Average electron momenta in many-electron atoms

Abstract

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 〉. For the 102 atoms He through Lr in their ground states, the momenta 〈p 〉 are systematically examined at the Hartree–Fock limit level. It is also shown that the sum 〈p>〉+〈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.