Use of S-matrix approach to develop a theory of perturbations in 1/Z

Abstract

On the basis of the S-matrix approach, a theory of perturbations in 1/Z is developed; the energy of a multielectron system is written in the form of a double series in powers ofα andαZ and a method of determining the coefficients of this series in a j-j coupling scheme is given. The method is applied to configurations of the type$1s^2 2s^{n_1 } 2p_{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^{n_2 } 2_{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}}^{n_3 }$, and numerical results are given for the wavelength of transitions between several states of the isoelectronic as sequence of carbon, illustrating the good agreement between experiment and theory.