Electron Compton Profiles Research Articles

Ion and Electron Momentum Distributions from Single and Double Ionization of Helium Induced by Compton Scattering.

We present the momentum distributions of the nucleus and of the electrons from double ionization of the helium atom by Compton scattering of photons with hν=40 keV. We find that the doubly charged ion momentum distribution is very close to the Compton profile of the nucleus in the ground state of the helium atom, and the momentum distribution of the singly charged ion to give a precise image of the electron Compton profile. To reproduce these results, nonrelativistic calculations require the use of highly correlated initial- and final-state wave functions.

Anisotropy of electron Compton profiles of graphite investigated by electron energy-loss spectroscopy

We report the high-resolution electron Compton profiles of graphite along three main crystallographic directions of [101¯0], [112¯0], and [0001] by recording electron energy-loss spectra at a large momentum transfer using a transmission electron microscope. A significant anisotropy is observed. The experimental results are in good agreement with theoretical calculations that use the full-potential linearized augmented plane wave method based on the local-density approximation. Electron Compton scattering from solids (ECOSS) is shown to be a sensitive probe of the binding structure in a material. ECOSS should be considered as a viable technique to determine the electron momentum distribution in nano-materials because of its short recording time and high momentum resolution.

Combined study of the ground and unoccupied electronic states of graphite by electron energy-loss spectroscopy

Both the unoccupied and ground electronic states of graphite have been studied by electron energy-loss spectroscopy in a transmission electron microscope. Electron energy-loss near-edge structures of the K-edge of carbon have been investigated in detail for scattering angles from 0 to 2.8 mrad. The π* and σ* components were separated. The angular and energy dependences of the π* and σ* structures were in fair agreement with theory. Electron energy loss Compton spectra of graphite were recorded at scattering angles from 45 to 68 mrad. One Compton scattering spectrum was obtained in 1 min compared with several hours or days using photons. The contributions of core electrons were calculated by the exact Hartree-Slater method in the Compton scattering region. The electron Compton profile for graphite is in good agreement with other conventional Compton profile measurements, as well as with theory, thus establishing the validity of the technique.

Calculation of valence electron momentum densities using the projector augmented-wave method

We present valence electron Compton profiles calculated within the density-functional theory using the all-electron full-potential projector augmented-wave method (PAW). Our results for covalent (Si), metallic (Li, Al) and hydrogen-bonded ((H2O)2) systems agree well with experiments and computational results obtained with other band-structure and basis-set schemes. The PAW basis set describes the high-momentum Fourier components of the valence wave functions accurately when compared with other basis set schemes and previous all-electron calculations.

Asymmetry of Compton profiles

The asymmetry and observed anomalous broadening of experimental Compton profiles measured at synchrotron radiation sources have raised questions on the validity of the impulse approximation and the strength of the electron–electron interaction in metals. However, asymmetry and broadening can also be introduced by experimental artifacts. In order to address these issues we have made a systematic study on simple systems using various incident photon energies and different spectrometers. In addition, we have performed simulations on the effect of dead time and an asymmetric instrument function in the measured Compton profiles. We conclude that the observed asymmetry of Compton profiles of Be and Na does not originate from any experimental artifacts, but is due to the failure of the impulse approximation. This is confirmed by quasi-self consistent field calculations of the core electron Compton profiles, which agree quite well with the experimental results.

Influence of lattice dynamics on electron momentum density of lithium

High resolution Compton profile measurements of single crystalline Li were performed for momentum transfer q → ∥[110] with 0.12 a.u. momentum space resolution at room temperature and at 95 K using the Compton spectrometer of ID 15 B at ESRF. The valence electron Compton profile at room temperature is higher around p z=0 a.u. and lower for |p z|>0.4 a.u. when compared with the one at 95 K. The experimental results are in good agreement with calculations using an empirical pseudopotential scheme, where the variation of lattice constant with temperature is taken into account when calculating the Fermi energy and Fourier coefficients of the empirical pseudopotential are multiplied by the corresponding Debye–Waller factor to simulate the thermal disorder. Thus the measured temperature effect can be traced back not only to the variation of the lattice constant with temperature but also to the decreasing contributions of higher momentum components to the total momentum density with increasing temperature.

