Compton Defect Research Articles

Asymmetries and anisotropies in the Compton scattering from the hydrogen molecule

AbstractThe Compton energy loss spectra of atomic targets exhibits usually a specific asymmetry due to the postcollisional electrostatic interaction between the remaining ion and the ejected electron. This asymmetry, or Compton defect, also exists in the scattering by molecules or solids. The first attempt to describe the Compton defect for the hydrogen molecule is proposed here. The Compton energy loss spectra depends particularly on the relative orientation of the momentum transferred by the incident particle and the molecular axis. A comparison between the respective magnitudes of Compton profiles and Compton defects was one of the aims of this article. The results emphasize the particular interest of a simultaneous interpretation of both symmetrical and antisymmetrical contributions in the study of molecular or solid‐state electronic structures. © 1995 John Wiley & Sons, Inc.

Compton scattering beyond the impulse approximation: Application to the core electrons of carbon.

The Compton profile produced by the 1s electrons of carbon has been calculated using (i) the impulse approximation, (ii) the hydrogenic approximation, and (iii) a type of Hartree-Fock self-consistent-field (HF-SCF) approximation. Significant deviations between the hydrogenic and the impulse results are found for incident photon energies below 25 keV. Between the hydrogenic and the quasi-HF-SCF results, the main difference is that the Compton defect and the maximum of the profile are much smaller when using the latter approximation. These differences are discussed in terms of simple models.

On the Compton defect

Simple analytical formulas are given for Compton profiles obtained from an exact first Born approximation for K, L, and M subshells. Compton profile asymmetries and Compton defects are investigated and compared with experimental data.

Electron impact induced post-collisional Auger decay. A two-potential complex coordinate treatment

The process of post-collisional Auger decay induced by electron impact is discussed. Close to the excitation threshold the situation is framed within the atomic and molecular resonance theory, and discussed from the point of view of electron Compton scattering. The connection between post-collisional effects in Auger decay and the Compton defect is indicated. For restricted classes of processes, the scattering amplitudes is derived. The derivation is based on the Gell-Mann-Goldberger two-potential formulation combined with the complex coordinate method, and provides an extension of the treatment recently proposed by us for photon-induced Auger decay.

Nonrelativistic Compton scattering in Furry’s picture. II. Bethe surface by means of the complex-coordinate method

Bethe surface as a means of characterizing the inelastic scattering of photons and electrons on atomic targets is discussed, and framed within the two-potential Furry’s picture of scattering theory. In particular, the cross section for inelastic photon scattering is considered, and its first distorted Born approximation is identified to be given in terms of Bethe surface along the path conserving energy and momentum transfer. The difficulties in obtaining accurate cross sections in situations where the energy transfer is close to the ionization threshold are indicated, and related to the so-called Compton defect. The method for calculating the inelastic photon scattering cross section, introduced in Part I of this work [J. Chem. Phys. 80, 5669 (1984)] is summarized. The scattering cross section, and the entire Bethe surface, is obtained by means of the L2 discretization of the continuum and implemented in terms of the complex-coordinate method, without explicit calculation of the final scattering waves. The method is tested for the case of photon scattering off the hydrogen atom. The results are encouraging, and may be relevant for applications of the complex-coordinate method to calculations of more general transition amplitudes. The method is predicted to be most useful in cases close to ionization threshold (e.g., appearance edges in Compton scattering, Compton defect). Although applied to the one-electron problem the procedure is readily applicable to many electron atoms.

