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High Precision Atomic Theory: Tests of Fundamental Understanding

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Modeling and Numerical Simulations

Part of the book series: Modern Aspects of Electrochemistry ((MAOE,volume 43))

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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.

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References

  1. W. Sheehan, N. Kollerstone, and C.B. Waff, The Case of the Pilfered Planet, Scientific American, December (2004).

    Google Scholar 

  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. 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. The latest values of the fundamental constants can be downloaded from the web site http://physics.nist.gov/cuu/Constants/index.html.

  5. E.A. Hylleraas, Z. Phys48, 469 (1928); 54, 347 (1929). See also ibid., Rev. Mod. Phys35, 421 (1963).

    Google Scholar 

  6. 6. E.A. Hylleraas and B. Undheim, Z. Phys65, 759 (1930).

    Article  CAS  Google Scholar 

  7. 7. J.K.L. MacDonald, Phys. Rev43, 830 (1933).

    Article  Google Scholar 

  8. 8. R.N. Hill, Int. J. Quantum Chem68, 357 (1998).

    Article  CAS  Google Scholar 

  9. 9. B. Klahn and W.A. Bingel, Theor. Chem. Acta 44, 27 (1977); Int. J. Quantum Chem11, 943 (1978).

    Article  CAS  Google Scholar 

  10. 10. Y. Accad, C.L. Pekeris, and B. Schiff, Phys. Rev. A 4, 516 (1971).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  13. 13. G.W.F. Drake, Adv. At. Mol. Opt. Phys31, 1 (1993).

    CAS  Google Scholar 

  14. 14. G.W.F. Drake, M.M. Cassar, and R.A. Nistor, Phys. Rev. A 65, 054501 (2002).

    Article  Google Scholar 

  15. 15. V.I. Korobov, Phys. Rev. A 66, 024501 (2002).

    Article  Google Scholar 

  16. 16. C. Schwartz, Int. J. Mod. Phys. E – Nucl. Phys15, 877 (2006).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  18. 18. A. Bürgers, D. Wintgen, and J.-M. Rost, J. Phys. B: At. Mol. Opt. Phys28, 3163 (1995).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  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. J. Ackermann and J. Shertzer, Phys. Rev. A 54, 365 (1996), and earlier references therein.

    Article  CAS  Google Scholar 

  22. 22. C.-Y. Hu, A.A. Kvitsinsky, and J.S. Cohen, J. Phys. B 28, 3629 (1995), and earlier references therein.

    Article  CAS  Google Scholar 

  23. 23. E.Z. Liverts, M.Y. Amusia, R. Krivec, and V.B. Mandelzweig, Phys. Rev. A 73, 012514 (2006), and earlier references therein.

    Article  Google Scholar 

  24. 24. J.S. Sims and S.A. Hagstrom, Int. J. Quantum Chem90, 1600 (2002).

    Article  CAS  Google Scholar 

  25. 25. S. Chakraborty and Y.K. Ho, Chem. Phys. Lett438, 99 (2007).

    Article  CAS  Google Scholar 

  26. 26. Z.-C. Yan and G.W.F. Drake, Phys. Rev. Lett81, 774 (1998).

    Article  CAS  Google Scholar 

  27. 27. Z.-C. Yan and G.W.F. Drake, Phys. Rev. A 66, 042504 (2002).

    Article  Google Scholar 

  28. 28. Z.-C. Yan and G.W.F. Drake, Phys. Rev. Lett91, 113004 (2003).

    Article  Google Scholar 

  29. 29. M. Puchalski and K. Pachucki, Phys. Rev. A 73, 022503 (2006).

    Article  Google Scholar 

  30. 30. M. Puchalski, A.M. Moro, and K. Pachucki, Phys. Rev. Lett97, 133001 (2006).

    Article  CAS  Google Scholar 

  31. 31. K. Pachucki and J. Komasa, J. Chem. Phys125, 204304 (2006).

    Article  Google Scholar 

  32. 32. K. Pachucki, Phys. Rev. A 74, 022512 (2006).

