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External Field Approximation

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Theory of Light Hydrogenic Bound States

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 222))

Abstract

We will first discuss corrections to the basic Dirac energy levels which arise in the external field approximation. These are leading relativistic corrections with exact mass dependence and radiative corrections.

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References

  1. G. Breit, Phys. Rev. 34, 553 (1929); ibid 36, 383 (1930); ibid 39, 616 (1932).

    Article  ADS  MathSciNet  Google Scholar 

  2. W. A. Barker and F. N. Glover, Phys. Rev. 99, 317 (1955).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum electrodynamics, 2nd Edition, Pergamon Press, Oxford, 1982.

    Google Scholar 

  4. H. Grotch and D. R. Yennie, Zeitsch. Phys. 202, 425 (1967).

    Article  ADS  Google Scholar 

  5. H. Grotch and D. R. Yennie, Rev. Mod. Phys. 41, 350 (1969).

    Article  ADS  Google Scholar 

  6. P. Lepage, Phys. Rev. A 16, 863 (1977).

    Article  ADS  Google Scholar 

  7. J. R. Sapirstein and D. R. Yennie, in Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore, 1990), p. 560.

    Google Scholar 

  8. H. A. Bethe, Phys. Rev. 72, 339 (1947).

    Article  ADS  Google Scholar 

  9. N. M. Kroll and W. E. Lamb, Phys. Rev. 75, 388 (1949).

    Article  MATH  ADS  Google Scholar 

  10. J. B. French and V. F. Weisskopf, Phys. Rev. 75, 1240 (1949).

    Article  MATH  ADS  Google Scholar 

  11. G. Bhatt and H. Grotch, Phys. Rev. A 31, 2794 (1985).

    Article  ADS  Google Scholar 

  12. G. Bhatt and H. Grotch, Ann. Phys. (NY) 178, 1 (1987).

    Article  ADS  Google Scholar 

  13. S. E. Haywood and J. D. Morgan III, Phys. Rev. A 32, 3179 (1985).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. J. Schwinger, Phys. Rev. 73, 416 (1948).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. E. A. Uehling, Phys. Rev. 48, 55 (1935).