The Compton profile of neon: Experimental study beyond the impulse approximation

High-precision relative energy-loss spectra of 25 keV electrons scattered from neon atoms are measured in the momentum transfer range 0.5 a.u.<K< 15 a.u. The corresponding generalized oscillator strengths are made absolute by use of the Bethe sum rule and then converted to Compton profiles (CP). These CP’s are shown to be K-independent in the K ranges 5–7 and 13–15 a.u., where effective valence and total CP’s are respectively defined. Neither of these profiles is reproduced by the impulse approximation (IA) because of the existence of the so-called Compton defect, i.e., a lack of symmetry in the intensity of the observed profile on the positive and negative q sides (q is the usual Compton parameter), and a shift of its maximum from the q=0 position predicted by the IA. Following a theoretical treatment proposed by Tavard and co-workers for H and He, the experimental profiles are divided into their symmetrical (SCP) and antisymmetrical (ASCP) parts with respect to the q variable: the ASCP agrees with Tavard’s qualitative predictions, while the SCP is not reproduced by the IA. The remaining difference might be attributed to higher order terms in Tavard’s series development of the Born operator. Comparison of our results to previous experimental ones is also given.

AtomicK- andL-shell Compton defects for the study of electronic structures

An accurate treatment is developed for the calculation of Compton defects and their physical interpretation. The case of atomic $K$ and $L$-shells analyzed here exhibits the strong dependency of Compton defects with overlapping properties of individual orbitals. For given azimuthal $l$ and magnetic $m$ quantum numbers, a simple generalization allows one to predict the sign of the Compton defect from the parity of $l+m$.

Asymmetry of the compton profile, the compton defect

An expansion of the Born operator is proposed, leading to correction terms to the impulse approximation and allowing a physical interpretation of the Compton defect.

The compton defect in neon and argon as observed using 25 kev incident electrons

Electron energy-loss spectra, obtained for Ne and Ar, are analysed in terms of Compton profiles (CPs). The experimental CPs do not peak at q = 0, nor are they symmetrical as to their maximum value, as predicted within the framework of the impulse approximation. This “Compton defect” is characterised by a shift parameter Δ q and an asymmetry parameter δ q, and is investigated as a function of momentum transfer K. A qualitative comparison is made with theoretical predictions for the Compton defect. We also emphasize the K range where partial or total K-independent CPs of the target may be determined.

Bethe surface and Compton profile of NH3 obtained by 35 keV electron impact

Complete inelastic electron impact spectra have been obtained for NH3 for a momentum transfer range from 0.4 to 12.5 a.u. using 35 keV electrons. These spectra were converted to relative generalized oscillator strengths (GOS), were placed onto an absolute scale by the Bethe sum rule, and higher order sum rules were used to test the accuracy of the GOS. The Compton profile (CP) of NH3 was determined from the GOS by means of the impulse approximation (IA) and it was found that the CP’s were asymmetric and shifted in respect to the free electron theoretical CP. This Compton defect was analyzed in detail and was shown to be due to the failure of the IA. The area under the CP is discussed in terms of the x-ray incoherent scattering factor and experimental results for the valence, inner shell, and total CP’s are compared to several theoretical profiles.

The compton defect in ammonia as observed using 35 keV incident electrons

Using a 35 keV electron beam incident on NH 3, precision measurements of the energy loss position of the Compton peak have been performed. The observed Compton peak is found to be at larger energy losses than predicted for an electron scattered through the same angle from a stationary unbound electron. This defect has been studied for the momentum transfer range 0.5 au < K < 11 au, and is shown to be nonzero even at large K values. A sudden increase in the magnitude of the defect is observed when the inner electrons start contributing to the maximum of the Compton profile. This could suggest the possibility that the defect is related to the binding energies of the target electrons.

A critical evaluation of high energy electron impact spectroscopy to measure Compton profiles

The authors present high precision Compton profile measurements on helium and molecular hydrogen obtained by high energy electron impact spectroscopy. Inelastic electron scattering cross sections at 35 keV incident energy have been studied for both He and H2 over the momentum transfer range of 1.5-12.5 au. It is shown that there is a disparity between the energy-loss spectra converted to Compton profiles by means of the binary encounter theory and the theoretical Compton profile. This discrepancy displays itself as an asymmetry of the profile and a shift of the peak to a lower energy loss, known as the 'Compton defect'. A critical evaluation of the technique, improvements made over the previous electron Compton work, the method of data analysis and a rigorous test of the binary encounter theory will be discussed in detail. The authors also analyse the problem of multiple scattering.

