An investigation of atomic structure in position and momentum space by means of "ideal shells"

For atomic systems, the boundaries in position and momentum space that enclose the exact electron number given by the aufbau principle have been numerically calculated. Their relatively irregular behavior as a function of the atomic number Z is demonstrated and explained in terms of corresponding irregularities of the aufbau principle. Direct comparisons of these radii with those derived from density functionals that are known to exhibit atomic shell structure are shown to be useful in judging the ability of the latter to define "physical" shells compatible with the aufbau principle. Keywords: atomic radii, shell structure, aufbau principle, charge density, momentum density.