Study on distribution of electron momentum density and Fermi surface in lead by positron annihilation

The momentum density of electrons and the Fermi surface are measured in metal lead by the technique of positron annihilation. The three-dimensional electron-positron momentum distribution is reconstructed from measurements of the two-dimensional angular correlation of positron annihilation radiation (2D-ACAR), followed by the image reconstruction technique based on a direct Fourier transformation. On the basis of the obtained experimental spectrum, the Fermi surface topology, the high momentum components (HMC), the enhancement effect, and the autocorrelation function are discussed. The obtained experimental results are in good agreement with theoretical calculations.     

Doppler broadening of in-flight positron annihilation radiation due to electron momentum.

We report the first observation of electron momentum contributions to the Doppler broadening of radiation produced by in-flight two-photon annihilation in solids. In these experiments an approximately 2.5 MeV positron beam impinged on thin polyethylene, aluminum, and gold targets. Since energetic positrons easily penetrate the nuclear Coulomb potential and do not cause a strong charge polarization, the experimental annihilation line shapes agree well with calculations based on a simple independent-particle model. Moreover, annihilations with the deepest core electrons are greatly enhanced.     

Influence of electron diffraction on measured energy-resolved momentum densities in single-crystalline silicon

Electron momentum spectroscopy is used to determine the spectral function of silicon single crystals. In these experiments 50 keV electrons impinge on a self-supporting thin silicon film and scattered and ejected electrons emerging from this sample with energies near 25 keV are detected in coincidence. Diffraction effects are present that give rise to additional structures in the measured spectral momentum densities. Spectra for a specific momentum value can be obtained at different orientations of the crystal relative to the analysers. By comparing these spectra for which the measured momentum density is the same, but the diffraction conditions of the incoming and outgoing electron trajectories differ, one can distinguish between features due to diffraction of the incoming and/or outgoing electrons, and those due to the electronic structure of the target itself.     

Electron correlations, spontaneous magnetization and momentum density in quantum dots

The magnetization of quantum dots (QDs) is discussed in terms of a relatively simple but exactly solvable model Hamiltonian. The model predicts oscillations in spin polarization as a function of dot radius for a fixed electron density. These oscillations in magnetization are shown to yield distinct signature in the momentum density of the electron gas, suggesting the usefulness of momentum resolved spectroscopies for investigating the magnetization of dot systems. We also present variational quantum Monte Carlo calculations on a square dot containing 12 electrons in order to gain insight into correlation effects on the interactions between like and unlike spins in a QD.     

Probing the spectral densities over the full three-dimensional momentum space

Electron momentum spectroscopy is often used to determine the spectral function of materials. It relies on the determination of the scattering angle of electrons with extremely high precision. In practice, it is important to calibrate these angles, and hence the momentum scales. Here we describe a method to do so and show how minor misalignments affect the measured momentum densities of Li₂O. Using the same procedure we further calibrated the momentum scale by measuring the spectral momentum density along a Brillouin zone boundary of a Si single crystal.     

Electron momentum density and Compton profile by a semi-empirical approach

Here we propose a semi-empirical approach to describe with good accuracy the electron momentum densities and Compton profiles for a wide range of pure crystalline metals. In the present approach, we use an experimental Compton profile to fit an analytical expression for the momentum densities of the valence electrons. This expression is similar to a Fermi–Dirac distribution function with two parameters, one of which coincides with the ground state kinetic energy of the free-electron gas and the other resembles the electron–electron interaction energy. In the proposed scheme conduction electrons are neither completely free nor completely bound to the atomic nucleus. This procedure allows us to include correlation effects.We tested the approach for all metals with Z=3–50 and showed the results for three representative elements: Li, Be and Al from high-resolution experiments.     

The Fermi surface of [Formula: see text

The heavy-fermion compound [Formula: see text] has been studied using the fully relativistic spin-polarized mean muffin-tin orbital method within the local density approximation. Two separate calculations, one where the f electron is treated as a valence electron and the other where it is treated as part of the core, have been performed and the Fermi surface is obtained. The angular-dependent de Haas - van Alphen (dHvA) frequencies are calculated in both cases and they are compared with the experimental dHvA frequencies. We also calculated the electron momentum densities and compared them with the electron - positron momentum densities measured from the two-dimensional angular correlation of electron - positron annihilation radiation. The spin polarization of the Fermi surface is analysed and we present a new interpretation of the experimental data of Harrison et al.     

