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Review of High Precision Theory and Experiment for Helium

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The Hydrogen Atom

Part of the book series: Lecture Notes in Physics ((LNP,volume 570))

Abstract

Progress in obtaining essentially exact solutions to the nonrelativistic Schrödinger equation for the entire singly-excited spectrum of helium and other three-body systems is reviewed, and a new upper bound for the ground state is presented. The calculation of relativistic and quantum electrodynamic corrections is discussed, including high precision values for the Bethe logarithm. The results are compared with high precision measurements of ionization energies in helium. Recent progress is reviewed in determining the fine structure intervals in helium with the objective of determining the fine structure constant to an accuracy of ±1.7 parts in 108 or better. Extensions to lithium-like systems are briefly summarized.

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References

  1. G.W.F. Drake: Phys. Scr. T83, 83 (1999)

    Article  ADS  Google Scholar 

  2. K.S.E. Eikema, W. Ubachs, W. Vassen, H. Horgorvorst: Phys. Rev. A 55, 1866 (1997)

    Article  ADS  Google Scholar 

  3. N.E. Claytor, E.A. Hessels, S.R. Lundeen: Phys. Rev. A 52, 165 (1995), and earlier references therein

    Article  ADS  Google Scholar 

  4. S.D. Bergeson, A. Balakrishnan, K.G.H. Baldwin, T.B. Lucatorto, J. P. Marangos, T.J. McIlrath, T.R. O’Brian, S.L. Rolston, C. J. Sansonetti, J. Wen, and N. Westbrook: Phys. Rev. Lett. 80, 3475 (1998)

    Article  ADS  Google Scholar 

  5. G.D. Stevens, S.R. Lundeen: Phys. Rev. A 60, 4379 (1999)

    Article  ADS  Google Scholar 

  6. J. Wen, G. Gabrielse: Ph.D. Thesis, Harvard University, 1996 (unpublished)

    Google Scholar 

  7. C.H. Storry,, N.E. Rothery, E.A. Hessels: Phys. Rev. A 55, 967 (1997)

    Article  ADS  Google Scholar 

  8. D. Shiner, R. Dixson: 72, 1802 (1994); D. Shiner, R. Dixson: IEEE Trans. Instrum. Meas. 44, 518 (1995)

    Google Scholar 

  9. E. Riis, A.G. Sinclair, O. Poulsen, G.W.F. Drake, W.R. C. Rowley, A.P. Levick: Phys. Rev. A 49, 207 (1994)

    Article  ADS  Google Scholar 

  10. F. Marin, F. Minardi, F.S. Pavone, M. Inguscio, G.W.F. Drake: Z. Phys. D 32, 285 (1995)

    Google Scholar 

  11. T.J. Scholl, R. Cameron, S. D. Rosner, L. Zhang, R. A. Holt: Phys. Rev. Lett. 71, 2188 (1993)

    Article  ADS  Google Scholar 

  12. C. Dorrer, F. Nez, B. deBeauvoir, L. Julien, F. Biraben: Phys. Rev. Lett. 78, 3658 (1997)

    Article  ADS  Google Scholar 

  13. T.P. Dinneen, N. Berrah-Mansour, H.G. Berry, L. Young, R.C. Pardo: Phys. Rev. Lett. 66, 2859 (1991)

    Article  ADS  Google Scholar 

  14. C.H. Storry, E.A. Hessels: Phys. Rev. A 58, R8 (1998)

    Article  ADS  Google Scholar 

  15. J.K. Thompson, D.J.H. Howie, E.G. Myers: Phys. Rev. A 57, 180 (1998)

    Article  ADS  Google Scholar 

  16. C.H. Storry, M.C. George, E.A. Hessels: Phys. Rev. Lett. 84, 3274 (2000)

    Article  ADS  Google Scholar 

  17. E.G. Myers, P. Kuske, H.J. Andrä, I.A. Armour, N. A. Jelley, H.A. Klein, J.D. Silver, E. Träbert: Phys. Rev. Lett. 47, 87 (1981); E.G. Myers: Nucl. Instrum. Methods Phys. Res. Sect. B 9, 662 (1985). C.H. Storry,M.C. George, E.A. Hessels: Phys. Rev. Lett. 84, 3274 (2000)

    Article  ADS  Google Scholar 

  18. J. Castilega, D. Livingston, A. Sanders, and D. Shiner: Phys. Rev. Lett. 84, 4321 (2000)

    Article  ADS  Google Scholar 

  19. E.G. Myers, H.S. Margolis, J.K. Thompson, M.A. Farmer, J.D. Silver, M.R. Tarbutt: Phys. Rev. Lett. 82, 4200 (1999)

    Article  ADS  Google Scholar 

  20. C.J. Sansonetti, J.D. Gillaspy: Phys. Rev. A 45, R1 (1992)

    Article  Google Scholar 

  21. E.G. Myers and M.R. Tarbutt: Phys. Rev. A 61, 10501R (2000).

    ADS  Google Scholar 

  22. W. Lichten, D. Shiner, Z.-X. Zhou: Phys. Rev. A 43, 1663 (1991)

    Article  ADS  Google Scholar 

  23. E.A. Hylleraas: Z. Phys. 48, 469 (1928); 54, 347 (1929). See also ibid., Rev. Mod. Phys. 35, 421 (1963)

    Article  ADS  Google Scholar 

  24. E.A. Hylleraas, B. Undheim: Z. Phys. 65, 759 (1930); J.K.L. MacDonald, Phys. Rev. 43, 830 (1933)

    Article  ADS  Google Scholar 

  25. H.A. Bethe, E.E. and Salpeter: Quantum Mechanics of One-and Two-Electron Atoms (Springer-Verlag, New York. 1957), Sect. 32

