Electron-pair radial sum and difference density functions

For deeper understanding of electron-electron radial holes, we introduce and discuss electron-pair radial sum S(s) and difference T(t) density functions, which respectively represent the probability densities for the radial sum s=r(1)+r(2) and difference t=r(1)-r(2) variables of two electrons. Fundamental properties of the densities S(s) and T(t) are clarified. The appearance of radial holes given by T(0)=0 is shown to have a nontrivial effect on the sum density S(s) as well. Numerical illustrations are given for the 1s2s (1)S and (3)S states of the helium atom and for the ground state of the lithium atom.