This paper is devoted to study many-body effects in the positron annihilation experiment, both electron-positron (e-p) and electron-electron (e-e) correlations. Various theories of the e-p interaction in real solids were used to verify them by comparing theoretical and experimental e-p momentum densities in Cu and Y. We show that the lattice potential has an essential influence on the e-p correlation effects, i.e. their proper description must be done via periodic lattice potential as e.g. in the Bloch Modified Ladder (BML) theory. Moreover, it is not true that that the dynamic parts of the direct e-p and e-e interactions cancel each other because e-e correlations are observed not only in the Compton scattering but also in the positron annihilation experiments. Keywords: positron annihilation, Compton scattering, momentum densities, many-body effects
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