Averaged Electron Momentum Research Articles

Positron annihilation measurements of Dy-doped YBCO superconductors

Positron annihilation lifetime and Doppler broadening energy spectra have been measured in Dy-doped high-temperature YBCO superconductors as a function of temperature between 40 and 295 K. The defect-related lifetime component τ 2 was approximately constant from room temperature to above T c at about 90 K and then showed a step-like decrease. These results indicated that the electronic structure changed below T c. It was also found that a transition in the positron Doppler line-shape parameter S occurred at the superconducting transition temperature. These results show that the average electron momentum at the annihilation sites increases as temperature is lowered across the superconducting transition range.

Positron annihilation measurements of Pr-containing superconductor compounds

Positron annihilation lifetime and Doppler broadening energy spectra have been measured in Pr-containing YBa2Cu3O7−δ as a function of temperature between 18 and 295 K. The defect-related positron lifetime component τ2 was independent of temperature for the PrBa2Cu3O7−δ compound and was very close to the value τ1 associated with bulk or defect-free material. These results indicate that the structure of this compound is nearly free of defects which trap positrons and that there is no electronic structure change during cooling. There was a slight temperature dependence below Tc for the Y0.5Pr0.5Ba2Cu3O7−δ compound. It was also found that a change in the positron Doppler line-shape parameter S occurred at the superconducting transition temperature for 0.5 Pr-containing compound but not for the 1.0 Pr-containing compound. These results show that the average electron momentum at the annihilation sites increases as temperature is lowered across the superconducting transition range for the 0.5 Pr-containing compound but not for the PrBa2Cu3O7−δ compound.

ChemInform Abstract: Electron‐Momentum‐Specific Valence‐Shell Electronic Structure of and Many‐Body Effects in cis‐Dichloroethylene: Ionic‐State‐Resolved Orientationally Averaged Electron Momentum Density Measurement by Symmetric Noncoplanar (e,2e) Spectroscopy.

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Electron-momentum-specific valence-shell electronic structure of and many-body effects in cis-dichloroethylene: Ionic-state-resolved orientationally averaged electron momentum density measurement by symmetric noncoplanar (e,2e) spectroscopy

The ionization energy (IE) spectra and electron momentum distributions (MDs) of the valence shell of cis-dichloroethylene have been obtained using symmetric noncoplanar (e,2e) spectroscopy. The IE spectra were found to be in good accord with earlier photoelectron data and in qualitative agreement with a literature pole-strength spectrum generated by a Green’s function (GF) calculation. In particular, extensive many-body features were observed above ∼22 eV in the IE spectra and found to be consistent with the pole-strength splitting of the three innermost valence states (7a1)−1, (6b2)−1, and (6a1)−1, as predicted by the GF calculation. The measured MDs were compared with ab initio calculations using self-consistent-field wave functions of 4-31G, 6-31G, and 6-31++G** basis sets. The general lack of quantitative agreement between experiment and calculations indicated the need for improved wave functions beyond the 6-31++G** level for the outer-valence orbitals. Moreover, the experimental MDs have provided an unambiguous assignment of the ordering of the D(8b2)−1 and E(2b1)−1 ionic states. A new satellite feature at ∼21 eV was found to have a MD similar to that of the H(7b2)−1 state, confirming the GF result. Furthermore, the many-body features above 26 eV were dominated by s-type angular dependence and could be ascribed predominantly to ionization of the innermost valence orbital 6a1. Finally, the bonding morphology of the valence orbitals was found to be different from other related ethylene derivatives due to ligand substitution effects.

Valence-shell electronic structures of cis- and trans-butene: ionic-state-resolved orientationally averaged electron momentum densities by symmetric noncoplanar (e, 2e) spectroscopy

Electron momentum distributions (MDs) of selected valence-shell ionic states of cis- and trans-butene have been obtained using symmetric noncoplanar (e, 2e) spectroscopy. The measured MDs are compared with ab initio calculations using self-consistent-field wavefunctions of 4-31G, 6-31G and 6-31 + +G ** basis sets. For the highest occupied molecular orbitals (HOMOs), only MDs generated by the more diffuse 6-31 + +G ** basis set appear to adequately reproduce the experimental results. More pronounced discrepancies between experiment and calculations in the low-momentum region are found for the next HOMOs of both isomers. The level of agreement generally indicates the importance of and the need for more diffuse wavefunctions for the outer-valence orbitals. On the other hand, generally good agreement between experiment and calculations has been observed in the MDs of the two prominent inner-valence ionic states between 17 and 22 eV, which provides strong support for their assignments for the first time. Furthermore, experimental MDs measured at higher energies in the inner-valence region provide further evidence for the observation that the many-body states above 22 eV may be ascribed predominantly to ionization of the innermost valence orbitals. Finally, despite the similarity in the calculated orbital energies for the corresponding orbitals between the cis and trans isomers, their calculated MDs are found to be qualitatively different, particularly in the case of the outer-valence orbitals. This sensitivity of MDs to the physical structures of the isomers is demonstrated.

