Introduction.
Most of atomic physics is concerned with the behavior of valence electrons, where energies are of the order of the square of the fine structure constant (alpha approximately 1/137) times the rest energy of the electron, mc(2). Well-known relativistic corrections, such as fine splitting of energy levels, are smaller than usual atomic transition energies by two extra powers of the fine structure constant, and are even smaller for hyperfine splitting. In valence-electron atomic physics, therefore, relativistic effects are normally treated as small corrections.
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