In the previous chapter we introduced the nonrelativistic Hamiltonian of a complex atom and we saw how it can be separated into two parts using the central field approximation: a zero order Hamiltonian whose eigenvectors, in general degenerate, are the states belonging to the different configurations, and a “corrective” Hamiltonian containing various terms including, in particular, the Coulomb repulsion between electrons. By neglecting the interaction between configurations, which is equivalent to consider the corrective Hamiltonian as a perturbation of the zero order Hamiltonian, we have seen, in the particular case of the helium atom, how we can express the energies of the terms by means of integrals which involve single particle eigenfunctions relative to the zero order Hamiltonian. In this chapter we generalise the results obtained for the helium atom to any atom, also using perturbation theory. We will obtain general results that can be directly compared with the spectroscopic data. These results, although approximated, constitute the starting point for the development of more sophisticated treatments that are currently used for the detailed analysis of atomic spectra.
KeywordsMatrix Element Quantum Number Coulomb Interaction Helium Atom Angular Part
- Condon, E.U., Shortley, G.H.: The Theory of Atomic Spectra. Cambridge University Press, Cambridge (1935) Google Scholar