    Article  MATH  ADS  Google Scholar 

  17. J. Weneser, R. Bersohn, and N. M. Kroll, Phys. Rev. 91, 1257 (1953).

    Article  MATH  ADS  Google Scholar 

  18. M. F. Soto, Phys. Rev. Lett. 17, 1153 (1966); Phys. Rev. A 2, 734 (1970).

    Article  ADS  Google Scholar 

  19. T. Appelquist and S. J. Brodsky, Phys. Rev. Lett. 24, 562 (1970); Phys. Rev. A 2, 2293 (1970).

    Article  ADS  Google Scholar 

  20. B. E. Lautrup, A. Peterman, and E. de Rafael, Phys. Lett. B 31, 577 (1970).

    Article  ADS  Google Scholar 

  21. R. Barbieri, J. A. Mignaco and E. Remiddi, Lett. Nuovo Cimento 3, 588 (1970).

    Article  Google Scholar 

  22. A. Peterman, Phys. Lett. B 34, 507 (1971); ibid. 35, 325 (1971)

    Article  ADS  Google Scholar 

  23. J. A. Fox, Phys. Rev. D 3, 3228 (1971); ibid. 4, 3229 (1971); ibid. 5, 492 (1972).

    Article  ADS  Google Scholar 

  24. R. Barbieri, J. A. Mignaco and E. Remiddi, Nuovo Cimento A 6, 21 (1971).

    Article  ADS  Google Scholar 

  25. E. A. Kuraev, L. N. Lipatov, and N. P. Merenkov, preprint LNPI 46, June 1973.

    Google Scholar 

  26. R. Karplus and N. M. Kroll, Phys. Rev. 77, 536 (1950).

    Article  MATH  ADS  Google Scholar 

  27. A. Peterman, Helv. Phys. Acta 30, 407 (1957); Nucl. Phys. 3, 689 (1957).

    Google Scholar 

  28. C. M. Sommerfield, Phys. Rev. 107, 328 (1957); Ann. Phys. (NY) 5, 26 (1958).

    Article  ADS  Google Scholar 

  29. M. Baranger, F. J. Dyson, and E. E. Salpeter, Phys. Rev. 88, 680 (1952).

    Article  ADS  MATH  Google Scholar 

  30. G. Kallen and A. Sabry, Kgl. Dan. Vidensk. Selsk. Mat.-Fis. Medd. 29 (1955) No.17.

    Google Scholar 

  31. J. Schwinger, Particles, Sources and Fields, Vol.2 (Addison-Wesley, Reading, MA, 1973).

    Google Scholar 

  32. K. Melnikov and T. van Ritbergen, Phys. Rev. Lett. 84, 1673 (2000).

    Article  ADS  Google Scholar 

  33. T. Kinoshita, in Quantum Electrodynamics, ed. T. Kinoshita (World Scientific, Singapore, 1990), p. 218.

    Google Scholar 

  34. S. Laporta and E. Remiddi, Phys. Lett. B 379, 283 (1996).

    Article  ADS  Google Scholar 

  35. P. A. Baikov and D. J. Broadhurst, preprint OUT-4102-54, hep-ph 9504398, April 1995, published in the proceedings New Computing Technique in Physics Research IV, ed. B. Denby and D. Perret-Gallix, World Scientific, 1995.

    Google Scholar 

  36. M. I. Eides and H. Grotch, Phys. Rev. A 52, 3360 (1995).

    Article  ADS  Google Scholar 

  37. S. G. Karshenboim, J. Phys. B: At. Mol. Opt. Phys. 28, L77 (1995).

    Article  ADS  Google Scholar 

  38. M. I. Eides and V. A. Shelyuto, Phys. Rev. A 52, 954 (1995).

    Article  ADS  Google Scholar 

  39. J. L. Friar, J. Martorell, and D. W. L. Sprung, Phys. Rev. A 59, 4061 (1999).

    Article  ADS  Google Scholar 

  40. R. Karplus, A. Klein, and J. Schwinger, Phys. Rev. 84, 597 (1951).

    Article  ADS  Google Scholar 

  41. R. Karplus, A. Klein, and J. Schwinger, Phys. Rev. 86, 288 (1952).

    Article  MATH  ADS  Google Scholar 

  42. M. Baranger, Phys. Rev. 84, 866 (1951); M. Baranger, H. A. Bethe, and R. Feynman, Phys. Rev. 92, 482 (1953).

    Article  MATH  ADS  Google Scholar 

  43. A. A. Abrikosov, Zh. Eksp. Teor. Fiz. 30, 96 (1956) [Sov. Phys.-JETP 3, 71 (1956)].

    MathSciNet  Google Scholar 

  44. H. M. Fried and D. R. Yennie, Phys. Rev. 112, 1391 (1958).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  45. S. G. Karshenboim, V. A. Shelyuto, and M. I. Eides, Yad. Fiz. 47, 454 (1988) [Sov. J. Nucl. Phys. 47, 287 (1988)].

