Average electron momenta in many-electron atoms

In many-electron atoms, the average electron momentum p represents the mean momentum of a single electron when all the electron motions are averaged. If any two electrons are considered simultaneously, however, the average momentum p splits into two different momenta, low momentum p_< and high momentum p_>. For the 102 atoms He through Lr in their ground states, the momenta p_< and p_> are systematically examined at the Hartree–Fock limit level. It is also shown that the sum p_>+p_< and the difference p_>–p_< of the two momenta constitute upper and lower bounds to the electron-pair relative momentum p₁₂=|p₁–p₂| and to the electron-pair center-of-mass momentum P=|p₁+p₂|/2. The tightness of the bounds is discussed for the 102 atoms.