  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
