Complex atomic spectra

The long history of the theory of complex atomic spectra, as distinct from series spectra, is reviewed from the period of the 1930s, when quantum mechanics was rapidly applied to solve a variety of problems, to the present day, when, at a single stroke, elaborate computer programs are used to fit many hundreds of atomic energy levels to theoretical models. Emphasis is placed on the use of of annihilation and creation operators. With their help, the role that Lie groups play in atomic spectra can be described in analogy to SO(3), the special orthogonal group corresponding to rotations in ordinary three-dimensional space. Configuration interaction is represented by effective operators that act within the states of the unperturbed configuration under study. These effective operators are also usefully constructed from annihilation and creation operators. A table is given in which the least-squares fits to the levels of atomic configurations comprising at least three electrons (or electron holes and electrons) are listed.