    MATH  Google Scholar 

  26. Y. Accad, C.L. Pekeris, B. Schi.: Phys. Rev. A 4, 516 (1971)

    Article  ADS  Google Scholar 

  27. G.W.F. Drake, Z.-C. Yan: Phys. Rev. A 46, 2378 (1992)

    Article  ADS  Google Scholar 

  28. G.W.F. Drake: ‘High-Precision Calculations for the Rydberg States of Helium’ in: Long Range Casimir Forces:The ory and Recent Experiments in Atomic Systems, ed. by F.S. Levin, D.A. Micha (Plenum Press, New York, 1993), pp. 107–217

    Google Scholar 

  29. G.W.F. Drake: Adv. At. Mol. Opt. Phys. 31, 1 (1993)

    Google Scholar 

  30. V.I. Korobov: Phys. Rev. A 61, 64503 (2000)

    Article  ADS  Google Scholar 

  31. S.P. Goldman: Phys. Rev. A 57, R677 (1998)

    Article  ADS  Google Scholar 

  32. A. Bürgers, D. Wintgen, J.-M. Rost, J.-M., J. Phys. B: At. Mol. Opt. Phys. 28, 3163 (1995)

    Article  ADS  Google Scholar 

  33. J.D. Baker, D.E. Freund, R.N. Hill, J.D. Morgan III: Phys. Rev. A 41, 1247 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  34. G.W.F. Drake, Z.-C. Yan: Chem. Phys. Lett. 229, 486 (1994).

    Article  ADS  Google Scholar 

  35. G.W.F. Drake: ‘High Precision Calculations for Helium’. in: Atomic, Molecular, and Optical Physics Handbook, ed. by G. W. F. Drake (AIP press, New York, 1996), pp. 154–171

    Google Scholar 

  36. R.J. Drachman: ‘High Rydberg States of Two-Electron Atoms in Perturbation Theory’. in: Long-Range Casimir Forces: Theory and Recent Experiments on Atomic Systems, ed. by F.S. Levin and D. Micha (Plenum Press, New York, 1993) pp. 219–272, and earlier references therein

    Google Scholar 

  37. A. Dalgarno, J.T. Lewis: Proc. Roy. Soc. (London) Ser. A 233, 70 (1956), and A. Dalgarno, A.L. Stewart: ibid., 238, 269 (1956).

    Article  ADS  MathSciNet  Google Scholar 

  38. R.A. Swainson, G.W.F. Drake: Can. J. Phys. 70, 187 (1992)

    ADS  Google Scholar 

  39. A.P. Stone: Proc. Phys. Soc. (London) 77, 786 (1961); 81, 868 (1963)

    Article  ADS  Google Scholar 

  40. P.K. Kabir, E.E. Salpeter: Phys. Rev. 108, 1256 (1957)

    Article  MATH  ADS  Google Scholar 

  41. C. Schwartz: Phys. Rev. 123, 1700 (1961)

    Article  ADS  Google Scholar 

  42. J.D. Baker, R.C. Forrey M. Jerziorska, J.D. Morgan III: private communication. See also J.D. Baker, R.C. Forrey, J.D. Morgan, R.N. Hill, M. Jeziorska J. Schertzer: Bull. Am. Phys. Soc. 38, 1127 (1993)

    Google Scholar 

  43. V.I. Korobov, S.V. Korobov: Phys. Rev. A 59, 3394 (1999)

    Article  ADS  Google Scholar 

  44. G.W.F. Drake, S.P. Goldman: Can. J. Phys. 77, 835 (1999)

    Article  ADS  Google Scholar 

  45. S.P. Goldman, G.W.F. Drake: Phys. Rev. Lett. 68, 1683 (1992)

    Article  ADS  Google Scholar 

  46. S.P. Goldman: Phys. Rev. A 50, 3039 (1994)

    Article  ADS  Google Scholar 

  47. G.W.F. Drake, R.A. Swainson: Phys. Rev. A 41, 1243 (1990)

    ADS  Google Scholar 

  48. H. Araki: Prog. Theor. Phys. 17, 619 (1957)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  49. J. Sucher: Phys. Rev. 109, 1010 (1958)