Doppler broadening of positron annihilation photons in metals

The Doppler broadening of positron annihilation photons was measured in 17 metals. A model which considers the positron lifetime spectra in metals to be composed of terms for annihilation with conduction and core electrons and surface centers of low electron momentum is used to correlate calculated core annihilation rates with the Doppler lineshape. Ta metal was doped with defects with high energy implantations of¹⁴N⁺⁴ ions at variable doses. Differences in the Doppler linewidths were ascribed as being principally a reflection of the probabilty of annihilation with core electrons relative to annihilation with conduction electrons.     

Experimental and calculated momentum densities for the complete valence orbitals of the antimicrobial agent diacetyl

The first electronic structural study of the complete valence shell binding energy spectra of the antimicrobial agent diacetyl, encompassing both the outer and inner valence regions, is reported. The binding energy spectra as well as the individual orbital momentum profiles have been measured by using a high resolution （e, 2e） electron momentum spectrometer （EMS） at an impact energy of 1200eV plus the binding energy, and using symmetric noncoplanar kinematics. The experimental orbital electron momentum profiles are compared with self-consistent field （SCF） theoretical profiles calculated using the Hartree-Fock approximation and Density Functional theory predictions in the target Kohn-Sham approximation which includes some treatment of correlation via the exchange and correlation potentials with a range of basis sets. The pole strengths of the main ionization peaks from the inner valence orbitals are estimated.     

环戊烯分子内价轨道1a′的电子动量谱学研究

报道了环戊烯（C₅H₈）分子1a′轨道的电子动量谱，并且给出了价 轨道的电离能谱信息 .实验在非共面对称几何条件下用能量多道型电子动量谱仪完成，入射电子的能量为1200 eV 加结合能.通过Hartree-Fock 和密度泛函方法计算得到了C₅H₈分子 1a′轨道的动量谱. 对1a′轨道的电子动量谱的实验值和理论计算进行了比较，得到了该轨道的极强度（pole s trength）的信息.     

An extraction algorithm for core‐level excitations in non‐resonant inelastic X‐ray scattering spectra

Non‐resonant inelastic X‐ray scattering of core electrons is a prominent tool for studying site‐selective, i.e. momentum‐transfer‐dependent, shallow absorption edges of liquids and samples under extreme conditions. A bottleneck of the analysis of such spectra is the appropriate subtraction of the underlying background owing to valence and core electron excitations. This background exhibits a strong momentum‐transfer dependence ranging from plasmon and particle–hole pair excitations to Compton scattering of core and valence electrons. In this work an algorithm to extract the absorption edges of interest from the superimposed background for a wide range of momentum transfers is presented and discussed for two examples, silicon and the compound silicondioxide.     

Study of silica aerogel grain surfaces by using a positron age–momentum correlation technique

The effect of heat treatment on silica aerogel has been studied by a positron age–momentum correlation technique and infrared measurement. A difference was observed between the momentum distributions of the electrons on the first layers of the silica aerogel grain surfaces and the electrons in the grains in an as-supplied sample, but not in the sample heat treated at 800 °C. A large change in the S parameter for the momentum distribution of the electrons on the first layer occurs around 200 °C. This change correlates well with that of the infrared spectra, which show oxidation of the methoxyl groups at temperatures above around 200 °C. This correlation reveals that those groups are mainly located on the first layer of the silica grains. Received: 13 November 2000 / Accepted: 23 July 2001 / Published online: 30 October 2001     

Electronic structure and positron annihilation in alkali metals: Isolation of ionic core contribution and valence high-momentum components

Momentum densities of annihilation pairs from valence as well as from ionic core electrons in alkali metals are calculated ab initio and compared with the experimental results. It is shown that the valence high-momentum components constitute a great deal (23–34% in Na-Cs and probably even more in Li) of the Gaussian part of the angular correlation curves. The average core enhancement factor γ_c ranges from 1.5 (Li) to 7.1 (Cs) and may be well expressed by a logarithmic function of ionic core polarizability. The presented values of γ_c are much higher than the core enhancement factors in the high-momentum (?15 mrad) region which, according to the recent theory of Bonderup, Andersen and Lowy, should not be very different from unity.     

Systematics of the rare-gas core contributions to the positron annihilation spectra of some simple and transition metals

Taking into account the core electron enhancement factor the rare-gas core contribution to the angular correlation positron annihilation spectra and to the total annihilation rate in some simple and transition metals are calculated. It is shown that the valence high-momentum part of the Gaussian fraction is not negligible in simple metals. In 3d and 4d metals, the rare-gas core part of the total annihilation rate amounts from 9 to 37%. The results are expected to help in the correct interpretation of the positron annihilation data.     

