Reconstructed three-dimensional electron momentum density in lithium: A Compton scattering study

The three-dimensional electron momentum density rho (p) in Li is reconstructed via a direct Fourier transform method which is free from functional assumptions concerning the shape of rho (p). For this purpose, 12 high-resolution Compton profiles are measured, and corresponding highly accurate computations carried out within the band theory framework. Extensive comparisons between the rho (p)'s reconstructed from the theoretical and experimental profiles with each other and with the true (without reconstruction) underlying computed rho (p) are used to gain insight into the accuracy of our procedures, and to delineate the effects of various parameters (filtering, resolution, etc.) on the reconstructed rho (p). The propagation of errors is considered in detail, and a general formula appropriate for the present direct Fourier method is derived. The experimental rho (p) (in comparison to the theoretical results) shows a substantially more smeared out break at the Fermi momentum p(f), and a shift of spectral weight from below to above p(f), clearly indicating the importance of electron correlation effects beyond the local-density approximation for a proper description of the ground-state momentum density. The question of deducing Fermi-surface radii in terms of the position of the inflection point in the slope of rho (p) in the presence of finite resolution is examined at length. The experimental Fermi surface and its asphericity is in good overall accord with theoretical predictions, except that band theory predicts a bulging of the Fermi surface along the [110] direction, which is greater than seen in the measurements; however, our analysis suggests that the set of 12 directions used in the present experiments may not be optimal (in number or orientations) for observing this rather localized Fermi-surface feature.