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 manychannel 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.

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Using the code autostructure, extensive calculations of inner-shell atomic data have been made for the chemical elements He, C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Cr, Mn, Fe and Ni. The results are used to obtain updated opacities from the Opacity Project (OP). A number of other improvements on earlier work have also been included. Rosseland-mean opacities from the OP are compared with those from OPAL. Differences of 5-10 per cent occur. The OP gives the 'Z-bump', at log(T) 5.2, to be shifted to slightly higher temperatures. The opacities from the OP, as functions of temperature and density, are smoother than those from OPAL. The accuracy of the integrations used to obtain mean opacities can depend on the frequency mesh used. Tests involving variation of the numbers of frequency points show that for typical chemical mixtures the OP integrations are numerically correct to within 0.1 per cent. The accuracy of the interpolations used to obtain mean opacities for any required values of temperature and density depends on the temperature-density meshes used. Extensive tests show that, for all cases of practical interest, the OP interpolations give results correct to better than 1 per cent. Prior to a number of recent investigations which have indicated a need for downward revisions in the solar abundances of oxygen and other elements, there was good agreement between properties of the Sun deduced from helioseismology and from stellar evolution models calculated using OPAL opacities. The revisions destroy that agreement. In a recent paper, Bahcall et al. argue that the agreement would be restored if opacities for the regions of the Sun with 2 × 106T 5 × 106 K (0.7-0.4 R) were larger than those given by OPAL by about 10 per cent. In the region concerned, the present results from the OP do not differ from those of OPAL by more than 2.5 per cent

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