Advertisement

High Precision Atomic Theory: Tests of Fundamental Understanding

  • G. W. F. Drake
  • Qixue Wu
  • Zheng Zhong
Chapter
Part of the Modern Aspects of Electrochemistry book series (MAOE, volume 43)

Abstract

The unifying theme of these two volumes is the use of mathematical models to describe various aspects of the physical world around us. In many cases, the system in question is too complicated to be described from first principles, and so various models are introduced, containing perhaps arbitrary parameters whose values can be adjusted to give the best fit to experimental data. In other sufficiently simple cases, an exact analytic solution is possible, at least within the context of various physical approximations. The present chapter will be concerned with systems of intermediate complexity that are too complicated to allow exact analytic solutions, but are simple enough to permit solutions by numerical methods that are essentially exact for all practical purposes.

Keywords

Helium Atom Isotope Shift Exact Analytic Solution Nuclear Mass Linear Variational Parameter 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. Sheehan, N. Kollerstone, and C.B. Waff, The Case of the Pilfered Planet, Scientific American, December (2004).Google Scholar
  2. 2.
    2. H.A. Bethe and E.E. Salpeter, Quantum mechanics of one- and two-electron atoms, (Springer, Berlin Heidelberg New York, 1957).Google Scholar
  3. 3.
    For a complete discussion of units, see W.E. Baylis and G.W.F. Drake, in Handbook of Atomic, Molecular and Optical Physics, Edited by G.W.F. Drake (Springer, Berlin Heidelberg New York, 2005), p. 1.Google Scholar
  4. 4.
    The latest values of the fundamental constants can be downloaded from the web site http://physics.nist.gov/cuu/Constants/index.html.
  5. 5.
    E.A. Hylleraas, Z. Phys48, 469 (1928); 54, 347 (1929). See also ibid., Rev. Mod. Phys35, 421 (1963).Google Scholar
  6. 6.
    6. E.A. Hylleraas and B. Undheim, Z. Phys65, 759 (1930).CrossRefGoogle Scholar
  7. 7.
    7. J.K.L. MacDonald, Phys. Rev43, 830 (1933).CrossRefGoogle Scholar
  8. 8.
    8. R.N. Hill, Int. J. Quantum Chem68, 357 (1998).CrossRefGoogle Scholar
  9. 9.
    9. B. Klahn and W.A. Bingel, Theor. Chem. Acta 44, 27 (1977); Int. J. Quantum Chem11, 943 (1978).CrossRefGoogle Scholar
  10. 10.
    10. Y. Accad, C.L. Pekeris, and B. Schiff, Phys. Rev. A 4, 516 (1971).CrossRefGoogle Scholar
  11. 11.
    11. G.W.F. Drake, in Long-range Casimir forces: Theory and recent experiments on atomic systems, Edited by F.S. Levin and D.A. Micha (Plenum, New York, 1993), pp. 107–217.Google Scholar
  12. 12.
    12. G.W.F. Drake and Z.-C. Yan, Phys. Rev. A 46, 2378 (1992).CrossRefGoogle Scholar
  13. 13.
    13. G.W.F. Drake, Adv. At. Mol. Opt. Phys31, 1 (1993).Google Scholar
  14. 14.
    14. G.W.F. Drake, M.M. Cassar, and R.A. Nistor, Phys. Rev. A 65, 054501 (2002).CrossRefGoogle Scholar
  15. 15.
    15. V.I. Korobov, Phys. Rev. A 66, 024501 (2002).CrossRefGoogle Scholar
  16. 16.
    16. C. Schwartz, Int. J. Mod. Phys. E – Nucl. Phys15, 877 (2006).CrossRefGoogle Scholar
  17. 17.
    17. S.P. Goldman, Phys. Rev. A 57, R677 (1998).CrossRefGoogle Scholar
  18. 18.
    18. A. Bürgers, D. Wintgen, and J.-M. Rost, J. Phys. B: At. Mol. Opt. Phys28, 3163 (1995).CrossRefGoogle Scholar
  19. 19.
    19. J.D. Baker, D.E. Freund, R.N. Hill, and J.D. Morgan III, Phys. Rev. A 41, 1247 (1990).CrossRefGoogle Scholar
  20. 20.
    20. G.W.F. Drake, in Handbook of Atomic, Molecular and Optical Physics, Edited by G.W.F. Drake (Springer, Berlin Heidelberg New York, 2005), p. 1355.Google Scholar
  21. 21.
    21. J. Ackermann and J. Shertzer, Phys. Rev. A 54, 365 (1996), and earlier references therein.CrossRefGoogle Scholar
  22. 22.
    22. C.-Y. Hu, A.A. Kvitsinsky, and J.S. Cohen, J. Phys. B 28, 3629 (1995), and earlier references therein.CrossRefGoogle Scholar
  23. 23.
    23. E.Z. Liverts, M.Y. Amusia, R. Krivec, and V.B. Mandelzweig, Phys. Rev. A 73, 012514 (2006), and earlier references therein.CrossRefGoogle Scholar
  24. 24.
    24. J.S. Sims and S.A. Hagstrom, Int. J. Quantum Chem90, 1600 (2002).CrossRefGoogle Scholar
