Electron Ejection Angle Research Articles

Antiproton impact ionization of hydrogen atom: Differential cross sections computed by Coulomb wave function discrete variable representation method

Our aim is using the Coulomb wave function discrete variable representation method (CWDVR) for the calculation of collision problem in first time. Nonrelativistic collision of antiproton with hydrogen atom is described by solving the time-dependent Schrodinger equation numerically. Two collision amplitudes are used for calculation of the differential cross sections, one of them corresponds to impact parameter of the projectile while other one is determined by projectile momentum transfer and found by Fourier transform of the first one. The ionization amplitude calculated by projecting of the wave function onto continuum wave function of the ejected electron. The differential cross sections calculated depending on projectile impact energy, scattering angle and electron ejection energy and angles, which is a result that can be measured experimentally. Our results are in good agreement with the relativistic calculation results.

Post Collision Interraction Effect on the magnitude(e, 2e) Autoionization Amplitude

Post collision interaction effect on the magnitude of the He(e,2e)He* direct and resonant amplitudes as a function of electron ejection angle has been considered. Calculated values are found in good agreement with the extracted experimental data. It is shown that the 3-body Coulomb interaction in final state may give a considerable contribution to the direct cross section, but a small account to the resonant cross section.

Monte Carlo simulations of energy, time and spatial evolution of primary electrons generated by 511 keV photons in various scintillators

The intermediate phases between the initial interaction of ionizing radiation in scintillators and the production of scintillation light have been extensively studied over the years. Observable features of scintillators such as energy and time resolution have been in part explained through pre-scintillation mechanisms. Whereas the early energy transfer processes following the photoelectric (or Compton) interaction of an energetic photon with an atomic electron in scintillator materials were fully described, their spatio-temporal characteristics have had limited quantification. For 511 keV photon interaction in (TOF-)PET detectors, the production of a primary electron carrying most of the energy leads to non-localized energy deposit distribution having some temporal extent. Here, we characterize the spatial, temporal and energy evolution of the primary electron generated by 511 keV photons in different scintillators using Monte Carlo simulations. We aim to provide a general quantitative description detailing the dynamics of energy transfer, such as the electron ejection angle, track length and tortuosity, time course and remaining energy as a function of the initial interaction point. Simulation results show that the electron track is tortuous with a short extent and a rapid energy transfer within 100 μm in high-Z (e.g., BGO) or high density (e.g., LuAP:Ce) materials while the extent nearly doubles in lighter materials like BaF2 in which the track tortuosity is 10%–50% lower. The time fluctuations of the photoelectron full energy deposit remain below 1 ps FWHM, therefore adding negligible jitter to the time resolution of coincident detectors. These simulations provide a better understanding of the main carrier dynamics from simple characteristics as some detector concepts require low-range, contained energy deposit (e.g., pixelated crystal arrays) whereas others benefit from a greater extent of energy deposition (e.g., structures designed for energy sharing).

Sub-GeV dark matter detection with electron recoils in carbon nanotubes

Directional detection of Dark Matter particles (DM) in the MeV mass range could be accomplished by studying electron recoils in large arrays of parallel carbon nanotubes. In a scattering process with a lattice electron, a DM particle might transfer sufficient energy to eject it from the nanotube surface. An external electric field is added to drive the electron from the open ends of the array to the detection region. The anisotropic response of this detection scheme, as a function of the orientation of the target with respect to the DM wind, is calculated, and it is concluded that no direct measurement of the electron ejection angle is needed to explore significant regions of the light DM exclusion plot. A compact sensor, in which the cathode element is substituted with a dense array of parallel carbon nanotubes, could serve as the basic detection unit.

Two-photon double ionization of helium: investigating the importance of correlation in the final state

AbstractIn this paper, we present theoretical results for the process of non-sequential two-photon double ionization of helium at the photon energy 42 eV. Our approach is based on solving the time-dependent Schrödinger equation in a B-spline based numerical framework. Information about the process is obtained by extracting the double-ionized component by means of uncorrelated final states. The total (generalized) cross section for the process is extracted, as well as differential cross sections resolved in electron energies and ejection angles. We focus on the impact the final-state correlation has on the accuracy of the cross sections.

