Calculations were made of the momentum densities of electron-positron pairs which annihilated at various vacancy clusters. The densities as integrated along one direction, which corresponded to the spectra which were measured by using the 2-dimensional angular correlation of annihilation radiation method, were shown to be isotropic if the positron was captured by a small vacancy cluster. The densities which were integrated along 2 directions corresponded to the 1-dimensional angular-correlation distribution or the Doppler-broadened annihilation radiation line-shape. A characteristic narrowing of these 1-dimensional distributions at vacancy clusters was demonstrated. The line-shape parameters, S and W, which described mainly the annihilation with valence and core electrons, respectively, were calculated. It was found that there was a systematic increase in S, and a decrease in W, as the size of the vacancy increased.

M.Hakala, M.J.Puska, R.M.Nieminen: Physical Review B, 1998, 57[13], 7621-7