Application of the S-matrix approach to the development of the perturbation theory in 1/Z

Developed is the perturbation theory in 1/Z on the basis of the S-matrix approach to the descritption of interaction between electrons. The multielectron system energy is presented as a double series in α and αZ. The method of determining coefficients of the series in the j-j-coupling scheme is presented. Also presented are numerical results for the wave lengths of the transition between several states of the isoelectron equence of hydrogen. Achieved is a substantial simplification of the calculation at the expense of the introduction of atom residue with filled shells into the electron-positron vacuum. The hole introduction into the residue reduced the problem of a considerable number of electrons to the problem with a smaller number of electrons. The residue introduction permits to use the data obtained in the LS-coupling scheme. This approach is applied to the configuration of the 1ssup(2)2ssup(n1)2psub(1/2)sup(n2)2psub(3/2)sup(n3) type, and numerical results are presented for several states to illustrate a good agreement between the theory and the experiment