Measuring the Doppler broadening of the positron annihilation radiation or the angular correlation between the two annihilation gamma quanta reflects the momentum distribution of electrons seen by positrons in the material.Vacancy-type defects in solids localize positrons and the measured spectra are sensitive to the detailed chemical and geometric environments of the defects. However, the measured information is indirect and when using it in defect identification comparisons with theoretically predicted spectra is indispensable. In this article we present a computational scheme for calculating momentum distributions of electron-positron pairs annihilating in solids. Valence electron states and their interaction with ion cores are described using the all-electron projector augmented-wave method, and atomic orbitals are used to describe the core states. We apply our numerical scheme to selected systems and compare three different enhancement (electron-positron correlation) schemes previously used in the calculation of momentum distributions of annihilating electron-positron pairs within the density-functional theory. We show that the use of a state-dependent enhancement scheme leads to better results than a position-dependent enhancement factor in the case of ratios of Doppler spectra between different systems. Further, we demonstrate the applicability of our scheme for studying vacancy-type defects in metals and semiconductors. Especially we study the effect of forces due to a positron localized at a vacancy-type defect on the ionic relaxations.
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