The Slaterndash;Zener expression for the energy of an atom is generalized to include hypothetical states for which the Slater atomic shielding constants do not minimize the energy. The generalized energy expression is used with Slater's rules for atomic shielding constants to study the Koopmans' theorem ionization potential for core electrons and its dependence on nuclear charge and the number of valence electrons on an atom. An electronic relaxation energy for xhyphen;ray states is defined and is shown to be proportional to the number of electrons in shells outside the core hole, independent of nuclear charge, and quadratic in the change of shielding constant for each shell upon corehyphen;hole formation. Finally, arguments are given to show that the core hole should be thought of as localized, even when there are several equivalent atomic sites over which it may be delocalized.
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