Electron-momentum spectroscopy based on the (e,2e) reaction has been used to observe the energy-momentum density of valence electrons in the ͓110͔ direction for an ultrathin, free-standing film of crystalline silicon. An asymmetric scattering geometry is used in which the incident, scattered and ejected electron energies are 20.8, 19.6, and 1.2 keV, respectively. The measurement is complicated by the possibility of diffraction of the free electrons. The theory of the reaction including diffraction is summarized and applied to experiments with different target orientations. The orientation is determined from an independent electron diffraction experiment. Very good agreement between theory and experiment is observed. ͓S0163-1829͑98͒01220-X͔

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Electron-momentum spectroscopy ͑EMS͒ or (e,2e) measurements with oxidized aluminum thin films have been performed. Due to the surface sensitive nature of the EMS spectrometer employed, the measured (e,2e) events come from the front oxidized layer as viewed by the electron detectors. The measurements show clearly two major features in the spectral momentum density distribution and they are related to the upper valence band and the lower valence band of aluminum oxide. The first is a ''dual parabola'' energy-momentum dispersion pattern spanning about 8 eV in the upper valence band. This dual parabola pattern has been qualitatively reproduced by a linear muffin-tin orbital ͑LMTO͒ calculation on spherically averaged ␣-Al 2 O 3 with nearly the same energy span. In the lower valence band, the LMTO calculation indicates a dispersion spanning about 5 eV, and the measured spectral momentum density plot shows a similar ''bowl'' shape but with less dispersion. The possible causes that blur the dispersion in the lower valence band are discussed. Other features in the spectral momentum density distribution are also discussed and compared with the LMTO calculation. ͓S0163-1829͑96͒08147-7͔

The spectral-momentum density of electrons in a copper thin film has been directly measured using electron momentum spectroscopy. The measured spectral-momentum density shows two distinct features. The first is a free-electron-like parabola with dispersion spanning 10 eV in energy and 0.65 a.u. in momentum. The other is a weak and extended band located in a narrow range of energies from about 2 to 5 eV below the Fermi level. A spherically averaged linear muffin-tin orbital ͑LMTO͒ calculation of copper reproduces these features in both the dispersion pattern and the intensity. After taking into account the elastic and inelastic multiple scattering through a Monte Carlo simulation, the agreement between the calculation and the measurement is good. The measurement and the LMTO calculation are also compared with an available linear-augmentedplane-wave calculation for the energy-integrated electron momentum distribution of the valence band and the agreement is also good.

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