Compton scattering, positron annihilation, and the electronic properties of quantum dots

In this work we study electronic properties of quantum dots relevant to Compton scattering and positron annihilation. The system is modeled by an electron gas confined by a spherical potential of given radius and depth. Electron-electron correlations are not considered in this study. We find that the broadening of the electronic momentum density around a suitably defined Fermi momentum scales with dot radius as 1/R . The Compton profiles tend to the homogeneous electron gas ~HEG! form for high electron densities and large dot radius. The broadening of the electron-positron annihilation probability as a function of total momentum also scales as 1/R , but the positron increases the broadening by around 20% with respect to the electronic momentum density result. The Doppler profiles deviate more noticeably from the HEG form for small radius and low electron densities. This is reflected well in the Doppler profile shape parameter. Also, positron lifetimes are quite sensitive to electron density and dot radius. Positron lifetimes were calculated taking into account positron-electron correlation through the local-density approximation and the generalized gradient approximation. Within these approximations, the positron lifetime dependence on radius is not monotonic. For large radii, the lifetimes increase with radius toward the HEG values, converging more rapidly for higher electron densities. For a radius smaller than a certain value, however, the lifetime does not continue decreasing with radius but starts to increase, reflecting the increasing spillout of the positron from the dot.