    Google Scholar 

  46. M. I. Eides, H. Grotch, and D. A. Owen, Phys. Lett. B 294, 115 (1992).

    Article  ADS  Google Scholar 

  47. K. Pachucki, Phys. Rev. A 48, 2609 (1993).

    Article  ADS  Google Scholar 

  48. S. Laporta, as cited in [47].

    Google Scholar 

  49. M. I. Eides and H. Grotch, Phys. Lett. B 301, 127 (1993).

    Article  ADS  Google Scholar 

  50. M. I. Eides and H. Grotch, Phys. Lett. B 308, 389 (1993).

    Article  ADS  Google Scholar 

  51. M. I. Eides, H. Grotch, and V. A. Shelyuto, Phys. Rev. A 55, 2447 (1997).

    Article  ADS  Google Scholar 

  52. M. I. Eides, H. Grotch, and P. Pebler, Phys. Lett. B 326, 197 (1994); Phys. Rev. A 50, 144 (1994).

    Article  ADS  Google Scholar 

  53. M. I. Eides, S. G. Karshenboim, and V. A. Shelyuto, Phys. Lett. B 312, 358 (1993); Yad. Phys. 57, 1309 (1994) [Phys. Atom. Nuclei 57, 1240 (1994)].

    Article  ADS  Google Scholar 

  54. M. I. Eides, S. G. Karshenboim, and V. A. Shelyuto, Yad. Phys. 57, 2246 (1994) [Phys. Atom. Nuclei 57, 2158 (1994)].

    Google Scholar 

  55. K. Pachucki, Phys. Rev. Lett. 72, 3154 (1994).

    Article  ADS  Google Scholar 

  56. M. I. Eides and V. A. Shelyuto, Pis’ma Zh. Eksp. Teor. Fiz. 61, 465 (1995) [JETP Letters 61, 478 (1995)].

    ADS  Google Scholar 

  57. K. Pachucki, D. Leibfried, M. Weitz, A. Huber, W. König, and T. W. Hänch, J. Phys. B 29, 177 (1996); 29, 1573(E) (1996).

    Article  ADS  Google Scholar 

  58. M. I. Eides and V. A. Shelyuto, Phys. Rev. A 68, 042106 (2003).

    Article  ADS  Google Scholar 

  59. M. I. Eides and V. A. Shelyuto, Phys. Rev. A 70, 022506 (2004).

    Article  ADS  Google Scholar 

  60. A. J. Layzer, Phys. Rev. Lett. 4, 580 (1960); J. Math. Phys. 2, 292, 308 (1961).

    Article  ADS  Google Scholar 

  61. H. M. Fried and D. R. Yennie, Phys. Rev. Lett. 4, 583 (1960).

    Article  ADS  Google Scholar 

  62. G. W. Erickson and D. R. Yennie, Ann. Phys. (NY) 35, 271 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  63. G. W. Erickson and D. R. Yennie, Ann. Phys. (NY) 35, 447 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  64. G. W. Erickson, Phys. Rev. Lett. 27, 780 (1971).

    Article  ADS  Google Scholar 

  65. P. J. Mohr, Phys. Rev. Lett. 34, 1050 (1975); Phys. Rev. A 26, 2338 (1982).

    Article  ADS  Google Scholar 

  66. J. R. Sapirstein, Phys. Rev. Lett. 47, 1723 (1981).

    Article  ADS  Google Scholar 

  67. V. G. Pal’chikov, Metrologia 10, 3 (1987) /in Russian/.

    Google Scholar 

  68. L. Hostler, J. Math. Phys. 5, 1235 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  69. J. Schwinger, J. Math. Phys. 5, 1606 (1964).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  70. K. Pachucki, Phys. Rev. A 46, 648 (1992).

    Article  ADS  Google Scholar 

  71. K. Pachucki, Ann. Phys. (NY) 236, 1 (1993).

    Article  ADS  Google Scholar 

  72. S. S. Schweber, QED and the Men Who Made It, Princeton University Press, 1994.

    Google Scholar 

  73. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics, McGraw-Hill Book Co., NY, 1964.

