholar
  64. 64.
    Tomanaga, S.: On Infinite Field Reactions in Quantum Field Theory. Phys. Rev. 74, 224–25 (1948)Google Scholar
  65. 65.
    Wick, G.C.: Properties of Bethe-Salpeter Wave Functions. Phys. Rev. 96, 1124–34 (1954)Google Scholar
  66. 66.
    Yerokhin, K.P.V.A.: Reexamination of the helium fine structure. Phys. Rev. Lett. 79, 62,616 (2009)Google Scholar
  67. 67.
    Yerokhin, K.P.V.A.: Fine Structure of Heliumlike Ions and Determination of the Fine Structure Constant. Phys. Rev. Lett. 104, 70,403 (2010)Google Scholar
  68. 68.
    Zelevinsky, T., Farkas, D., Gabrielse, G.: Precision Measurement of the Three 2 3 P J Helium Fine Structure Intervals. Phys. Rev. Lett. 95, 203,001 (2005)Google Scholar
  69. 69.
    Zhang, T.: Corrections to O(α 7(ln α)mc 2 ) fine-structure splittings and O(α 6(ln α)mc 2 ) energy levels in helium. Phys. Rev. A 54, 1252–1312 (1996)Google Scholar
  70. 70.
    Zhang, T., Drake, G.W.F.: Corrections to O(α 7  mc 2 ) fine-structure splitting in helium. Phys. Rev. A 54, 4882–4922 (1996)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of GothenburgGöteborgSweden

Personalised recommendations