Average, variance, asymmetry, excess of a spectrum

The average energy of an atom or ion in a given configuration, being the first initial moment of the energy spectrum, is widely used as one of the main characteristics of the system considered. It may be defined as follows  

Here I(nik) is given by (19.23), whereas Ee nilfi) and EfAnilf njl 1) are the average energies of electrostatic interactions in the itn shell as well as between the ith and jth shells. The latter have the following definitions  

Radial integrals Fk(nih,n2l2) and Gk(nih,n2l2) are defined by (19.31) and (20.10), respectively. Let us recall that the average value of spin-orbit interaction equals zero. 

The variance of spectrum consists of the contributions of spin-orbit and electrostatic interactions 

The spin-orbit contribution simply equals the sum of the relevant interactions in each shell of equivalent electrons 

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