Quantum and Correlation Corrections to the Thomas–fermi Potential

The paper studies the correction to the Thomas–Fermi potential arising from the exchange, inhomogeneity, and correlation effects. An alternative derivation of the Baraff equation is given, based on simple physical considerations. Starting from the Baraff equation and making use of the simple analytical formula of Tietz for the Thomas–Fermi potential, analytical expressions for the correction to the Thomas–Fermi potential are given (a) within the radius of the atom applying the Gellmann–Brueckner high-density formula for the correlation energy of an electron gas and (b) outside this range wherein the correlation energy can be approximated by the Wigner low-density formula. It is found that the main contribution to the solution of the Baraff equation arises from the inhomogeneity, screening, and the exchange terms.