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An approximation to the Lamb shift and hyperfine splitting as nonlinear effective Coulomb-like interactions in the Dirac equation

S. Bruce·J. Diaz-Valdes
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Abstract

The Dirac equation for the Coulomb problem is restated by incorporating a nonlinear effective interaction into the Dirac Hamiltonian: one keeps the $1/r$ dependence for the Coulomb field, but the coupling constant is modified by a factor depending on the n (principal quantum number) power of the mean value of the Hamiltonian. In this simple context we study the Lamb shift and the hyperfine splitting of the s-levels of hydrogenic atoms. We discuss to what extent the corresponding calculations fit the energy splittings to the appropriate order in the fine structure constant.

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S. Bruce, J. Diaz-Valdes. 1999-05-20. An approximation to the Lamb shift and hyperfine splitting as nonlinear effective Coulomb-like interactions in the Dirac equation. https://arxiv.org/abs/quant-ph/9905063

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