Averaged Electron Momentum Research Articles

Deep learning for retrieval of the internuclear distance in a molecule from interference patterns in photoelectron momentum distributions

We use a convolutional neural network to retrieve the internuclear distance in the two-dimensional H$_2^{+}$ molecule ionized by a strong few-cycle laser pulse based on the photoelectron momentum distribution. We show that a neural network trained on a relatively small dataset consisting of a few thousand of images can predict the internuclear distance with an absolute error less than 0.1 a.u. We study the effect of focal averaging, and we find that the convolutional neural network trained using the focal averaged electron momentum distributions also shows a good performance in reconstructing the internuclear distance.

Synthesis, defect characterization and photocatalytic degradation efficiency of Tb doped CuO nanoparticles

Monoclinic undoped and Tb doped CuO are prepared by solution combustion method and annealed at different temperatures. The effect of annealing and doping on their structural and optical properties of CuO are examined using XRD, FTIR and DRS. The surface and lattice defects in CuO and Tb doped CuO is analyzed qualitatively and quantitatively using positron lifetime and Doppler broadening spectroscopy. The average positron lifetime and electron momentum (energy) S parameter increases owing to the number of vacancies in the CuO lattice upon doping and decreases with increasing temperature. The migration of vacancies from grain to grain boundary region is observed at 600°C annealed samples. At 800 °C, the overall behavior of lifetime value denotes that the vacancy type defect is recovered, cluster vacancy and microvoids exists with reducing size. The photocatalytic performance of undoped and Tb doped CuO on degradation of methylene blue (MB) and methyl orange (MO) is investigated under visible light for two different lamp power and dye concentration. The influence of annealing temperature and dopant ion on the efficiency is also elaborated. Enhanced photocatalytic efficiency in Tb doped CuO is observed upon annealing. X-ray photoelectron spectroscopy (XPS) result indicates that the valence states of Cu, O and Tb ions exist at the surface of the particles. Brunauer–Emmett–Teller N2 adsorption–desorption analyses were employed to characterize specific surface area and porosity of Tb doped CuO. The doped CuO with pore size of about ∼34nm have a surface area of 16–28m2/g. The surface area effect plays an important role in the enhanced catalytic performance on Tb doped catalysts.

Photon-momentum transfer in photoionization: From few photons to many

In most models and theoretical calculations describing multiphoton ionization by infrared light, the dipole approximation is used. This is equivalent to setting the very small photon momentum to zero. Using numerical solutions of the (nondipole) three-dimensional time-dependent Schr\odinger equation for one-electron (H-like) systems, we investigate the effect the photon-momentum transfer to the photoelectron in various regimes: from the few (one, two, three, eight) absorbed photons to multiphoton and tunneling regimes. We find that in all regimes the average electron momentum acquired from absorbed photons is a linear function of the average energy of the photoelectron, but the slope is different in the few-photon and multiphoton regimes. In the multiphoton regime, the photon-momentum signature in the photoelectron-momentum distributions (along the photon momentum) depends on the ellipticity of the laser polarization, with linear laser polarization spectra different from circular polarization spectra. For a given laser intensity the average electron-momentum gain from an absorbed photon is over two and a half times smaller for linear polarization than for circular polarization. However, for both polarizations, the average electron-momentum gain is nearly equal to the average electron energy divided by the speed of light.

Recollision as a probe of magnetic-field effects in nonsequential double ionization

Fully accounting for non-dipole effects in the electron dynamics, double ionization is studied for He driven by a near-infrared laser field and for Xe driven by a mid-infrared laser field. Using a three-dimensional semiclassical model, the average sum of the electron momenta along the propagation direction of the laser field is computed. This sum is found to be an order of magnitude larger than twice the average electron momentum along the propagation direction of the laser field in single ionization. Moreover, the average sum of the electron momenta in double ionization is found to be maximum at intensities smaller than the intensities satisfying previously predicted criteria for the onset of magnetic field effects. It is shown that strong recollisions are the reason for this unexpectedly large value of the sum of the momenta along the direction of the magnetic component of the Lorentz force.

