Complex Atoms

Complex Atoms
1. Shell Model of the Atom
Consider forming a system of several electrons electrostatically bound to an infinitely heavy nucleus of charge Ze. The electrons also electrostatically repel each other, so a Hamiltonian for the system can be written that, in atomic units, looks like. written that, in atomic units, looks like
ri is the position of electron i with respect to the nucleus. ri and rij are defined by the corresponding expression in the equation above. While the Hamiltonian is not complete, all additional terms can quite successfully be treated as perturbations.
Using a central potential H may be written as:
The Schr?dinger equation is:, Here ui(ai) is the wave function of the ith electron having a set of quantum numbers ai. It follows then that each ui is a solution of the one-electron central force problem and must be of the form.
which is a one-electron spin orbital. The form of the is unspecified and depends on the particular choice of central potential. So ai must represent the set of four quantum numbers: