ABSTRACT
In the previous chapter we discussed the self-consistent field method for finding energy levels and wave functions for atoms. We saw that any numerical calculation is very cumbersome, especially for atoms with many electrons. For these, there exists a simpler method to obtain at least a fair approximation. Developed by Thomas and Fermi, it is based on Fermi-Dirac statistics. The results admittedly are less accurate than those of the Hartree-Fock calculations. The Thomas-Fermi method nevertheless is very useful for calculating form factors and for obtaining effective potentials which can be used as initial trial potentials in the self-consistent field method. It is also applicable to the study of nucleons in nuclei and electrons in a metal. Exchange is not treated in the Thomas-Fermi model. However, a statistical model for the exchange effects can be given also. We discuss this at the end of this chapter, after the presentation of the model without exchange.