Magneto transport in crossed electric and magnetic fields in compensated bulk GaN

Low-temperature high-field electron transport is studied for compensated bulk GaN subjected to crossed electric and magnetic fields. The electron kinetics, distribution function, and field dependencies of the magneto transport characteristics are analyzed by using the Monte-Carlo method. At zero magnetic field, for an ionized impurity concentration of 1016 cm−3 and an electron concentration of 1015 cm−3, it is shown that dissipative streaming transport with a strong anisotropic electron distribution in the momentum space is realized at electric fields in the range 3−10 kV/cm and for a lattice temperature of 30 K. The magnetic field destroys the dissipative streaming transport. Indeed, for a magnetic field greater than 4 T, the electrons are predominantly confined in a region of the momentum space where their energy is smaller than the optical phonon energy and the strong inelastic scattering by optical phonons is practically eliminated. A quasi-ballistic electron transport occurs in the form of a vortex-like motion in the momentum space. The axis of rotation of this vortex coincides with the average electron momentum. A general analysis of the distribution function suitable for any configuration of the Hall circuit is presented. The main magneto transport characteristics (dissipative current, Hall current, and Hall electric field) are studied for the short and open Hall circuits. We show that the magneto transport measurements can provide valuable information on the main features of the electron distribution function and electron dynamics in GaN. Finally, we suggest that the strong dependency of the dissipative current on the parameters of the Hall circuit can be used for current modulation and current switching.

Electron Momentum Spectroscopy of 1-Butene: A Theoretical Analysis Using Molecular Dynamics and Molecular Quantum Similarity

The results of experimental studies of the valence electronic structure of 1-butene by means of electron momentum spectroscopy (EMS) have been reinterpreted on the basis of molecular dynamical simulations in conjunction with the classical MM3 force field. The computed atomic trajectories demonstrate the importance of thermally induced nuclear dynamics in the electronic neutral ground state, in the form of significant deviations from stationary points on the potential energy surface and considerable variations of the C-C-C-C dihedral angle. These motions are found to have a considerable influence on the computed spectral bands and outer-valence electron momentum distributions. Euclidean distances between spherically averaged electron momentum densities confirm that thermally induced nuclear motions need to be fully taken into account for a consistent interpretation of the results of EMS experiments on conformationally flexible molecules.

Interference Effects on (e,2e) Electron Momentum Profiles ofCF4

Interference effects on electron momentum profiles have been studied using binary (e, 2e) spectroscopy for the three outermost molecular orbitals of CF(4), which are composed of the F 2p nonbonding atomic orbitals. An analysis of the measured spherically averaged electron momentum densities has clearly shown the presence of oscillatory structures having direct information about the internuclear distance between the F atoms. Furthermore, it is demonstrated that the phase of the oscillatory structures depends upon the orientation in space of the constituent atomic orbitals.

Heat transport across metal–semiconductor (dielectric) structure under steady state conditions

With continued size reduction in microelectronic devices, the thermal boundary conductance between two materials becomes the main channel on thermal dissipation. In this work, we present a theoretical work on heat transport in two-layered systems consisting in metal and a semiconductor (dielectric) and considering the role of the interface thermal conductivity between them.In a metal because the electrons are preferentially scattered by phonons with phonon momentum smaller than the average electron momentum (electron Fermi momentum), the electron–phonon collisions are more efficient in terms of energy relaxation than the phonon–phonon relaxation frequency and, in this case the phonon system can be described by the same temperature as the electron gas. Therefore the heat diffusion equation in a metal is solved in one temperature approximation with appropriate boundary conditions at the surface and at the interface. On the other hand, in the semiconductor the heat diffusion transport is described by the two-temperature approximation model.

Electron Momentum Spectroscopy Study on Valence Electronic Structures of Ethylamine

The valence-shell binding energy spectra and electron momentum profiles of gaseous ethylamine are measured by (e, 2e) electron momentum spectroscopy. When taking into account the Boltzmann-weighted abundance of 39% for trans and 61% for two equivalent gauche conformers coexisted in ethylamine, the thermally averaged electron momentum profiles for all valence orbitals calculated using B3LYP method with 6-311++G** and aug-cc-pVTZ basis sets reproduce the experimental ones well, which supports that the trans conformer is more stable. In addition, the controversial ordering of 2a'' and 7a' orbitals for the trans conformer is reassigned and an ionization band at about 13.7 eV, which was uncertain in previous literatures, is confirmed by comparing the experimental momentum profiles with the theoretical ones for the respective molecular orbitals. Furthermore, the ionization potentials and pole strengths for the inner valence orbitals are reported for the first time.

A family of model Kohn–Sham potentials for exact exchange

The exact-exchange Kohn-Sham potential is partitioned into Slater's averaged exchange charge potential and a correction. A family of nonempirical approximations to the correction term is proposed based on the known second-order gradient expansion of the exact potential. By taking the uniform electron gas limit of the correction term and using alternative definitions of the average relative electron momentum that are motivated by analysis of the Negele-Vautherin density matrix expansion, we recover the "modified Slater potential" of Harbola and Sen and the much more accurate Becke-Johnson approximation [J. Chem. Phys. 124, 221101 (2006)]. Inclusion of an explicit gradient-dependent term in the Becke-Johnson model yields an even more realistic approximation, as demonstrated by comparing the shapes of these potentials and integrated exchange energies for a series of atoms.