Explicit general solutions to relativistic electron dynamics in plane-wave electromagnetic fields and simulations of ponderomotive acceleration

This study examines single-particle electron motions in both a plane electromagnetic wave and a Gaussian focus in vacuum. Exact, explicit analytic expressions for relativistic electron trajectories in a plane wave are obtained, using the proper time as a parameter, in the general case of arbitrary initial positions and velocities. It is shown that previous analyses can be completed using the proper-time parameter. The conditions under which localized oscillatory motions (‘figure-of-eight’ orbits) occur are derived from the new solutions. The general solutions are also connected with the figure-of-eight orbits by a Lorentz transformation. The analytic solutions for arbitrary initial conditions and an arbitrary initial field phase can be used to determine the ranges of electron ejection angle and emerging electron energy in a vacuum laser accelerator, in which electrons are ejected externally, and provide a basis for explaining the spectrum of nonlinear Thomson scattering radiation. Numerical solutions are used for electron motions in the focus of a Gaussian laser beam, and the mean motion allows one to test a new expression for the relativistic ponderomotive force. It is suggested that plane wave solutions can provide a basis for approximating the orbital motion of particles in Gaussian beams.

Molecular orientation influence on the interference pattern

The interference effect in the double differential cross section for ionization of hydrogen molecule is investigated theoretically for different molecular orientation. We applied our theory presented in Nagy et al. [L. Nagy, L. Kocbach, K. Póra, J.P. Hansen, J. Phys. B: At. Mol. Opt. Phys. 35 (2002) L453] for the calculation of the differential ionization cross section. We have studied the cross section ratio of the hydrogen molecule and two hydrogen atoms as a function of the ejected electron velocity for different molecular orientation and electron ejection angle. One may observe, that at certain ejected electron velocities the interference is totally destructive, and the oscillations in the cross section ratio are the most pronounced for parallel orientation of the molecular axis relative to the beam direction.

Collisional ionization ofCq+byHe2+and its applications in the inertial controlled fusion diagnostics

The ionization process in collisions of ${\mathrm{He}}^{2+}$ with ${\mathrm{C}}^{q+}$ $(q=0--5)$ is investigated using a continuum-distorted-wave eikonal-initial-state approximation. Total and single- and double-differential cross sections for $1s$ and $2s$ electrons are calculated for projectile energies from $30\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{u}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}10\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\mathrm{u}$. From the double-differential cross sections at an electron-ejection angle of $\ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{}$, the variation of ionization mechanisms with $q$ has been studied and their dependences on the projectile energies and the electron subshells are also discussed. It is found that in the whole energy range considered, the absolute values of soft collision (SC) and binary encounter (BE) peaks decrease with increasing $q$. For the lower incident energies, the electron capture to the projectile continuum (ECC) peak, as well as SC and BE peaks, decreases with increasing $q$. For the higher incident energies $(>1\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\mathrm{u})$, the absolute value of the ECC peak increases with increasing $q$, so that the crossings of cross sections appear for ${\mathrm{C}}^{q+}$ with different $q$. This can be explained by the matching of velocities between the projectile and the initially bound active electron in the target. Finally, by comparing the ionization rate coefficients for $K$-shell electrons of ${\mathrm{C}}^{q+}$ by ion and electron impacts in an environment of inertial controlled fusion (ICF), the possibility to diagnose the ${\mathrm{He}}^{2+}$ distribution in ICF by the characteristic $K\ensuremath{\alpha}$ spectrum of ${\mathrm{C}}^{q+}$ is investigated.

Angular and high-frequency analysis of electron interference structures in∼60MeV∕uKr34++H2collisions

Detailed analyses of previous measurements, combined with additional measurements reported here, have been made of electron interference structures observed in 60 MeV/u Kr34+ + H2 collisions. Results are used to characterize the angular dependence of the primary interference structures over a wide range of electron ejection angles, particularly backward angles, and, additionally, to search for high-frequency structures as reported recently for 1–5 MeV/u H+ + H2 collisions [Hossain et al., Phys. Rev. A 72, 010701(R) (2005)]. The data for backward ejection angles, in combination with earlier data, permit a detailed comparison with theory over the range 30°–150°, showing that none of the existing theories predict accurately the observed oscillation frequencies for backward angles. Electron spectra for 90° and 150° taken in small energy steps and with improved statistics compared to earlier measurements were examined by means of a Fourier analysis but no evidence of the high-frequency structures reported for H+ + H2 collisions was found.

Interference phenomena associated with electron-emission fromH2by(1–5)−MeVH+impact

Primary and secondary interference structures attributed to coherent electron emission from the identical atomic centers of H{sub 2} have been observed in the velocity distributions of ejected electrons resulting from (1-5)-MeV H{sup +} impact. The primary interference structures are found to depend on the projectile velocity, in addition to the previously observed dependence on electron ejection angle. In contrast, the secondary structures, attributed to intramolecular scattering, do not change with projectile velocity and show only slight variations with the electron ejection angle. The data also provide evidence for significantly higher-frequency structures for which no explanation currently exists.

