Electron - electron coalescence and counterbalance densities of atoms in position and momentum spaces

The electron - electron coalescence h(0) and counterbalance d(0) densities are probability densities of finding any two electrons, respectively, at the same position and at the reflection points in the three-dimensional position space. The momentum-space counterparts and represent the probability densities for any pair of electrons to have exactly the same and opposite momenta, respectively. These electron-pair densities, as well as the average position and momentum one-electron densities, are computed systematically for the atoms He through Xe in their ground state by using the numerical Hartree - Fock method. The results are discussed in terms of the atomic number, electronic configuration and subshell-pair contributions with our particular interest in the electron - electron coalescence densities h(0) and .