We present a unitary cluster approach to the calculation of several electron and photon spectroscopies, ranging from core and valence level photoelectron diffraction and absorption to electron, Auger and anomalous diffraction. Electron energy loss and Auger-photoelectron coincidence spectroscopies can also be treated in the same frame. This approach is based on multiple-scattering theory with a complex optical potential of the Hedin-Lundqvist type and is valid for all electron kinetic energies. Similarities and differences between these diffraction techniques are examined and cluster size convergence is discussed in connection with the electron mean free path. Applications to selected problems are presented to illustrate the method, both for structural and electronic analysis. Contents1. Introduction 176 2. Calculation of cross-sections 178 2.1. General expression of the cross-section 178 2.2. Cross-section for incoming photons 179 2.3. Cross-section for incoming electrons 183 2.4. Doubly differential ionization cross-section 185 3. Reduction of the many-body problem to an effective one-particle problem for photoemission and photoabsorption 186 3.1. The photoemission case 187 3.2. The photoabsorption case 192 3.3. The mean free path 197

We present a theoretical study of the polarization-averaged molecular-frame photoelectron angular distributions (PA-MFPADs) emitted from the 1s orbital of oxygen atoms of dissociating dicationic carbon monoxide CO2+. Due to the polarization average, the contribution of the direct wave of the photoelectron, which represents the largest contribution to the MFPADs, is removed, so that the PA-MFPADs clearly show the details of the scattering image of the photoelectron. As a result, it is necessary to employ an accurate theory for the theoretical analysis of the continuum state. In this study, we apply a full-potential multiple scattering theory, where the space is partitioned into Voronoi polyhedra and truncated spheres, to take into account the electron charge density outside the physical atomic spheres. We do not use the spherical harmonic expansion of the cell shape functions to avoid divergence problems. The potentials in the scattering cells are computed using the multiconfigurational second-order perturbation theory restricted active space method to take into account the influence of the core hole in the electron charge density in the final state, so that a realistic relaxation can be achieved. We show that the full-potential treatment plays an important role in the PA-MFPADs at a photoelectron kinetic energy of 100 eV. In contrast, the PA-MFPADs are not sensitive to any type of major excited states in the Auger final state. We also study the dynamics of the CO2+ dissociation. We find that the PA-MFPADs dramatically change their shape as a function of the C–O bond length.

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