Abstract
By applying a method which exploits the O(4) symmetry of the nonrelativistic hydrogen atom, the Lamb shift is calculated without making the dipole approximation. Similar calculations in the dipole approximation have been previously carried out by Lieber. The advantage of our calculations is that, without introducing a cutoff-frequency, analytical and numerical results for energy-level (Lamb) shifts, in which the self-energy of the free electron is completely separated, are obtained. Since the obtained results are finite, the significance of the retardation effects is clearly demonstrated. Furthermore, a comparison is also made with the results obtained by other authors.
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References
Bethe, H. A., Phys. Rev. 72, 339 (1947).
Au, C. K. and Feinberg, G., Phys. Rev. A 9, 1794 (1974); Addendum and erratum: Phys. Rev. A 12, 1722, 1733 (1975).
Seke, J. and Herfort, W., Phys. Rev. A 38, 833 (1988); Lett. Math. Phys. 18, 185 (1989); Lett. Math. Phys. 18, 247 (1989); Seke, J., Phys. Rev. A 45, 542 (1992).
Gavrila, M. and Costescu, A., Phys. Rev. A 2, 1752 (1970).
Schwinger, J., J. Math. Phys. 5, 1606 (1964).
Lieber, M., Phys. Rev. 174, 2037 (1968).
Fock, V., Z. Phys. 98, 145 (1935).
Englefield, M. J., Group Theorie and the Coulomb Problem, Wiley, New York, 1972.
McIntyre, D. H., Beausoleil, R. G., Foot, C. J., Hildum, E. A., Couillaud, B. C., and Hänsch, T. W., Phys. Rev. A 39, 4591 (1989).
Erickson, G. W. and Yennie, D. R., Ann. Phys. 35, 271 (1965).
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Seke, J., Mödritsch, W. Nonrelativistic calculation of the Lamb shift without applying the dipole approximation. Lett Math Phys 24, 115–124 (1992). https://doi.org/10.1007/BF00402675
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DOI: https://doi.org/10.1007/BF00402675