    Google Scholar 

  74. E. E. Salpeter, Phys. Rev. 87, 553 (1952).

    Article  Google Scholar 

  75. T. Fulton and P. C. Martin, Phys. Rev. 95, 811 (1954).

    Article  MATH  ADS  Google Scholar 

  76. I. B. Khriplovich, A. I. Milstein, and A. S. Yelkhovsky, Physica Scripta, T46, 252 (1993).

    Article  ADS  Google Scholar 

  77. W. E. Caswell and G. P. Lepage, Phys. Lett. B 167, 437 (1986).

    Article  ADS  Google Scholar 

  78. J. A. Fox and D. R. Yennie, Ann. Phys. (NY) 81, 438 (1973).

    Article  ADS  Google Scholar 

  79. K. Pachucki, as cited in [112].

    Google Scholar 

  80. A. Czarnecki, U. D. Jentschura, and K. Pachucki, Phys. Rev. Lett. 95, 180404 (2005).

    Article  ADS  Google Scholar 

  81. U. D. Jentschura, A. Czarnecki, and K. Pachucki, Phys. Rev. A 72, 062102 (2005).

    Article  ADS  Google Scholar 

  82. U. Jentschura and K. Pachucki, Phys. Rev. A 54, 1853 (1996).

    Article  ADS  Google Scholar 

  83. U. Jentschura, G. Soff, and P. J. Mohr, Phys. Rev. A 56, 1739 (1997).

    Article  ADS  Google Scholar 

  84. U. D. Jentschura, E.-O. Le Bigot, P. J. Mohr, et al, Phys. Rev. Lett. 90, 163001 (2003).

    Article  ADS  Google Scholar 

  85. E.-O. Le Bigot, U. D. Jentschura, P. J. Mohr, et al, Phys. Rev. A 68, 042101 (2003).

    Article  ADS  Google Scholar 

  86. R. Serber, Phys. Rev. 48, 49 (1935).

    Article  MATH  ADS  Google Scholar 

  87. E. H. Wichmann and N. M. Kroll, Phys. Rev. 101, 843 (1956).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  88. V. G. Ivanov and S. G. Karshenboim, Yad. Phys. 60, 333 (1997) [Phys. Atom. Nuclei 60, 270 (1997)].

    Google Scholar 

  89. N. L. Manakov, A. A. Nekipelov, and A. G. Fainstein, Zh. Eksp. Teor. Fiz. 95, 1167 (1989) [Sov.Phys.-JETP 68, 673 (1989)].

    Google Scholar 

  90. M. H. Mittleman, Phys. Rev. 107, 1170 (1957).

    Article  ADS  Google Scholar 

  91. D. E. Zwanziger, Phys. Rev. 121, 1128 (1961).

    Article  ADS  Google Scholar 

  92. P. J. Mohr, At. Data and Nucl. Data Tables, 29, 453 (1983).

    Article  ADS  Google Scholar 

  93. P. J. Mohr, in Beam-Foil Spectroscopy, ed. I. A. Sellin and D. J. Pegg (Plenum Press, New York, 1976), Vol. 1, p. 89.

