Hyperfine Shifts, Radiative Corrections
Atomic fine and hyperfine structures are normally small and may be treated as perturbations of the nonrelativistic Schrödinger Hamiltonian. However, many level splittings are measured so precisely that their calculation would require second-order and even third-order perturbation theory. It is then much easier to take the fine structure from the Dirac equation, and to calculate the hyperfine structure as a perturbation of the Dirac equation. The experimental hyperfine splittings of the hydrogen and muonium ground states are 1 420 405.751767 kHz and 4 463 302.8 kHz, respectively (1 kHz 4.1357 × 10-12 eV). For such cases, the first-order hyperfine splitting of the Dirac equation follows from (5.11) below to all orders in αz.
KeywordsDirac Equation Radiative Correction Vacuum Polarization Lamb Shift Quantum Defect
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