  25. 25.
    25. S. Chakraborty and Y.K. Ho, Chem. Phys. Lett438, 99 (2007).CrossRefGoogle Scholar
  26. 26.
    26. Z.-C. Yan and G.W.F. Drake, Phys. Rev. Lett81, 774 (1998).CrossRefGoogle Scholar
  27. 27.
    27. Z.-C. Yan and G.W.F. Drake, Phys. Rev. A 66, 042504 (2002).CrossRefGoogle Scholar
  28. 28.
    28. Z.-C. Yan and G.W.F. Drake, Phys. Rev. Lett91, 113004 (2003).CrossRefGoogle Scholar
  29. 29.
    29. M. Puchalski and K. Pachucki, Phys. Rev. A 73, 022503 (2006).CrossRefGoogle Scholar
  30. 30.
    30. M. Puchalski, A.M. Moro, and K. Pachucki, Phys. Rev. Lett97, 133001 (2006).CrossRefGoogle Scholar
  31. 31.
    31. K. Pachucki and J. Komasa, J. Chem. Phys125, 204304 (2006).CrossRefGoogle Scholar
  32. 32.
    32. K. Pachucki, Phys. Rev. A 74, 022512 (2006).CrossRefGoogle Scholar
  33. 33.
    33. K. Pachucki, Phys. Rev. A 74, 062510 (2006).CrossRefGoogle Scholar
  34. 34.
    34. G.W.F. Drake and Z.-C. Yan, Phys. Rev. A 46, 2378 (1992).CrossRefGoogle Scholar
  35. 35.
    35. G.W.F. Drake, Adv. At. Mol. Opt. Phys31, 1 (1993).Google Scholar
  36. 36.
    36. A.K. Bhatia and A. Temkin, Phys. Rev137, 1335 (1965).CrossRefGoogle Scholar
  37. 37.
    37. A.K. Bhatia and R.J. Drachman, Phys. Rev. A 35, 4051 (1987).CrossRefGoogle Scholar
  38. 38.
    38. A.K. Bhatia and R.J. Drachman, J. Phys. B: At. Mol. Opt. Phys36, 1957 (2003).CrossRefGoogle Scholar
  39. 39.
    39. A.P. Stone, Proc. Phys. Soc. (London) 77, 786 (1961); 81, 868 (1963).CrossRefGoogle Scholar
  40. 40.
    J. Sapirstein and K.T. Cheng, Can. J. Phys85 (2007).Google Scholar
  41. 41.
    41. M.I. Eides, H. Grotch, and V.A. Shelyuto, Phys. Rep342, 63–261 (2001).Google Scholar
  42. 42.
    42. P.K. Kabir and E.E. Salpeter, Phys. Rev108, 1256 (1957).CrossRefGoogle Scholar
  43. 43.
    43. H. Araki, Prog. Theor. Phys17, 619 (1957).CrossRefGoogle Scholar
  44. 44.
    44. J. Sucher, Phys. Rev109, 1010 (1958).CrossRefGoogle Scholar
  45. 45.
    45. G.W.F. Drake, Adv. At. Mol. Phys18, 399 (1982).CrossRefGoogle Scholar
  46. 46.
    46. G.W.F. Drake and W.C. Martin, Can. J. Phys76, 679 (1998).CrossRefGoogle Scholar
  47. 47.
    47. M. Douglas and N.M. Kroll, Ann. Phys. (N. Y.), 82, 89 (1974).CrossRefGoogle Scholar
  48. 48.
    48. V. Korobov and A. Yelkhovsky, Phys. Rev. Lett87 193003 (2001); A. Yelkhovsky, Phys. Rev. A 64, 062104 (2001).CrossRefGoogle Scholar
  49. 49.
    49. J.D. Morgan III and J.S. Cohen, in Handbook of Atomic, Molecular and Optical Physics, Edited by G.W.F. Drake (Springer, Berlin Heidelberg New York, 2005), p. 1355.Google Scholar
  50. 50.
    50. G.W.F. Drake, Z.-T. Lu, W. Nörtershäuser, and Z.-C. Yan, in Precision Physics of Simple Atoms and Molecules, Edited by S. Karshenboim (Springer, Berlin Heidelberg New York, 2007).Google Scholar
  51. 51.
    51. K.S.E. Eikema, W. Ubachs, W. Vassen, and H. Horgorvorst, Phys. Rev. A 55, 1866 (1997).CrossRefGoogle Scholar
  52. 52.
    52. 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. Lett80, 3475 (1998).CrossRefGoogle Scholar
  53. 53.
    53. C. Dorrer, F. Nez, B. de Beauvoir, L. Julien, and F. Biraben, Phys. Rev. Lett78, 3658 (1997).CrossRefGoogle Scholar
  54. 54.
    54. C.J. Sansonetti and W.C. Martin, Phys. Rev. A 29, 159 (1984).CrossRefGoogle Scholar
  55. 55.
    55. D.C. Morton, Q.X. Wu, and G.W.F. Drake, Can. J. Phys84, 83 (2006), and earlier references therein.CrossRefGoogle Scholar
  56. 56.
    56. P.C. Pastor, G. Giusfredi, P. De Natale, G. Hagel, C. de Mauro, and M. Inguscio, Phys. Rev. Lett92, 023001 (2004).CrossRefGoogle Scholar
  57. 57.
    57. G.W.F. Drake and S.P. Goldman, Can. J. Phys77, 835 (1999).CrossRefGoogle Scholar
  58. 58.
    58. G.W.F. Drake, Phys. ScrT95, 22 (2001).CrossRefGoogle Scholar
  59. 59.
    G.W.F. Drake and Z.-C. Yan, Can. J. Phys85 (2007).Google Scholar
  60. 60.
    60. G.W.F. Drake, Can. J. Phys80, 1195 (2002).CrossRefGoogle Scholar
  61. 61.
    61. K. Pachucki and J. Sapirstein, J. Phys. B: At. Mol. Opt. Phys35, 1783 (2002).CrossRefGoogle Scholar
  62. 62.
    62. K. Pachucki, Phys. Rev. Lett97, 013002 (2006).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of WindsorWindsorCanada

Personalised recommendations