    Article  ADS  Google Scholar 

  50. G.W.F. Drake, W.C. Martin: Can. J. Phys. 76, 597 (1998)

    Article  Google Scholar 

  51. G.W.F. Drake, I.B. Khriplovich, A.I. Milstein, A.S. Yelkovsky: Phys. Rev. A 48, R15 (1993)

    Article  ADS  Google Scholar 

  52. K. Pachucki: J. Phys. B, At. Mol. Opt. Phys. 31, 2489, 3547 (1998)

    Article  ADS  Google Scholar 

  53. K. Pachucki, J. Sapirstein: J. Phys. B, 33, 455 (2000)

    Article  ADS  Google Scholar 

  54. K. Pachucki: Phys. Rev. Lett. 84, 4561 (2000)

    Article  ADS  Google Scholar 

  55. Z.-C. Yan, G.W.F. Drake: Phys. Rev. Lett. 74, 4791 (1995)

    Article  ADS  Google Scholar 

  56. G.W.F. Drake: Adv. At. Mol. Opt. Phys. 32, 93 (1994)

    Google Scholar 

  57. M.S. Dewey, R.W. Dunford: Phys. Rev. Lett. 60, 2014 (1988).

    Article  ADS  Google Scholar 

  58. A. van Wijngaarden, F. Holuj, G.W.F. Drake: Phys. Rev. A 62, in press (2000)

    Google Scholar 

  59. T. Kinoshita, D.R. Yennie: ‘High Precision Tests of Quantum Electrodynamics’. In: Quantum Electrodynamics. ed. by T. Kinoshita (World Scientific, Singapore, 1990) pp. 1–14

    Google Scholar 

  60. M. Douglas, N. M. Kroll: Ann. Phys. (N.Y.) 82, 89 (1974)

    Article  ADS  Google Scholar 

  61. T. Zhang: Phys. Rev. A 53, 3896 (1996)

    Article  ADS  Google Scholar 

  62. T. Zhang: Phys. Rev. A 54, 1252 (1996)

    Article  ADS  Google Scholar 

  63. T. Zhang, G.W.F. Drake: Phys. Rev. A 54, 4882 (1996)

    Article  ADS  Google Scholar 

  64. T. Zhang, Z.-C. Yan, G.W.F. Drake: Phys. Rev. Lett. 77, 1715 (1996)

    Article  ADS  Google Scholar 

  65. K. Pachucki: J. Phys.B 32, 137 (1999)

    Article  ADS  Google Scholar 

  66. K. Pachucki, J. Sapirstein: J. Phys.B, submitted (2001)

    Google Scholar 

  67. F. Minardi, G. Bianchini, P. Cancio Pastor, G. Giusfredi, F.S. Pavone, M. Inguscio: Phys. Rev. Lett. 82 1112 (1999)

    Article  ADS  Google Scholar 

  68. W. Frieze, E.A. Hinds, V.W. Hughes, F.M. Pichanick: Phys. Rev. A 24, 279 (1981) and earlier references therein. The value for υ 0,1 has recently been revised by V.W. Hughes: private communication

    Article  ADS  Google Scholar 

  69. Z.-C. Yan, M. Tambasco, G.W.F. Drake: Phys. Rev. A 57, 1652 (1998)

    Article  ADS  Google Scholar 

  70. Z.-C. Yan, G.W.F. Drake: Phys. Rev. Lett. 81, 774 (1998)

    Article  ADS  Google Scholar 

  71. F.W. King, D.G. Ballegeer D.J. Larson, P.J. Pelzl, S.A. Nelson, T.J. Prosa, B.M. Hinaus: Phys. Rev. A 58, 3597 (1998)

    Article  ADS  Google Scholar 

  72. Z.-C. Yan, G.W.F. Drake: Phys. Rev. Lett. 79, 1646 (1997)

    Article  ADS  Google Scholar 

  73. C.H. Storry, N.E. Rothery, E.A. Hessels: Phys. Rev. A 55, 128 (1997)

    Article  ADS  Google Scholar 

  74. A.K. Bhatia, R.J. Drachman: Phys. Rev. A 55, 1842 (1997)

    Article  ADS  Google Scholar 

  75. Z.-C. Yan, G.W.F. Drake: Phys. Rev. A 61, 022504 (2000)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics, University of Windsor, N9B 3P4, Windsor, Ontario, Canada

    Gordon W. F. Drake

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  1. Gordon W. F. Drake
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Editor information

Editors and Affiliations

  1. D.I. Mendeleev Institute for Metrology, 198005, St. Petersburg, Russia

    Savely G. Karshenboim

  2. MPI for Quantum Optics, 85748, Garching, Germany

    Savely G. Karshenboim  & T.W. Hänsch  & 

  3. Scuola Normale Superiore, Piazza dei Cavalieri, Pisa, Italy

    F. Bassani

  4. Dept.of Physics, University of Perugia, Perugia, Italy

    F.S. Pavone

  5. LENS and INFM, University of Florence, 50125, Florence, Italy

    F.S. Pavone

  6. Dept. of Physics and LENS, University of Florence, Florence, Italy

    M. Inguscio

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Drake, G.W.F. (2001). Review of High Precision Theory and Experiment for Helium. In: Karshenboim, S.G., Bassani, F., Pavone, F., Inguscio, M., Hänsch, T. (eds) The Hydrogen Atom. Lecture Notes in Physics, vol 570. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45395-4_4

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  • DOI: https://doi.org/10.1007/3-540-45395-4_4

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