Radial electron-pair densities and shell structure of atoms

The radial electron-pair intracule (relative motion) H(u) and extracule (centre-of-mass motion) D(R) densities are studied for the 102 atoms from He (atomic number Z=2) to Lr (Z=103). The radial densities H(u) and D(R) have either one or two maxima, and the numbers of maxima in H(u) and D(R) are the same for 96 atoms. For these atoms, the locations umax and Rmax and the heights Hmax and Dmax of the corresponding maxima satisfy approximate relations umax ≅ 2Rmax and Hmax ≅ Dmax /2. Based on their Z-dependence, the maxima in H(u) and D(R) of the 102 atoms are classified into four types. Subshell-pair and shell-pair decompositions of the radial densities show that these four types of maxima are related to the first four electron shells K, L, M, and N of the atoms, respectively. (author)