    Google Scholar 

  94. L. D. Landau and E. M. Lifshitz, “Quantum Mechanics”, 3d Edition, Butterworth-Heinemann, 1997.

    Google Scholar 

  95. S. G. Karshenboim, Zh. Eksp. Teor. Fiz. 103, 1105 (1993) [JETP 76, 541 (1993)].

    Google Scholar 

  96. S. Mallampalli and J. Sapirstein, Phys. Rev. Lett. 80, 5297 (1998).

    Article  ADS  Google Scholar 

  97. I. Goidenko, L. Labzowsky, A. Nefiodov et al, Phys. Rev. Lett. 83, 2312 (1999).

    Article  ADS  Google Scholar 

  98. V. A. Yerokhin, Phys. Rev. A 62, 012508 (2000).

    Article  ADS  Google Scholar 

  99. A. V. Manohar and I. W. Stewart, Phys. Rev. Lett. 85, 2248 (2000).

    Article  ADS  Google Scholar 

  100. V. A. Yerokhin, Phys. Rev. Lett. 86, 1990 (2001).

    Article  ADS  Google Scholar 

  101. K. Pachucki, Phys. Rev. A 63, 042503 (2001).

    Article  ADS  Google Scholar 

  102. U. Jentschura and I. Nándori, Phys. Rev. A 66, 022114 (2002).

    Article  ADS  Google Scholar 

  103. U. D. Jentschura, Phys. Lett. B 564, 225 (2003).

    Article  ADS  Google Scholar 

  104. S. G. Karshenboim, Zh. Eksp. Teor. Fiz. 109, 752 (1996) [JETP 82, 403 (1996)].

    Google Scholar 

  105. S. G. Karshenboim, J. Phys. B: At. Mol. Opt. Phys, 29, L29 (1996).

    Article  ADS  Google Scholar 

  106. S. G. Karshenboim, Yad. Phys. 58, 707 (1995) [Phys. Atom. Nuclei 58, 649 (1995)].

    Google Scholar 

  107. S. G. Karshenboim, Zh. Eksp. Teor. Fiz. 106, 414 (1994) [JETP 79, 230 (1994)].

    Google Scholar 

  108. U. D. Jentschura, J. Phys. A: Math. Gen. 36, L229 (2003).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  109. K. Pachucki and U. Jentschura, Phys. Rev. Lett. 91, 113005 (2003).

    Article  ADS  Google Scholar 

  110. U. D. Jentschura, Phys. Rev. A 70, 052108 (2004).

    Article  ADS  Google Scholar 

  111. D. R. Yennie, S. C. Frautchi, and H. Suura, Ann. Phys. (NY) 13, 379 (1961).

    Article  ADS  Google Scholar 

  112. U. Jentschura, P. J. Mohr, and G. Soff, Phys. Rev. Lett. 82, 53 (1999).

    Article  ADS  Google Scholar 

  113. P. J. Mohr and Y.-K. Kim, Phys. Rev. A 45, 2727 (1992).

    Article  ADS  Google Scholar 

  114. P. J. Mohr, Phys. Rev. A 46, 4421 (1992).

    Article  ADS  Google Scholar 

  115. A. van Wijngaarden, J. Kwela, and G. W. F. Drake, Phys. Rev. A 43, 3325 (1991).

    Article  ADS  Google Scholar 

  116. P. J. Mohr, Phys. Rev. A 44, R4089 (1991); Errata A 51, 3390 (1995).

    Article  ADS  Google Scholar 

  117. P. J. Mohr, in Atomic, Molecular and Optical Physics Handbook, ed. G.W. F. Drake, AIP Press, 1996, p. 341.

    Google Scholar 

  118. S. G. Karshenboim, Yad. Phys. 58, 309 (1995) [Phys. Atom. Nuclei 58, 262 (1995)].

    Google Scholar 

  119. U. D. Jentschura, P. J. Mohr, and G. Soff, Phys. Rev. A 63, 042512 (2001).

    Article  ADS  Google Scholar 

  120. U. D. Jentschura and P. J. Mohr, Phys. Rev. A 69, 064103 (2004).

    Article  ADS  Google Scholar 

  121. U. D. Jentschura and P. J. Mohr, Phys. Rev. A 72, 014103 (2005).

    Article  ADS  Google Scholar 

  122. S. G. Karshenboim, Can. J. Phys. 76, 169 (1998); Zh. Eksp. Teor. Fiz. 116, 1575 (1999) [JETP 89, 850 (1999)].

    Article  ADS  Google Scholar 

  123. V. A. Yerokhin, P. Indelicato, and V. M. Shabaev, Phys. Rev. A 71, 040101(R) (2005).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Kentucky, Lexington, KY, 40506, U.S.A.

    Michael I. Eides & Howard Grotch

  2. Mendeleev Institute for Metrology, Moskovsky Pr. 19, 190005, St. Petersburg, Russia

    Valery A. Shelyuto

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  1. Michael I. Eides
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Eides, M.I., Grotch, H., Shelyuto, V.A. (2007). External Field Approximation. In: Theory of Light Hydrogenic Bound States. Springer Tracts in Modern Physics, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45270-2_3

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