Electron-positron interaction in an inhomogeneous electron liquid

This work is an exploratory attempt to investigate directly the many-body problem of a positron in an inhomogeneous electron liquid. The inhomogeneity consists of a sphere in jellium from which the positive background is subtracted and put on its surface with the purpose of simulating in this way an interstitial space in a metal lattice. Two effects absent in jellium and overlooked up to now arise immediately and are considered for a simple model: the partial concentration on the surface of the inhomogeneity of the electronic cloud screening the positron and the modification of the lattice potential (understood as the potential of the inhomogeneity) by this particle. As a result, the annihilation rate in the center of the sphere is lower than for jellium of any density available in the system. Approaches using some effective density instead of the local one would act in the opposite direction. A possible discrepancy between theory and experiment due to this effect is reduced if one applies (as most authors do) for the annihilation rate in jellium the figures of Boronski and Nieminen, which are lower by 8-17% than the results of more rigorous calculations.