Reconstruction of momentum distribution from point-geometry positron-annihilation data

A method is presented by which the momentum distribution of the electrons in a metal, ρ(→p), may be reconstructed from point-geometry angular-correlation positron-annihilation data taken in a plane. The result is in the form of a truncated Fourier series in polar coordinates in that plane in momentum space. The number of terms in the ρ(→p) series is determined by the number of crystal orientations at which data were taken. The effect of statistical errors in the data on the reconstruction of ρ(→p) is examined for a hypothetical free-electron metal. The method is applied to real data taken in the (100) plane of Cu, and it is found that the comparison to the theoretically predicted ρ(→p) is remarkably good. In particular, the results show that surprisingly rich detail in ρ(→p) can be reproduced using data taken for a minimum number of crystal orientations.