Asymmetries in electron Compton profiles of silicon — a coherence effect

Electron Compton scattering in crystals in the case of large Ewald spheres is treated both theoretically and experimentally. The incident and scattered probe electron is represented by a sum of Bloch waves in the crystal leading to interference terms in the scattering cross section. The interference terms show a shift towards lower energies with respect to the diagonal Compton profile which depends only on the reciprocal lattice vectors of the excited Bragg reflexions. For a symmetric two-beam case the expression for the cross section is evaluated and it is shown that in contrast to the case of a small Ewald sphere the interference terms cannot be extracted from an experiment. For silicon the cross section is evaluated numerically for a (220) two-beam case and compared to experimental data from a transmission electron microscope. The agreement between theory and experiment is excellent and the shift of the interference terms with respect to the diagonal Compton profile can be observed in the measured profile.

K-shell radiative electron capture with bare 60-MeV/u Kr ions channeled in a Si crystal: Experiments and simulations.

We have performed K-shell radiative electron capture (K-REC) measurements with bare 60.1-MeV/u incident krypton ions, both in channeling conditions and for random orientation of a 37-\ensuremath{\mu}m silicon crystal. The sampled electron densities are quite different in each case, which has an influence both on the shape and on the amplitude of the K-REC photon peak. We have developed simulations of the K-REC photon lines: for this we have determined the impact parameter distribution at statistical equilibrium for various beam incidence conditions (direction and angular spread) using the continuum potential model for channeled ions. Multiple scattering effects were included. The K-REC photon peak was calculated within the nonrelativistic dipole approximation, K-REC being assumed to be a purely local process. Solid state electron densities were used, and impact parameter dependent electron momentum distributions (Compton profiles) were calculated for 2s and 2p silicon electrons. A remarkable agreement is found between the spectra measured with very high statistics, and the calculated ones, which leads to the following results: (i) The dependence of the K-REC yield on the beam incidence angle is obtained separately for silicon core and valence electrons, which was never observed before. We find that the core electron contribution to REC is still significant for axial alignment, whereas it is generally neglected in the literature. (ii) Electron Compton profiles are found to vary significantly with impact parameter. (iii) The free electron gas model represents a fair approximation for the description of valence electron Compton profiles. (iv) The K-REC cross section is measured with an absolute accuracy better than 20%, and found to be close to the value calculated within the nonrelativistic dipole approximation. \textcopyright{} 1996 The American Physical Society.

Progress in electron Compton scattering

Use of electrons as a probe instead of photons for Compton scattering experiments has been suggested in 1981 by B.G. Williams et al. The advantages, compared to conventional Compton scattering, are evident: a cross section higher by five orders of magnitude, extraordinary spatial resolution, on-line specimen manipulation, and all the additional information that is available in an analytical electron microscope. With PEELS nowadays available, and with the solution of the background problem, electron Compton profiles (CPs) can now be studied. Directional electron CPs of Si could be obtained by use of a two-beam geometry. In the intermediate momentum region, theory fits our results better than the results from conventional γ-ray and X-ray experiments. Electron CPs of amorphous allotropes of carbon could be interpreted in terms of a charge transfer between s and p orbitals. In a crystal, the CP contains interference terms from scattering with different momentum transfer. They are caused by momentum correlation (off-diagonal elements of the momentum density in the reciprocal lattice), and can be described by the mixed dynamical form factor. In the two-beam case these terms are proportional to the excitation error. An experiment is suggested in order to obtain the off-diagonal elements of the momentum density.

Temperature Dependence of the Magnetic Compton Profile of Ferrimagnetic HoFe2

Circularly polarised synchrotron radiation has been used to measure the spin-dependent magnetic Compton profile of the ferromagnet HoFe 2 at six temperatures from 10 K to 300 K. The magnetic Compton profiles have been analysed using appropriate free atom Compton profiles and a free electron Compton profile which has allowed the determination of the individual spin moments on the Ho and Fe sites and the diffuse moment; the last two are, to a first approximation, temperature independent. The Ho moment, which is antiferromagnetically coupled to them, reduces by a factor of two across the temperature range, leading to a spin compensation temperature of 210±10 K. The experiments were performed with 45.9 keV photons at the KEK ARNE-1 station of the Accumulation Ring.

A non‐local pseudopotential in the FSGO model: Study of some organometallic systems

AbstractA non‐local core pseudopotential has been used in the framework of floating spherical Gaussian orbital (FSGO) model to study the equilibrium geometries and valence electronic structures of some organolithium and organoberyllium systems. The calculated equilibrium geometries, heats of hydrogenation, average electric polarizabilities, and magnetic susceptibilities are in good agreement with the results of the all‐electron FSGO model calculations. Valence electron wave functions obtained here have been used to predict the valence electron Compton profiles (CP) and electron momentum distributions (EMD) of the systems studied. A good correlation has been shown among the peak height of the CP (J(0)), valence electron energy (Ev), and number of valence electrons (Nv).

