In a lengthy review, it was recalled that various experimental methods which were based upon positron annihilation had evolved into important tools for studying the structure and properties of condensed matter. In particular, positron techniques were useful for the investigation of defects in solids and for the investigation of solid surfaces, but a comprehensive theory was needed in order to obtain a deep quantitative understanding of test results. In the case of positron annihilation, the relevant theory included models which were required in order to describe the positron states as well as the various interaction processes in matter. Here, the present status of the theory of positrons in solids and on solid surfaces was presented. The review was divided into 3 main parts which described interaction processes, theories and methods for calculating positron states, and some recent results for condensed matter. The detailed subject headings included: positron/solid interactions before thermal equilibrium (high-energy region, low-energy region), during thermal equilibrium (positron diffusion equation, positron diffusion coefficient), positron trapping into defects (positron trapping model, positron trapping coefficient, resonance trapping, positron trapping in semiconductors, positron trapping at voids in metals, positron trapping at surfaces). Models for positron states in solids: 2-component density functional theory (generalized Kohn-Sham method, local density approximation, delocalized positron states, localized positron states), positron states in semiconductors and insulators, positron states on solid surfaces, methods for positron states in solids, momentum distribution of electron-positron pairs. Positron states in solids: delocalized positron states in perfect solids (positron and electron energy levels in solids, positron deformation potential, positron bulk lifetimes), localized positron states at vacancy-type defects in solids (results of 2-component density functional theory - vacancies in metals, beyond the local-density approximation - clean vacancies and vacancy clusters, vacancies and vacancy clusters decorated with impurities, rare-gas bubbles in metals, defects in semiconductors - electronic and ionic structures, defects in semiconductors - positron states), positron states on solid surfaces (properties of the positron surface state, positron annihilation-induced Auger spectroscopy), exotic systems (high-Tc superconductors, fullerenes and related materials)

M.J.Puska, R.M.Nieminen: Reviews of Modern Physics, 1994, 66[3], 841-98