Multiple scattering approach for two-electron resonant emission studied by angle-resolved coincidence spectroscopy

We have developed a generalization of the multiple-scattering formalism to deal with Auger-photoelectron coincidence spectroscopy (APECS) in the solid state. We have merged the exact atomic treatment of the angular correlations between the two electrons and the single-particle approach, on which the multiple-scattering description of condensed matter relies. This allows the recovering, even in extended systems, of the entangled form of the electron-pair wave function characterizing the coincidence angular diffraction pattern. In the atomic limit our formalism correctly reproduces the cross section, as calculated within the statistical-tensors approach, usually employed in atomic physics. We have then performed numerical calculations for the Ge(100) $L_3{M}_{45}{M}_{45}$ APECS and compared the results with previous experiments. We found that, in the given geometry, the diffraction patterns in coincidence with different directions of the photoelectron keep little memory of the atomic anisotropy. We speculate on the conditions to be fulfilled in order to enhance the atomic-orbital sensitivity in APECS through solid-state diffraction effects.

Figure 1

(Color online) The experimental setup of Ref. 11.

Figure 2

(Color online) Theoretical curve for Ge(100) $L_3{M}_{45}{M}_{45}$ AED and comparison with the experimental data from Ref. 11.

Figure 3

Theoretical curve for Ge(100) $L_3{M}_{45}{M}_{45}$ APECS (summed over the five photoelectron directions) and comparison with the experimental data from Ref. 11.

Figure 4

APECS theoretical results corresponding to the five different directions of the photoelectron for Ge(100) $L_3{M}_{45}{M}_{45}$ [(a) photoelectron detected by analyzer 1, (b) by analyzer 2, (c) by analyzer 3, (d) by analyzer 4, and (e) by analyzer 5] and comparison with the experimental data from Ref. 11.

Figure 5

Ge(100) $L_3{M}_{45}{M}_{45}$ APECS direct signals corresponding to the five different directions of the photoelectron.

Figure 6

Auger angular scan in coincidence with the photoelectron detected at analyzer 5, originating at different planes, in order to highlight the formation of the diffraction pattern.