Average Low and High Momenta in Singly-Excited 1snl States of the He Atom

Average low and high > momenta are examined for 28 singly-excited 1snl singlet and triplet states (0 ≤ l decreases with increasing n and decreasing l, while the high momentum > is nearly equal to 16/(3π)≅1.698, independent of n and l. Comparing the low and high > momenta with the average electron momentum of a hydrogenlike atom, we show that an electron with a lower momentum behaves like an nl electron of the hydrogen atom and another electron with a higher momentum behaves like the 1s electron of the helium cation. A decomposition of an uncertainty product finds that the largest contribution to comes from an outer electron and a high momentum electron, where and are the usual average electron radius and momentum, respectively.

Limitations on the validity of impulse approximation in Compton scattering

The validity of impulse approximation (IA), which is commonly used in the description of Compton scattering of photons from atomic electrons, is discussed with particular attention to the kinematical region in which the photon momentum transfer k is not much larger than the average bound electron momentum a of a given shell. IA can be justified in the Compton peak region of the spectrum if a/k≪1. However, for the doubly differential cross-section of photon–atom scattering (ejected electrons not observed) IA is commonly used, and viewed as adequate, while only requiring that a/k<1. In addition to a general discussion of the validity of IA (and the relativistic version RIA) for doubly and triply differential cross-sections, in this paper, we are particularly concerned with (1) the asymmetry around the IA peak of the Compton profile and (2) the contribution of the p→·A→ interaction term (neglected in IA) in the peak region for a/k<1. We argue that the observed asymmetry of the Compton profile is to a large extent just a shift of the IA profile. We find that p→·A→ contribution to the peak region for a/k≈1 is important only for scattering from high Z K-shells.

Study of the molecular structure, ionization spectrum, and electronic wave function of 1,3-butadiene using electron momentum spectroscopy and benchmark Dyson orbital theories

The scope of the present work is to reconcile electron momentum spectroscopy with elementary thermodynamics, and refute conclusions drawn by Saha et al. in J. Chem. Phys. 123, 124315 (2005) regarding fingerprints of the gauche conformational isomer of 1,3-butadiene in electron momentum distributions that were experimentally inferred from gas phase (e,2e) measurements on this compound [M. J. Brunger et al., J. Chem. Phys. 108, 1859 (1998)]. Our analysis is based on thorough calculations of one-electron and shake-up ionization spectra employing one-particle Green's function theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. Accurate spherically averaged electron momentum distributions are correspondingly computed from the related Dyson orbitals. The ionization spectra and Dyson orbital momentum distributions that were computed for the trans-conformer of 1,3-butadiene alone are amply sufficient to quantitatively unravel the shape of all available experimental (e,2e) electron momentum distributions. A comparison of theoretical ADC(3) spectra for the s-trans and gauche energy minima with inner- and outer-valence high-resolution photoelectron measurements employing a synchrotron radiation beam [D. M. P. Holland et al., J. Phys. B 29, 3091 (1996)] demonstrates that the gauche structure is incompatible with ionization experiments in high-vacuum conditions and at standard temperatures. On the other hand, outer-valence Green's function calculations on the s-trans energy minimum form and approaching basis set completeness provide highly quantitative insights, within approximately 0.2 eV accuracy, into the available experimental one-electron ionization energies. At last, analysis of the angular dependence of relative (e,2e) ionization intensities nicely confirms the presence of one rather intense pi(-2) pi(*+1) satellite at approximately 13.1 eV in the ionization spectrum of the s-trans conformer.

Probing Dyson orbitals with Green’s Function theory and Electron Momentum Spectroscopy

Results of an experimental study of the valence electronic structure of difluoromethane employing high-resolution Electron Momentum Spectroscopy with various impact energies are reported. One-particle Green’s Function theory is utilized, for the first time, for computing accurate spherically averaged electron momentum distributions. These are derived from Dyson orbitals obtained using the third-order Algebraic Diagrammatic Construction (ADC(3)) scheme. The corresponding eigen-energies also accurately reproduce the (e, 2e) ionization spectrum. Shortcomings of empirical analyses of (e, 2e) experiments based on Kohn–Sham orbitals and eigen-energies are comparatively discussed. A failure of the target Hartree-Fock approximation is noted for the momentum distribution pertaining to the 1b 1 + 3b 2 + 5a 1 levels.

