Complete Lamb-Shift Calculation to Order α5 without Applying the Concept of Relativistic Quantum Electrodynamics
In our previous papers nonrelativistic calculations of the Lamb shift for 1S-, 2S- and 2P-states  as well as a complete treatment of spontaneously decaying atomic state in nonrelativistic QED [where all shortcomings contained in the Weisskopf-Wigner method (gauge dependence, two-level-atom, rotating-wave, dipole and Markov approximations) were removed]  were carried out by using a new unambiguous renormalization procedure based on a new self-consistent projection-operator method developed by the author recently . The discrepancy between the relativistic and nonrelativistic results was large in the case of the 2P-state. For the first time, it will be demonstrated that the complete Lamb-shift result to order of α 5 for all states of hydrogenic atoms can be derived by applying the formalism of nonrelativistic quantum electrodynamics. This can be acomplished, in the case of non-S-states, by taking into account the spin-orbit interaction being neglected in all previous nonrelativistic calculations (see  and references quoted therein). As yet, only by using the methods of relativistic QED (Dirac equation and the second quantization for the electron) were the authors able to obtain complete Lamb-shift results to order of α 5 .