The Experimental Determination of Electron Momentum Densities

Abstract

Recent developments and the current state of experimental methods for the determination of electron momentum densities (EMD's) are reviewed. The remarkable growth both in applications of traditional techniques as well as in the development of new techniques over the last three years is described. A general analysis of the determination of EMD's in atoms, molecules and solids provides the context within which the recent work is discussed. This leads to a consideration of the physical information contained in the EMD and hence to the experimental conditions needed to ensure that the information obtained is meaningful. The potential for improving the quality of the information obtained by separating the partial contributions to the total EMD on the basis of the electron spin, orbital energy or position is discussed. The three commonly used probes, inelastic photon or electron scattering and positron annihilation are discussed in turn. Photon scattering experiments are subdivided into X-ray and γ-ray work. These techniques are well established but experiments with new sources such as Au, which emits high energy γ-rays, and synchrotrons, which provide polarized radiation, promise to open up new areas for investigation. Refinements of the technique, such as the detection of the ejected electron in coincidence with the scattered photon, are also discussed. Inelastic scattering of high energy electrons, a refinement of which is the (e,2e) technique, has been developed mainly in the last few years but is already making major contributions to the understanding of EMD's. Using both methods excellent resolution is available and the (e,2e) technique allows one to measure all three components of the EMD while at the same time separating out contributions to the total profile on the basis of orbital energies. The potential application of this technique to solids opens up many exciting possibilities. Developments in the determination of EMD's from angular correlation measurements of two photon positron annihilation are then described. Recent work in this relatively well established field includes the development of multi-counter detecting systems for the direct determination of two components of the EMD as well as the possibility of determining all three components. Other developments such as the use of polarized positrons to determine the EMD of unpaired spin electrons are also considered. The main difficulty associated with the interpretation of positron data arises from uncertainty in the analysis of the behaviour of the positron and this remains the outstanding problem. Results for specific samples obtained over the last three years using the above techniques are then described with a view to assessing the importance of EMD work as well as to providing guidance for future work.

An examination and assessment of available incoherent scattering s-matrix theory, also compton profile information, and their impact on photon attenuation coefficient compilations

“…It was concluded that reproducibility of ± 1 % of the peak height of the profile is quite feasible, and that in a differential experiment ±0.5 % or even better is possible. The techniques are extensively reviewed in Williams (1977b), with further details in the chapters in Williams (1977a) by Halonen et al (1977), Mendelsohn and Smith (1977) and by Berggren et al (1977).…”

Molecular Hartree-Fock equations for iteration-variation calculations in momentum space

“…Furthermore, momentum quantities may be useful in quantum mechanics to interpret experimental results such e.g. Compton profiles [28], cross sections from (e, 2e) spectroscopy [20], etc.…”

Compton profile of VO2 across the metal-insulator transition: Evidence of a non-Fermi liquid metal

“…Both the momentum distribution and Compton profile are powerful probes for understanding the ground state properties of materials. The momentum distribution of the electrons can be experimentally studied by scattering methods such as Compton scattering, positron annihilation, the (e, 2e) process and high energy electron scattering [28][29][30][31]. In general, the differential cross sections can be related to the momentum distribution.…”