Compton scattering from bound electrons: comparisons of the impulse approximation with exact IPA calculation

The doubly differential cross section for Compton scattering from K-shell atomic electrons is calculated in the relativistic impulse approximation (lA) and compared with an exact relativistic second order S-matrix calculation based on the independent particle approximation (IPA). Comparison is made for several atoms and for incident photon energies up to 320 keV. A new criterion for the validity of the impulse approximation is given in terms of the average electron momentum contributing to the scattered photon spectrum rather than the momentum expectation value of the orbital electron. In the energy range considered here the impulse approximation gives a good description of the portion of the spectrum in which the new criterion is fulfilled.

Improved lower bounds to the total atomic kinetic energy and other density-dependent quantities

By means of a variational procedure the authors find a lower bound to the Thomas-Fermi kinetic energy of a fermionic system in the ground state, in terms of the moments (r-2), (r-1) of the fermionic density rho (r), and the number of particles, N, given by a formula which improves previous results. This expression allows them to bound the exact kinetic energy of a fermionic system by using the works of Lieb and Thirring. This variational technique can also be applied in order to bound density-dependent quantities of atoms as the exchange energy in Dirac's form and the average electron radial ( rho ) and momentum ( gamma ) densities, numerical and asymptotically because in these cases it is not possible to find exact analytical solutions.

Rigorous lower bounds to average electron radial and momentum densities for atomic systems.

Rigorous lower bounds to the average electron radial density 〈\ensuremath{\rho}〉 in terms of any two moments of the charge density have been found for N-electron systems. Similar bounds to the average electron momentum density 〈\ensuremath{\gamma}〉 are also given by means of any two momentum expectation values. These bounds allow us to establish rigorous inequalities to 〈\ensuremath{\rho}〉 and 〈\ensuremath{\gamma}〉 (which have been recently found to be experimentally measurable) and other fundamental and/or measurable quantities such as the electronic energy, the diamagnetic susceptibility, and the Compton profile peak height J(0). The quality of the bounds is analytically discussed and numerically studied within the Hartree-Fock framework. Best bounds turn out to be (1) 〈\ensuremath{\rho}〉\ensuremath{\ge}〈${r}^{\mathrm{\ensuremath{-}}1}$${〉}^{3}$/9\ensuremath{\pi}N, (2) 〈\ensuremath{\gamma}〉\ensuremath{\ge}8[J${(0)]}^{3}$/9\ensuremath{\pi}N. .AE

Hydrodynamic hot-electron transport model with Monte Carlo-generated transport parameters

A unique hot-electron transport model suitable for studying submicron GaAs device structures is presented. The model is based on the semiclassical “hydrodynamic” conservation equations for the average electron density, momentum, and energy. The model includes electron relaxation times, momentum relaxation times, energy relaxation times, electron temperature tensors and heat flow vectors as a function of average electron energy for the Γ, X and L valleys of GaAs. The relaxation times represent rates of exchange of electrons between valleys and rates of loss of average momentum and average energy between and within the individual valleys. The electron temperature tensor and heat flow vector depend on the electron velocity distribution about the average electron velocity and ultimately affect transport when spatial variations in average velocity and average energy exist. Transport parameters are calculated using the Monte Carlo method and the ergodic principle applied directly to the integral definitions for the parameters. Therefore, the model includes nonequilibrium transport effects such as velocity overshoot and nonuniform average electron energy. The new model should prove instrumental in optimizing electron transport through submicron structures for high-speed device applications.

Temperature dependence of positron-annihilation parameters in YBa2Cu3O7-x above and below the superconducting transition.

The temperature dependence of positron-annihilation parameters for $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ $x=0.7, 0.4, \mathrm{and} 0.0$ are reported. It was found that a transition in the Doppler line-shape parameter $S$ was associated with the superconducting transition temperature (${T}_{c}$) in $\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}x}$ $x=0.4 \mathrm{and} 0.0$, while no transition was observed in the nonsuperconducting Y${\mathrm{Ba}}_{3}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.3}$. Positron lifetime parameters in Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ were found to be consistent with positrons localized at open volume regions (probably unoccupied crystallographic sites) in this material with a lifetime of 210 psec. The positron lifetime decreased by approximately 5% across the superconducting transition and subsequently by 4% to 193\ifmmode\pm\else\textpm\fi{}1 psec at 12 K. These results indicate that the electron density at this site increases approximately 9% between 100 and 12 K. Doppler line-shape results show that the average electron momentum at the annihilation site increases across the superconducting transition and from sample to sample as the oxygen concentration decreases.

Density functional calculation of Compton profiles of metals using phase-space approach

Spherically averaged electron momentum densities (EMD) in Al, V and Cu metals have been calculated by using density functional theory in the phase-space approach. Compton profiles, J(q) and expectation values 〈 p n 〉 have been computed. These theoretical results show satisfactory agreement with the experimental data for Al, V and Cu.

