Electron-pair radial sum and difference moments in atoms

Discussed are physical implications of two sets of moments 〈sn〉 and 〈tn〉 associated with the electron-pair radial sum S(s) and difference T(t) densities. The first moments 〈s〉 and 〈|t|〉 are equivalent to the sum 〈r>〉+〈r<〉 and the difference 〈r>〉-〈r<〉 of the inner 〈r<〉 and outer 〈r>〉 radii, respectively. The variances σs2=〈s2〉-〈s〉2 and σt2=〈t2〉-〈t〉2 of S(s) and T(t) are found to be connected with the statistical radial correlation coefficient τ[r] in a straightforward manner. For the 53 atoms He through Xe in their ground states and for some singly-excited states of the He atom, the first and second moments as well as the radial correlation coefficient are systematically studied at the Hartree-Fock limit level. The effect of electron correlations is also examined for the He atom and its isoelectronic ions.