Electron-pair radii and relative sizes of atoms

The electron-pair intracule (relative motion) h(u) and extracule (center-of-mass motion) d(R) densities represent probability densities for the interelectronic distance and the center-of-mass radius of any pairs of electrons, respectively. For 102 atoms from He (atomic number Z = 2) to Lr (Z = 103), we report that electron-pair radii R_2i and R_2e, defined by h(R_2i) = c_2i and d(R_2e) = c_2e, have good linear correlations with the relative sizes R_1 of atoms introduced based on the single-electron density ρ(r) such that ρ(R_1) = c_1, where c_1, c_2i, and c_2e are constants common to the 102 atoms. It is also shown that an interesting relation R_2e ≅ R_2i/2 holds, if c_2e is set equal to 8_c2i