The radial charge distribution and the shell structure of atoms and ions

The radial charge distribution, D(r), for the neutral atoms, hydrogen through uranium, and the singly positive ions, helium through barium and lutetium through radium, are computed from the non-relativistic SCF wavefunctions of Clementi and Roetti and McLean and McLean. The radial charge distribution is examined to see how effective it is for the determination of the shell structure of an atom or an ion with the results indicating that the maxima are the topological features of D(r) most indicative of shells. At most five shells are apparent based on the criterion that the maxima in D (r) correspond to the shells. The positions of the maxima in D(r) are shown to correlate well with the shell radii from the Bohr–Schrödinger theory of an atom. The small deviations are consistent with the shielding of the outer electrons from the nucleus, by the inner electrons. Furthermore, it is shown that the effects of shielding are more pronounced on the values of the radial distribution function at the extremal points. The spherically averaged charge density, [Formula: see text] is seen to be monotonically decreasing for all these ground states, a result which extends the previously known range of atomic systems for which this is true.