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A formula is developed which corrects for self-interaction in the Thomas-Fermi statistical theory of the atom. By its aid it is possible to write down an effective Schrödinger equation for any separate orbital. This equation is solved for the 4f and 5f series of atoms. The results show the expected sudden contraction in mean radius at about Z = 61 and Z = 91 respectively. A short discussion is given showing the difficulty in making adequate allowance for exchange in a one-electron scheme of this kind.
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Coulson et al. (1962) studied this question.
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