Transition matrices for the theory of spectra. Techniques for their construction and calculation

Analytical techniques are developed for constructing nth-order (i.e., n-electron) tensor matrices pertaining to transitions of an N-electron atom between two of its stationary states. These matrices serve to calculate the transition amplitude for the atom under the influence of an external field acting on n electrons (typically $n=1$). Their calculation requires, in turn, the solution of a truncated hierarchy of Schr\"odinger equations introduced in the preceding paper. The techniques presented here are applied to construct the matrices and their Schr\"odinger equation for the example of Ar atoms treated in the preceding paper.