Experimental electron Compton profile beyond the impulse approximation. Comparison of results on NH3 and Ne

The symmetrical part of the neon Compton profile, obtained by 25 keV electron scattering is compared to impulse approximation calculations, and the antisymmetrical part is compared to a qualitative estimate by Tavard for hydrogenic orbitals. Previous results on NH3 are recalled and a physical interpretation is attempted.

Self-consistent Compton profile of selenium

The valence electron Compton profile of trigonal and polycrystalline trigonal selenium has been determined using the self-consistent OPW method. The anisotropy of the Compton profile between directions parallel and perpendicular to the c-axis is discussed. The results are compared with experimental data. The difference of the Compton profiles of the amorphous and polycrystalline phases is examined.

Compton profiles of trigonal and amorphous selenium

Compton profiles of trigonal and amorphous Selenium were measured with 241Am γ-radiation using two crystalline and amorphous samples of identical geometric dimensions. As a result the difference profiles of amorphous and polycrystalline Se are reported and discussed. The valence electron Compton profile of the polycrystalline phase is compared to SCOPW-calculations by Krusius.

Reconstructed Three‐Dimensional Valence Electron Momentum Density of Si from Compton Profile Measurements

AbstractRecently measured anisotropies of Si valence electron Compton profiles with the scattering vector in the [100], [110], and [111] direction are analyzed together with calculated anisotropies of the corresponding Compton profiles from a modified free electron model. From both sets of profiles the momentum density ϱ(p) is reconstructed. In comparison with the modified free electron model the experimental momentum density is strongly reduced in the vicinity of p =0.6 to 1.0 at. units along the [100] direction and enhanced mainly in the vicinity of p =1.1 at. units along the [110] direction. These main features of the reconstructed experimental momentum density are well reproduced by a pseudopotential band calculation of valence electron momentum densities along the [100], [110], and [111] directions. Also the influence of the orthogonalization term on the momentum density is estimated.

Hartree-Fock directional Compton profiles for diamond

The electron Compton profiles for diamond have been calculated in the impulse approximation from two self-consistent crystalline Hartree-Fock momentum distributions in the [100], [111], [110], [112], and [221] directions. The two calculations use slightly different Gaussian basis sets. The results agree closely with experiment both in magnitude and in directional dependence.

Quantum mechanical first Born binary encounter theory of electron impact ionization. II Electron Compton scattering

The first Born binary encounter theory of electron Compton scattering is developed. The theory includes the relationship between the usual x-ray Compton profile and its electron scattering counterpart including corrections for scattering from pairs of target electrons (a correction also necessary in the x-ray case at small scattering angles) and for exchange and interference scattering. In addition correction terms are derived for the difference between the complete first Born treatment and the binary encounter model. The corrections in the angular range of 10°–60° at an incident electron energy of 25 keV are shown to be negligible. The target electron pair corrections at an incident electron energy of 25 keV are important only for small angle scattering for the lighter elements (< 7° for He) but may extend to larger angles for the heavier elements (< 30° for Ar). Exchange and interference between exchange and direct scattering become significant at the 1% accuracy level at a scattering angle of 4° at the same incident energy. Between 4° and 45° interference between the exchange and direct amplitude dominates the correction term which can amount to 25% of the direct scattering contribution at 35° although it largely vanishes at 45°. Beyond 45° the pure exchange terms rapidly dominate the scattering with increasing angle, and relativistic corrections become increasingly important. In this region the theory can break down and it is suggested that accurate experimental data could be helpful in arriving at a detailed description of the exchange process. A definition for an electron Compton profile including exchange and interference corrections from which the one-electron target momentum density can be extracted is suggested. The theory is also compared with recent experimental work for the case of He, and predictions for the scattered electron intensity as a function of energy loss and scattering angle are made for He at an incident electron energy of 25 keV.

Compton Scattering of High-Energy Electrons from Helium

The electron-impact energy-loss spectrum of He at a scattering angle of 7\ifmmode^\circ\else\textdegree\fi{} has been measured with an energy resolution of 2.7 eV full width at half-maximum using 25-keV incident electrons. A binary-encounter approximation was used to obtain the electron Compton profile from the cross-section differential with respect to both the energy loss of the incident electron and solid angle of the scattered electron $\frac{{d}^{2}\ensuremath{\sigma}}{\mathrm{dEd}\ensuremath{\Omega}}$. The electron Compton profile was corrected for interference scattering from pairs of target electrons and exchange. It was then compared to theoretical and x-ray experimental values for the Compton profile. The effects of background, multiple scattering, and energy resolution are discussed. The electron-impact and x-ray methods for measuring Compton profiles are compared.