The summation of the matrix elements of Hamiltonian and transition operators. The variance of the emission spectrum

The general method to obtain the explicit expressions for sums of the matrix elements of Hamiltonian and transition operators has been extended. It can be used for determining the main characteristics of atomic spectra, such as the mean energy, the variance, the asymmetry coefficient, etc., as well as for the average quantities which describe the configuration mixing. By mean of this method the formula for the variance of the emission spectrum has been derived. It has been shown that this quantity of the emission spectrum can be expressed by the variances of the energy spectra of the initial and final configurations and by additional terms, caused by the distribution of the intensity in spectrum