Abstract
The model problem of atomic closed shells in a bare Coulomb field has been the subject of considerable interest following the recent demonstration by Blinder [Phys. Rev. A 29, 1674 (1984)], with subsequent generalization by March [Phys. Lett. 111A, 47 (1985)], that the electron density in an arbitrary closed shell in a bare Coulomb field is expressible solely in terms of its s-state contribution. The present paper will provide a simple derivation of this important relationship by application of the methods of supersymmetric quantum mechanics to the radial Coulomb problem. Using this relation, differential equations are derived which are satisfied by the electron density for an arbitrary closed shell and the Slater sum for an arbitrary number of closed shells in a bare Coulomb field.
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