Two-dimensional angular correlation of annihilation radiation (2D-ACAR) and Compton scattering are both powerful techniques to investigate the bulk electronic structure of crystalline solids through the momentum density of the electrons. Here we apply both methods to a single crystal of Pd to study the electron momentum density and the occupancy in the first Brillouin zone, and to point out the complementary nature of the two techniques. To retrieve the 2D spectra from 1D Compton profiles, a new direct inversion method (DIM) is implemented and benchmarked against the well-established Cormacks method. The comparison of experimental spectra with first principles density functional theory calculations of the electron momentum density and the two photon momentum density clearly reveals the importance of positron probing effects on the determination of the electronic structure. While the calculations are in good agreement with the experimental data, our results highlight some significant discrepancies.
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