The average electron momentum density and rigorous bounds to average electron densities for atoms and molecules

Abstract

The average electron density in momentum space, viz. 〈γ〉, where γ( p) is the electron momentum density, is defined and shown to be experimentally measureable. The connection is obtained via the relation 8π 3〈γ〉 = ∝ B 2( s) ds, where B( s) is reciprocal form factor. The approximate relationships 〈 p〉 = 2 〈 r 3〉/3π 2 and 〈γ〉 = 2 〈 r 3〉/3π 2 have been phase space considerations. They have been examined for near Hartree-Fock atomic limit data. Rigorous bounds to atomic and molecular average electron densities in configuration and momentum spaces are derived without any reference to an independent-particle model.