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147) is obtained , the g; are replaced not by the average value, but with an eigenvalue, starting from where the series begins. This explains why the wave functions for excited states obtained without regard for the conditions given by Eq. 148) and used in many works yield results that are physically reliable. The variation principle can even be used to find the wave function of a free electron having kinetic energy e, orbital angular momentum L, and moving in the field of an atom . 152) (only the negative oneelectron energy _l/zenl ,nl changes by the positive energy e) n The expressions for Vefr) and Kefr) correspond to the replacement n -+ e and the substitution N = 1 in Eqs.

148) by way of incorporating the respective Lagrangian multipliers into the Hartree - Fock 40 Chapter 1 equations, but this substantially complicates the calculations and leads to an increase in the error [63]. For the case of highly excited states with internal vacancies, which have a large number of lower states with the same symmetry, this method is unusable in practice . The orthogonality condition can also be satisfied when a special function that is nonlinear in H is used [64], but this involves significant labor in the calculations .

207) is found for the relativistic operator 0 ' , An expression was obtained in [74] for the effective Breit interaction operator which contains two-electron operators of the ([at x Fundamentals of Atomic Theory a](klk2k )· [a t X a](kl 'k2 'k» 51 type (the orbital and spin ranks are combined into a common rank), 6j- and 9j-symbols, and relativistic radial integrals. , f j(2j+ I), g(j, } )=1 if n=n', /=/', l (2j+ 1)(2j'+ I) otherwise. 211) where K) and K h denote the lowest and highest subconfigurations, and c)l.

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