    Article  Google Scholar 

  33. 33. K. Pachucki, Phys. Rev. A 74, 062510 (2006).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  35. 35. G.W.F. Drake, Adv. At. Mol. Opt. Phys31, 1 (1993).

    CAS  Google Scholar 

  36. 36. A.K. Bhatia and A. Temkin, Phys. Rev137, 1335 (1965).

    Article  CAS  Google Scholar 

  37. 37. A.K. Bhatia and R.J. Drachman, Phys. Rev. A 35, 4051 (1987).

    Article  CAS  Google Scholar 

  38. 38. A.K. Bhatia and R.J. Drachman, J. Phys. B: At. Mol. Opt. Phys36, 1957 (2003).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  40. J. Sapirstein and K.T. Cheng, Can. J. Phys85 (2007).

    Google Scholar 

  41. 41. M.I. Eides, H. Grotch, and V.A. Shelyuto, Phys. Rep342, 63–261 (2001).

    Google Scholar 

  42. 42. P.K. Kabir and E.E. Salpeter, Phys. Rev108, 1256 (1957).

    Article  CAS  Google Scholar 

  43. 43. H. Araki, Prog. Theor. Phys17, 619 (1957).

    Article  CAS  Google Scholar 

  44. 44. J. Sucher, Phys. Rev109, 1010 (1958).

    Article  CAS  Google Scholar 

  45. 45. G.W.F. Drake, Adv. At. Mol. Phys18, 399 (1982).

    Article  CAS  Google Scholar 

  46. 46. G.W.F. Drake and W.C. Martin, Can. J. Phys76, 679 (1998).

    Article  CAS  Google Scholar 

  47. 47. M. Douglas and N.M. Kroll, Ann. Phys. (N. Y.), 82, 89 (1974).

    Article  CAS  Google Scholar 

  48. 48. V. Korobov and A. Yelkhovsky, Phys. Rev. Lett87 193003 (2001); A. Yelkhovsky, Phys. Rev. A 64, 062104 (2001).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  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).

    Article  CAS  Google Scholar 

  53. 53. C. Dorrer, F. Nez, B. de Beauvoir, L. Julien, and F. Biraben, Phys. Rev. Lett78, 3658 (1997).

    Article  CAS  Google Scholar 

  54. 54. C.J. Sansonetti and W.C. Martin, Phys. Rev. A 29, 159 (1984).

    Article  CAS  Google Scholar 

  55. 55. D.C. Morton, Q.X. Wu, and G.W.F. Drake, Can. J. Phys84, 83 (2006), and earlier references therein.

    Article  CAS  Google Scholar 

  56. 56. P.C. Pastor, G. Giusfredi, P. De Natale, G. Hagel, C. de Mauro, and M. Inguscio, Phys. Rev. Lett92, 023001 (2004).

    Article  Google Scholar 

  57. 57. G.W.F. Drake and S.P. Goldman, Can. J. Phys77, 835 (1999).

    Article  CAS  Google Scholar 

  58. 58. G.W.F. Drake, Phys. ScrT95, 22 (2001).

    Article  CAS  Google Scholar 

  59. G.W.F. Drake and Z.-C. Yan, Can. J. Phys85 (2007).

    Google Scholar 

  60. 60. G.W.F. Drake, Can. J. Phys80, 1195 (2002).

    Article  CAS  Google Scholar 

  61. 61. K. Pachucki and J. Sapirstein, J. Phys. B: At. Mol. Opt. Phys35, 1783 (2002).

    Article  CAS  Google Scholar 

  62. 62. K. Pachucki, Phys. Rev. Lett97, 013002 (2006).

    Article  Google Scholar 

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Authors and Affiliations

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

    G. W. F. Drake, Qixue Wu & Zheng Zhong

Authors
  1. G. W. F. Drake
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  2. Qixue Wu
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  3. Zheng Zhong
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Correspondence to G. W. F. Drake .

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Drake, G.W.F., Wu, Q., Zhong, Z. (2008). High Precision Atomic Theory: Tests of Fundamental Understanding. In: Modeling and Numerical Simulations. Modern Aspects of Electrochemistry, vol 43. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49582-8_2

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