A quasipotential theory for the relativistic hydrogen atom

Using a previously described relativistic quantum theory for two particles, the spectrum is calculated of an electron with spin 1/2, which is bound by Coulomb interaction to a spinless point nucleus of finite mass and charge Ze. Only states with positive energy are used in the theory. The spectrum is calculated to order α4 and includes recoil effects. In the static limit it coincides with the spectrum as calculated by the Dirac equation. Terms of order α5 lift the degeneracy between the 2S1/2 and 2P1/2 states. The critical value Zer of the nuclear charge above which the 1S1/2 state gets a binding energy larger than twice the mass of the electron, is found to be 142. This value will increase when also the nuclear structure is taken into account. (orig.)