Quantum defect theory

Quantum defect theory (QDT) is concerned with the properties of an electron in the field of a positive ion and, in particular, with expressing those properties in terms of analytical functions of the energy. It provides a unified theory of bound states, including series perturbations, autoionisation and electron-ion scattering, both elastic and inelastic. The main emphasis of the review is on the foundations of the theory. Properties of Coulomb functions are discussed in some detail and outline sketches are given of relevant topics in collision theory and radiative theory. One-channel and many-channel QDT are discussed separately. Applications to the following problems are considered: resonances, atomic collision calculations, systems with two energy levels of the ion core, helium, other rare gases, alkaline earths and other atomic systems, molecular hydrogen, dielectronic recombination.