General consideration of electronic transitions in many-electron atoms and ions

The relativistic electric multipole transition operators are considered, not specifying the gauge condition of the electromagnetic field potential. The nonrelativistic limit of the relativistic expressions obtained is found. The relativistic corrections to various forms of the electric dipole transition operators are investigated. The electric multipole transition operator contains an arbitrary parameter, the gauge constant, dependence on which can serve as one of the criteria for the accuracy of the wavefunctions used. Calculated examples of the theory, starting with the general expressions found, are presented. The methods described and the formulae presented allow the authors to investigate in an effective way the electric multipole transitions for atoms and their isoelectronic sequences, including very highly ionised atoms.