  We report a computational first-principles study of positron trapping at
vacancy defects in metals and semiconductors. The main emphasis is on the
energetics of the trapping process including the interplay between the positron
state and the defect's ionic structure and on the ensuing annihilation
characteristics of the trapped state. For vacancies in covalent semiconductors
the ion relaxation is a crucial part of the positron trapping process enabling
the localization of the positron state. However, positron trapping does not
strongly affect the characteristic features of the electronic structure, e.g.,
the ionization levels change only moderately. Also in the case of metal
vacancies the positron-induced ion relaxation has a noticeable effect on the
calculated positron lifetime and momentum distribution of annihilating
electron-positron pairs.
