The Independent-Particle Model

Abstract

In Chaps. 2–4 we have developed the theory of angular momentum and, in particular, its graphical representation. As illustrations we have also considered some physical problems, like the Coulomb interaction. We are now in a position to study atomic properties in a more systematic way. In the present chapter we shall investigate the Hamiltonian for many-electron atoms and the independent-particle model in which the electrons are assumed to move independently of each other in an average field due to the nucleus and the other electrons. The independent-particle model and the variational principle then lead to the (unrestricted) Hartree-Fock equations. In the next chapter we shall make the additional assumption that the average potential is spherically symmetric. This is the central-field model, which together with the variation principle leads to the restricted Hartree-Fock equations. The central-field model forms the basis of the atomic shell structure and the chemical regularity of the elements.