Electron Compton defect observed in He,H2,D2,N2, and Ne profiles

A high-energy electron-impact spectroscopy (HEEIS) apparatus has been constructed for high-precision Compton-scattering experiments. Electron-Compton-scattering experiments are performed by crossing a beam of high energy, but nonrelativistic, electrons with a beam of atoms or molecules and measuring the energy-loss spectrum of the scattered electrons over a range of scattering angles. The improvements of design and technique, the method of data analysis, and the theory used to convert cross sections to Compton profiles are discussed fully. It was found that the energy-loss spectra taken over a range of scattering angles do not reduce by means of the binary-encounter approximation (impulse approximation) to Compton profiles in agreement with theory. This disagreement is most apparent in a shift of the experimental Compton peak---the Compton defect---from the peak predicted by the binary-encounter theory. The Compton defect has been studied in detail for momentum transfers from 1.5-12 a.u. for both He and ${\mathrm{H}}_{2}$. Defect measurements for ${\mathrm{D}}_{2}$, ${\mathrm{N}}_{2}$, and Ne have also been made and it was found that the ${\mathrm{N}}_{2}$ and Ne defects were opposite in direction from the He and ${\mathrm{H}}_{2}$ defects. The ${\mathrm{D}}_{2}$ defect was identical to that for ${\mathrm{H}}_{2}$. The electron Compton defect is discussed in relation to other recent defect measurements using x-ray and ($e, 2e$) techniques as well as recent theoretical results. An evaluation of the theory used to convert cross sections to Compton profiles is presented and, on the basis of the defect measurements, it is suggested that, even when the binary-encounter conditions have been attained at large momentum transfers, the binary-encounter theory breaks down in the high accuracy (1%) limit. An explanation for this breakdown is given and recent theories, which at least qualitatively account for the Compton defect, are discussed.

A comment on the Compton defect at high momentum transfer

Abstract Recent experimental evidence has indicated that there may be a reduction of about 1% in the Compton energy shift to the peak of a Compton profile measured in a solid (compared to the corresponding shift for a photon scattered from a stationary, free electron). In this note suggestions that electron-electron interactions between the valence electrons may be responsible for this defect are examined. It is concluded that, for the very large momentum transfers at which the experiments were conducted (k/kF ∼ 10), arguments based on collective interactions cannot explain the large energy of the Compton defects (< 10 eV) obtained experimentally.

The Compton defect

Abstract Independent Compton scattering studies on polyethylene and lithium with MoKα and MoKβ X-radiation have revealed that their Compton profiles are centred around a shifted wavelength which is some 10 eV smaller than that for a photon scattered from a stationary electron through the same angle. This Compton defect has also been observed in beryllium, and it is suggested that the defect is a general feature of Compton scattering from valence electrons arising from a many-body correction to the impulse approximation.

High energy electron impact spectroscopy measurement on the Compton defect

Abstract Recent Compton scattering experiments with a 35 keV electron beam on helium, molecular hydrogen, and molecular deuterium, have shown that the energy loss spectra do not reduce to Compton profiles by means of the Binary Encounter theory. The observed Compton peak is shifted to smaller energy losses than those associated with a stationary unbound electron. This shift has been studied for momentum transfer from 1·5 to 12 a.u. for both He, and H2, and it is suggested that even at large momentum transfers electron correlations could be important.

The Compton profile and Compton defect in aluminium

Abstract Compton profile measurements of aluminium at MoKα failed to find any anisotropy between the [100] and [110] directions but by extending the measurements to MoKβ (where the doublet separation is much less critical) a Compton defect of ∼10 eV has been found for the valence electrons.