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

The three-dimensional electron momentum density $\rho \left(\mathbf{p}\right)$ in Li is reconstructed via a direct Fourier transform method which is free from functional assumptions concerning the shape of $\rho \left(\mathbf{p}\right).\mathrm{}$ 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 $\rho \left(\mathbf{p}\right)’\mathrm{s}$ reconstructed from the theoretical and experimental profiles with each other and with the true (without reconstruction) underlying computed $\rho \left(\mathbf{p}\right)$ 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 $\rho \left(\mathbf{p}\right).\mathrm{}$ The propagation of errors is considered in detail, and a general formula appropriate for the present direct Fourier method is derived. The experimental $\rho \left(\mathbf{p}\right)$ (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 $\rho \left(\mathbf{p}\right)$ 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.