Atomic Binding Energies from a Modified Thomas-Fermi-Dirac Theory

A "quantum correction" of the statistical model of the atom has been obtained by modifying March and Plaskett's region of integration in the ($n_r, l$), or quantum-number, plane. Integrations over the plane lead, in the unmodified case, to the Thomas-Fermi density expression and energy equation. Integrations over the modified region have here been shown to produce a modified Thomas-Fermi expression for the electron density, and a correction to the kinetic energy. The latter correction shows a similarity to the Weizsäcker correction, but is smaller by a slowly changing factor of the order of 10. A modified Thomas-Fermi-Dirac equation has been derived by the standard variational procedure. Numerical solutions of the equation have been obtained which yield atomic binding energies in much better agreement with experimental values than those of the unmodified theory.