We show that our generalization of the Fermi-Segr\`e formula to arbitrary angular momentum, as well as a different expression obtained by Bouchiat and Bouchiat, can both be understood as limiting cases of a common form. This new expression, which connects energy and normalization, makes no explicit reference to inner, outer, or excited states properties, or to the degree of ionization of the atom. The expression also indicates that for given nuclear charge energy and the square of the normalization scale with ionic charge in the same way through an isonuclear sequence.
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Iwiński et al. (1980) studied this question.
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