The density of an atom in a state of well-defined angular momentum has a
specific finite spherical harmonic content, without and with interactions.
Approximate single-particle schemes, such as the Hartree, Hartree-Fock, and
Local Density Approximations, generally violate this feature. We analyze, by
means of perturbation theory, the degree of this violation and show that it is
small. The correct symmetry of the density can be assured by a
constrained-search formulation without significantly altering the calculated
energies. We compare our procedure to the (different) common practice of
spherically averaging the self-consistent potential. Kohn-Sham density
functional theory with the exact exchange-correlation potential has the correct
finite spherical harmonic content in its density; but the corresponding exact
single particle potential and wavefunctions contain an infinite number of
spherical harmonics.Comment: 11 pages, 6 figures. Expanded discussion of spherical harmonic
expansion of Hartree density. Some typos corrected, references adde