Fig. 2: Momentum-space description of a photo-transition from the valence band.

a, b (k_x, k_z)-schemes describing direct interband transitions into a quasi-free-electron-like final state band at photon energies between 300 and 400 eV. The axes denote the momentum components k_x and k_z in units of the reciprocal lattice vectors G_1–10 and G₁₁₀, respectively, both along the high-symmetry direction ΓN. The plots are to scale for the body-centred cubic metal Mo. The final-state momentum k_f (radius of the final-state sphere) depends on photon energy hν (for fixed binding energy E_B) (a) and on E_B (for fixed hν) (b). The centre of the sphere C is displaced from the origin k = (0,0,0) by the vector of the photon momentum k_hν. The background patterns are cuts (at k_y = 0)) of the periodically repeated measured spectral-density arrays for the Fermi energy E_F (a) and for E_B = 1 eV (b). Dashed square in (a) marks the first Brillouin zone (BZ), dark denotes high spectral density. c Brillouin zone of bcc lattice with high-symmetry points; plane ΓNN (yellow) is shown in (a, b). d–g Measured energy isosurfaces (E_B = const. surfaces) at the Fermi energy (d) and at E_B = 1, 2 and 3 eV (e−g). The umbrella-shaped top marks the intersection area with the final-state sphere, which is recorded in a momentum microscope.