Lamb Shift -- from Eric Weisstein's World of Physics

Lamb Shift

Quantum electrodynamics requires an absence of vacuum polarization near the nucleus of a hydrogen atom. This means that the s state is slightly higher in energy than the p state. This result is known as the Lamb shift, and is given by

(Griffiths 1987, p. 156), where is the fine structure constant, is the electron mass, c is the speed of light, n is the principal quantum number, l is the azimuthal quantum number, and k(n,l) is a small number (; Bethe and Salpeter 1977, pp. 99 and 318-320) depending on n and l, and j is the total angular momentum quantum number.

The best measurement to date for the hydrogen atom is . This is in good agreement with quantum electrodynamics using the larger of the two current proton radius measurements of 0.862 ± 0.012 fm (Berkeland et al. 1995).

Hydrogen Atom, Hyperfine Splitting, Quantum Electrodynamics

References

Berkeland, D. J.; Hinds, E. A.; and Boshier, M. G. "Precise Optical Measurement of Lamb Shifts in Atomic Hydrogen." Phys. Rev. Let. 75, 2470-2473, 1995.

Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms. New York: Plenum, pp. 104-107, 1977.

Bjorken, J. D. and Drell, S. D. Relativistic Quantum Mechanics. New York: McGraw-Hill, pp. 56-57, 1964.

Feynman, R. P. In Proc. 1961 Solvay Conf. New York: Interscience, 1962.

Griffiths, D. J. "The Lamb Shift." §5.4 in Introduction to Elementary Particles. New York: Wiley, pp. 154-156, 1987.

Lamb, W. E. Jr. Rep. Progr. Phys. 14, 19, 1951.

Lamb, W. E. Jr. and Retherford, C. Phys. Rev. 72, 241, 1947.

Messiah, A. Quantum Mechanics, Vol. 2. Amsterdam, Netherlands: North-Holland, p. 933, 1962.

Sommerfeld, A. Phys. Rev. 107, 328, 1957.

Welton, T. A. Phys. Rev. 74, 1157, 1948.