SUPERSYMMETRIC QUANTUM-MECHANICAL APPROACH TO ATOMIC CLOSED SHELLS INA BARE COULOMB FIELD

The model problem of atomic closed shells in a bare Coulomb field has been the subject of considerable interest following the recent demonst ration by Blinder [Phys. Rev. A 29, 1674 (1984)], with subsequent gene ralization by March [Phys. Lett. 111A, 47 (1985)], that the electron d ensity in an arbitrary closed shell in a bare Coulomb field is express ible solely in terms of its s-state contribution. The present paper wi ll provide a simple derivation of this important relationship by appli cation of the methods of supersymmetric quantum mechanics to the radia l Coulomb problem. Using this relation, differential equations are der ived which are satisfied by the electron density for an arbitrary clos ed shell and the Slater sum for an arbitrary number of closed shells i n a bare Coulomb field.