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

The average electron density in momentum space, viz.(&#947;), where &#947;(p) is the electron momentum density, is defined and shown to be experimentally measureable. The connection is obtained via the relation 8&#960;<SUP>3</SUP>(&#947;) = &#945;B<SUP>2</SUP>(s) ds, where B(s) is reciprocal form factor. The approximate relationships (p) = 2(r<SUP>3</SUP>)/3&#960;<SUP>2</SUP> and (&#947;) = 2(r<SUP>3</SUP>)/3&#960;<SUP>2</SUP> 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