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The simultaneous ejection of two electrons from the ͑001͒ surface of W due to the collision of incident low-energy electrons with valence electrons has been studied experimentally and theoretically. Energy and momenta of the ejected electrons were measured simultaneously by a combination of coincidence and timeof-flight techniques. Calculations were performed in a relativistic distorted-wave Born approximation including exchange, in which the primary electron and the two emitted electrons are described by quasiparticle multiple scattering states. The valence electron is represented by linear combinations of Bloch waves matched at the surface. Screened Coulomb interaction matrix elements between these four states are evaluated. Experimental and calculated energy distributions from W͑001͒ for very-low-energy primary electrons at normal and grazing incidence are in fairly good overall agreement. Although some features of one-dimensional bulk densities of states are roughly reflected, Coulomb matrix elements with low-energy-electron-diffraction-type states play a vital role. Further analysis reveals in detail the importance of elastic scattering of the primary electron and of the two ejected electrons. Some observed features can be attributed to occupied surface states. ͓S0163-1829͑98͒05848-2͔

To study the electronic struchlre of femmagnetic clystalline compounds, their surfaces and adsorbed ultrathin films, a fully relativistic Green function formalism has been developed. For a semi-infinite system, which is described by a complex effective potential, the single-particle Green function and thence the layer-. kll-and spin-or symmetry-resolved densities of statesat the surface and in the bulk-are obtained using a layer Korringa-Kohn-Rostoker method. This Green function-for qlwsi-hole states-is employed in a relativistic one-step model formalism to yield spin-and angle-resolved photoemission intensities.