Electron-pair shell density approximation applied to inner and outer electron radii of atoms

Abstract

The shell density approximation to the electron-pair radial density of atoms is applied to the inner 〈r<〉 and outer 〈r>〉 electron radii, which are two components of the familiar average electron radius 〈r〉. The inner and outer radii with two-electron nature are found to be expressed by simple weighted sums of single-electron shell radii, where the weight factors are related to the numbers of shell electrons. A numerical examination of the 53 atoms He through Xe shows that the average relative errors of the approximation are only 3.5% and 1.1% for the inner and outer electron radii, respectively. Lower and upper bounds to 〈r<〉 and 〈r>〉 are discussed. The present results also bound the electron-pair relative distance and centre-of-mass radius in terms of the single-electron shell radii.