The self-consistent theory of hyperfine atomic structure is developed. The theory is based on Lorentz and gauge invariant equation for action of spin 1/2 particle. The specific feature of proposed equation for action (or Lagrangian) is that it is enable to introduce the three material constants: mass m 0 , charge q, and magneton (i.e. magnitude of magnetic moment) Β΅. The analytically tractable solutions of the wave equation for the electron motion in Coulomb field and electron motion in uniform magnetic field are found. In both cases the calculated spectra include the hyperfine splitting that is agreed well with the experimentally observed spectra. The calculated frequencies of 8(12)d 3/2 -8(12)d 5/2 transitions in hydrogen atom are compared with the results of experimental measurements by the highprecision spectroscopy methods. It is shown that the results of calculations are in good agreement with the experimentally measured data.
Profile of magnetic field of response for different electron states in external uniform magnetic field: n = 1, m = 1, Ο = -1 (a); n = 0, m = 0, Ο = -1 (g)