Average electron momenta in many-electron atoms

In many-electron atoms, the average electron momentum 〈p〉 represents the mean momentum of a single electron when all the electron motions are averaged. If any two electrons are considered simultaneously, however, the average momentum 〈p〉 splits into two different momenta, low momentum 〈p 〉. For the 102 atoms He through Lr in their ground states, the momenta 〈p 〉 are systematically examined at the Hartree–Fock limit level. It is also shown that the sum 〈p>〉+〈p 〉−〈p<〉 of the two momenta constitute upper and lower bounds to the electron-pair relative momentum 〈p12〉=〈|p1−p2|〉 and to the electron-pair center-of-mass momentum 〈P〉=〈|p1+p2|/2〉. The tightness of the bounds is discussed for the 102 atoms.

A fresh look at the computation of spherically averaged electron momentum densities for wave functions built from Gaussian‐type functions

AbstractA new method for deriving the spherical average of the product of the Fourier transforms of two Gaussians is described. The method generates the result in terms of a few spherical Bessel functions leading to expressions that are much more compact than those in the literature. These integrals are required in the computation of spherically averaged electron momentum densities, and rotationally averaged X‐ray and high‐energy electron scattering crossections. All integrals needed for spherically averaged momentum densities are tabulated for s, p, d, and f‐type Gaussians. As an illustration of the method, we apply it to calculate spherically averaged electron momentum densities and their moments for H2O. The calculations are performed at the Hartree–Fock and 2nd‐ and 4th‐order Møller–Plesset perturbation theory levels with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets. © 2001 John Wiley &amp; Sons, Inc. Int J Quantum Chem, 2001

Electron momentum densities near zero-momentum

The leading coefficients of the MacLaurin expansion of the spherically averaged electron momentum density Π 0( p) are calculated ab initio for Ne, Ar, CO, N 2, FH, H 2O, NH 3, CH 4, B 2H 6, C 2H 2, C 2H 6, CO 2, H 2CO and H 2O 2. The zero-momentum critical point of the three-dimensional electron momentum density Π( p → ) is classified by the rank and signature of the Hessian of Π( p → ) at the momentum-space origin. The effects of electron correlation and basis set variation on these quantities are assessed.

Approximate Bounds to the Average Electron Momentum Densityfor Atomic Systems

Approximate bounds to the average electron momentum density⟨γ⟩ in terms of momentum expectation values⟨pn⟩ have been derived for atomicsystems. These bounds are based on the semiclassical relationships inthe Thomas–Fermi model. Meanwhile, approximate bounds to theaverage electron density ⟨ρ⟩ in terms of the expectationvalues ⟨rn⟩ have also been obtainedemploying a similar procedure on the basis of the same model. Thequality of the bounds presented is numerically studied and discussedwithin the Hartree–Fock framework. Atomic units are usedthroughout.

Electron momentum densities of atoms

Spherically averaged electron momentum densities Π(p) are constructed by the numerical Hartree–Fock method for all 103 atoms from hydrogen (atomic number Z=1) to lawrencium (Z=103) in their experimental ground states. We find three different types of momentum densities spread across the periodic table in a very simple manner for the 98 atoms other than He, N, Mn, Ge, and Pd. Atoms in groups 1–6, 13, and 14, and all lanthanides and actinides have a unimodal momentum density with a maximum at p=0, atoms in groups 15–18 have a unimodal momentum density with a local minimum at p=0 and a maximum at p&amp;gt;0, and atoms in groups 7–12 have a bimodal momentum density with a primary maximum at p=0 and a small secondary maximum at p&amp;gt;0. Our results confirm the existence of nonmonotonic momentum densities reported in the literature, but also reveal some errors in the previous classification of atomic momentum densities. The physical origin for the appearance of the three different modalities in Π(p) is clarified by analysis of subshell contributions to momentum densities.

Dephasing of LO-phonon–plasmon hybrid modes inn-type GaAs

The relaxation dynamics of coherent phononlike LO-phonon--plasmon hybrid modes is investigated in $n$-doped GaAs using an infrared time-resolved coherent anti-Stokes Raman scattering technique. Measurements performed for different crystal temperatures in the range 10--300 K as a function of the electron density injected by doping show a large reduction of the hybrid mode dephasing time compared to the bare LO-phonon one for densities larger than ${10}^{16}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ The results are interpreted in terms of coherent decay of the LO-phonon--plasmon mixed mode in the weak-coupling regime and yield information on the plasmon and electron relaxation. The estimated average electron momentum relaxation times are smaller than those deduced from Hall mobility measurements, as expected from our theoretical model.