Electron-pair densities of group 2 atoms in their P-1 and P-3 terms

Electron-pair intracule (relative motion) and extracule (center-of-mass mot ion) densities are studied in both position and momentum spaces for the P-1 and P-3 terms of the group 2 atoms Be (atomic number Z = 4), Mg (Z = 12); Ca (Z = 20), Sr (Z = 38), Ba (Z = 56), and Ra (Z = 88). In position space, the P-1 - P-3 difference in the intracule densities shows that the probabil ity of a small interelectronic distance is larger in the triplet for all th e six atoms, as reported far the lightest Be atom in the literature. The po sition-space extracule density clarifies that the triplet electrons are mor e likely to be at opposite positions with respect to the nucleus than the s inglet electrons for all the atoms. In momentum space, the singlet generall y has a larger probability of a small relative momentum between two electro ns as a naive manifestation of the Fermi hole in the triplet. The extracule density in momentum space shows that the P-1 term has a distribution large r in a large center-of-mass momentum region than the P-3 term.