Experimental and theoretical investigations into the electronic structure of CF2Br2 by electron momentum spectroscopy

The binding energy spectra and electron momentum density distributions for the valence orbitals of CF₂Br₂ have been obtained by using electron momentum spectroscopy (EMS) at an impact energy of 1200 eV plus binding energy. The measured electron momentum profiles are compared with Hartree–Fock (HF) and density functional theory (DFT) calculations with different-sized basis sets. In general, the DFT-B3LYP calculation using the large basis sets of 6-311++G** and aug-cc-pVTZ fairly describe the experimental results. Moreover, the controversial orderings of the outer valence orbitals have been reassigned. The pole strength of the main ionization transition from the inner valence orbital of 1b₂ is determined.     

Compton profile of x rays and the momentum distribution functions of valence electrons in ZnSe

The momentum distribution functions of valence electrons are constructed from the measured Compton profile of cubic ZnSe. The Compton profile of ZnSe was measured using x rays (=0.071 nm, h=17.4 keV). The state of the valence electrons in ZnSe was investigated by comparing the experimental Compton profiles and the momentum distribution functions with those calculated theoretically with allowance for the change of the wave functions of the valence electrons in the crystal.Translated from Izvestiya Vysshikh Uchebnykh, Zavedenii, Fizika, No. 7, pp. 25–28, July, 1980.     

Density of states and the problem of Sm valence

Density of states for Sm metal has been calculated in DFT/GGA approximation using the same treatment for f and s-d bands. It is concluded that the 4f electrons of Sm must be considered as valence electrons, not shallow core states. Therefore the 4f-5d transition cannot change the valence of Sm, which may be characterized (if necessary) by the sum of all electrons in the s-d-f valence bands. The possibility of alternative interpretation of UPS spectra of Sm adsorbed films is illustrated by calculations of DOS (density of states) for oxygen-contaminated Sm crystal.     

Study of the electron momentum distribution in vanadium by positron annihilation

The angular correlation of the positron annihilation radiation has been measured with a bidimensional apparatus in four planes of V single crystals. The results are compared with calculations of the electron- positron momentum distribution and with theoretical Fermi surface.     

Simulating electron momentum spectra of iso-C2H2Cl2： A study of the core electronic structure

Electron momentum spectroscopy(EMS) has been used for the first time to study core electronic structure of isoC2H2Cl2. In the present work, the pronounced difference between ionization energies of two C1 score orbitals(2A1 and 3A1) is seen as a chemical shift of 3 eV, which is due to different chemical environments of the related carbon atoms. Both the calculated spherically averaged core electron momentum distributions(MDs) and three-dimensional electron momentum density maps show that these core molecular orbitals(MOs) 2A1and 3A1 exhibit strong atomic orbital characteristics in real and momentum space. However, the core states 2B2 and 4A1, which are almost degenerate and related to two equivalent atoms, exhibit notable differences between the momentum and position depictions. In contrast to the position space, the momentum density maps of these two core MOs highlight the interference effects which are due to the nuclear positions. The 2B2 orbital of iso-C2H2Cl2 is the antisymmetric counterpart of the 4A1 core orbital in real space. However, it relates to the 4A1 orbital by an exchange of maxima and minima in momentum space. Due to interference effects between electrons scattered from different atomic centers, modulations with a periodicity of 1.12 a.u. can be seen in the computed momentum densities, which tend to decay with increasing electron momenta. Accordingly, the EMS can not only effectively image the electronic structure of compounds by studying valence orbitals, but also provides direct information on the nature of the nuclear geometry by investigating the core states.     

Molecular orbital momentum distributions and binding energies for H2O using an electron impact coincidence spectrometer

The construction and operation of an instrument which uses the techniques of coincidence counting and electron impact spectroscopy is reported for the study of molecular ionization at large momentum transfer in which the two outgoing electrons are detected at 45° to the incident beam. Variation of the incident energy provides binding-energy spectra for Xe, CH₄ and H₂O up to 45 eV. Alternatively variation of the azimuthal angle (symmetric, non-coplanar geometry) gives a measure of the electron momentum distribution for any selected orbital in the binding-energy spectrum. Momentum distributions for the four valence orbitals of H₂O are compared with various wavefunctions from the literature.