Relativistic perturbation method for two-electron systems

The perturbation theory on the relativistic basis has been applied to calculate the energies of two-electron systems. The results for the energy of noninteracting electrons have been taken from the work by Johnson and Soff. For the first order both a precise calculation has been made and an αZ-expansion has been obtained. For the second order a precise calculation of the nonrelativistic limit is available, i.e. that of the first term of the αZ-expansion. Subsequent terms of the αZ-expansion have been evaluated on the basis of the screening constant method. General formulae for the first and second orders for any states of a two-electron system are given. Numerical results of the ionisation potential are given for the states 1 s 2 ½ , 1 s ½ 2 s ½ , 1 s ½ 2 p j with Z = 10-100.