Asymptotic expansions of the electron momentum densities of the atoms from hydrogen through lawrencium

The first three coefficients in each of the small p Maclaurin and large p asymptotic expansions of the spherically averaged electron momentum densities of the ground states of the 103 neutral atoms from hydrogen through lawrencium, 73 atomic cations and 41 atomic anions are calculated from nonrelativistic self-consistent-field wave functions. These coefficients should be useful in the analysis of experimental Compton profiles. An analysis of the periodic behavior of these coefficients is given.

A test by Monte Carlo simulation of the lucky drift theory of impact ionisation for a model with energy-dependent parameters

The lucky drift theory of the impact ionisation coefficient is tested against a Monte Carlo simulation for a model semiconductor with a multi-valley band structure and energy-dependent parameters. The lucky drift formulation due to Burt (1985) is applied to this model to calculate the steady-state drift velocity, average electron energy, energy and momentum relaxation lengths and the impact ionisation coefficient. The lucky drift predictions for these quantities are compared with estimates derived from a Monte Carlo simulation over a range of values of the applied electric field. The agreement between the lucky drift predictions and Monte Carlo results is quite encouraging, given the extreme simplicity of the theory and the generality of the model.

The average electron momentum density and rigorous bounds to average electron densities for atoms and molecules

The average electron density in momentum space, viz. 〈γ〉, where γ( p) is the electron momentum density, is defined and shown to be experimentally measureable. The connection is obtained via the relation 8π 3〈γ〉 = ∝ B 2( s) ds, where B( s) is reciprocal form factor. The approximate relationships 〈 p〉 = 2 〈 r 3〉/3π 2 and 〈γ〉 = 2 〈 r 3〉/3π 2 have been phase space considerations. They have been examined for near Hartree-Fock atomic limit data. Rigorous bounds to atomic and molecular average electron densities in configuration and momentum spaces are derived without any reference to an independent-particle model.

Electron Coincidence Spectroscopy: An Introduction to Momentum Space Chemistry

The application of electron coincidence or (e,2e) spectroscopy to obtaining detailed information on the dynamic structure of atoms and molecules is discussed. The technique obtains separation energy spectra and spherically averaged electron momentum distributions for each molecular orbital in the valence region. A brief discussion of molecular orbital density functions in momentum space is given. The results using Hartree-Fock wavefunctions for atomic orbitals and LCAO-MO wavefunctions for molecular orbitals are compared with (e, 2e) data. The sensitivity of the data to electron correlations in either the initial or final ion many body states is discussed and examples are given.

Electron momentum densities in disordered muffin-tin alloys

The application of average $t$-matrix (ATA) and coherent potential (CPA) approximations to the calculation of average electron momentum density $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}})$ in random muffin-tin alloys ${A}_{x}{B}_{1\ensuremath{-}x}$ is considered. The necessary equations for the general matrix elements of the operators describing scattering by the CPA atom and also by an $A$ or $B$ atom embedded in the effective medium are derived. Various versions of the ATA for $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}})$ are discussed. Several $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}})$ curves calculated on the basis of the CPA and ATA in ${\mathrm{Cu}}_{x}{\mathrm{Ni}}_{1\ensuremath{-}x}$ are presented. These results are used to delineate the effects on $\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}})$ of self-consistency in the treatment of disorder.

Electron momentum density in disordered muffin-tinCu1−xNixin the average-t-matrix approximation

In an earlier article we discussed the formalism for evaluating the average electron-momentum density in a random binary alloy by using the average-$t$-matrix approximation to treat the disorder and muffin-tin potentials to represent the constituent atoms. The present paper considers the application of this formalism to ${\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Ni}}_{x}$ over a range of alloy compositions. The characteristic effects of disorder on the spectral momentum density $〈\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}},E)〉$ are delineated. In discussing the momentum density $〈\ensuremath{\rho}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}})〉$ we focus on how this quantity changes as $x$ increases from 0 to 1 and the Ni $d$ band develops from a virtual bound state below the Fermi energy into a transition-metal $d$ band interacting the Fermi energy. Our detailed predictions in this regard should be amenable to experimental verification by two-dimensional positron-annihilation experiments.

Spectral Weight Function and Electron Momentum Distribution in the Normal Electron-Phonon System

A detailed calculation for the interacting electron-phonon system is carried out by using the double time Green's function method. The self-energy part and then the spectral weight function of the electron Green's function are given in detail to the second order of electron­ phonon interaction. The effects of the interaction on the chemical potential of the electron and the Fermi momentum of the electron distribution are investigated. The average electron momentum distribution at zero temperature is evaluated in an approximation which may be considered as a simplification of the Migdal approximation. The amount of the discontinuity at the Fermi momentum is obtained and the numerical results show that there is a distinct modification of the electron distribution near the Fermi momentum due to the presence of the electron-phonon interaction.