Fermi-Thomas Angular-dependent Potential for Iron

A method is developed for determining the angular-dependent solution of the Fermi-Thomas equation for the potential within a body-centred or face-centred cubic lattice, calculations being performed for iron. By comparison with the spherically symmetric solution of the form obtained by Slater and Krutter it is possible to obtain estimates of the errors involved in the use of a spherically symmetric potential field. For iron the correction to the potential causes an increase of 0.67 ev in energy of the Fermi level, a decrease of 1.32 ev in the potential energy barrier between atoms and an increase of 3.0 ev in the total energy per atom. The total energy per atom of any metal, in the angular-dependent case, is reduced to a sum of integrals over the surface of the atomic polyhedron.