Break-up of positronium (Ps) atom in collision with a He+ ion

The dynamics of electron loss to the continuum (ELC) from the light neutral projectile positronium (Ps) atom in collision with He+ ion is studied in the framework of post-collisional Eikonal approximation. The full three-body interaction, which is crucial for such ELC process is taken into account in the final channel. Both the triple differential cross sections (TDCS) and the double differential cross sections (DDCS) are studied at some intermediate and high incident energies, with respect to the threshold energy for this process. A distinct broad ELC peak centred around ve (velocity of the ejected electron) ≈vp (velocity of the positron) is noted in the ejected electron energy spectrum (DDCS) for forward ejection of e/e+, corroborating the experimental findings for the ELC process. The probability of emission of the e+ at higher angles is almost negligible as compared to its forward emission. Another salient feature noted in the present work is the shifting of the ELC DDCS (summed over the electron ejection angles) peak towards higher value of the ratio ve/vp with increasing incident energy, in agreement with the experimental findings of Armitage et al for Ps–He break-up process.

Determining the angular admittance of a cylindrical mirror analyser

AbstractRecent studies have demonstrated the need for the angular acceptance of a cylindrical mirror analyser (CMA) to be determined quantitatively. This acceptance probability function, with respect to the electron ejection angle, has not been reported previously. In this paper the angular acceptance function of a PHI‐550 double‐pass CMA has been determined quantitatively. A knowledge of this function makes it possible to extract some limited depth‐sensitive information from a standard CMA instrument without using a rotating aperture. Copyright © 2002 John Wiley & Sons, Ltd.

Dynamical theory of molecular photoionization: electron ejection kinematics and angular distributions from molecules fixed in space

Photoionization of molecules and other atomic aggregates fixed in space is studied from a dynamical perspective employing solutions of the time-dependent Schrödinger equation. The wave functions and associated kinematical behaviors of excited and ejected electrons are determined explicitly in short- and long-time limits, generalizing early results of Bethe for central potentials to anisotropic targets. Ehrenfest’s theorem is employed to clarify the origins of the transient forces and consequent kinematical behaviors of excited and ionized K-shell electrons obtained from explicit solutions of the time-dependent Schrödinger equation, revealing hybrid classical-quantal behaviors in wave functions and expectation values of position and momentum operators. In addition to providing pedagogical insights into time-resolved aspects of these fundamental photoprocesses, and a corresponding basis for theoretical studies of dynamical target relaxation, associated photoelectron-ion correlation, and other specifically time-dependent post-collision interaction phenomena, the new development resolves technical issues associated with the irreducibly infinite degeneracy of the scattering continuum for the anisotropic potentials characteristic of polyatomic molecules. Photoionization cross sections differential in electron ejection angles are derived from the formalism for fixed-in-space molecules of arbitrary complexity which are applicable in both time-resolved and steady-state situations, and an invariant subspace of excitation and ionization functions required in computational applications of the approach is constructed employing Lanczos–Krylov sequences of L 2 vectors and previously devised Stieltjes–Akhiezer methods, without reference to or calculations of the underlying individual discrete or continuum eigenstates. Electron angular-distribution data for fixed-in-space molecules measured over the full (4 π) range of emission angles for all molecular orientations are shown to be highly redundant, and to provide invariant physical information in the form of no more than three irreducible-tensor body-frame complex angular emission amplitudes at a given photon energy. These issues are illustrated with applications to ionization of fixed-in-space diatomic molecules for linear and circularly polarized incident radiation, in which cases the minimal set of molecular configurations and polarizations required to determine the invariant body-frame emission amplitudes is described in detail.

Ionization of atomic hydrogen by protons in thepresence of a laser field

The ionization of atomic hydrogen by protons in the presence of alaser background is studied. We describe the initial and finalstates of the proton by plane waves, the state of the target by adressed wavefunction obtained by time-dependent theory in the soft-photon approximation, and the state of the ejected electron bya two-centre Coulomb function modulated in time by the laserfield in the same way as a plane wave. The laser-modified doubledifferential cross sections for a geometry of laser polarizationparallel to the incident cross section of the proton are calculatedand compared with the laser-free results. For each small electronejection angle, a critical point is found in the electronenergy spectrum, behind which the cross section is notablyenhanced.

On the angular distributions of molecular photoelectrons: dipole cross-sections for fixed-in-space and randomly oriented molecules

New theoretical expressions are devised employing a dynamical perspective for photoionization cross-sections differential in electron ejection angles for both fixed-in-space and randomly oriented molecules, and comparisons made with K-shell ionization measurements in molecular nitrogen. Closed-form cross-sectional expressions are obtained in the dipole limit in terms of molecular body-frame transition moments and related normalized angular-distribution amplitudes which can be calculated employing interaction-prepared states without reference to specific scattering boundary conditions, and which reduce to more familiar atomic expressions in appropriate limits.

Multiple-scatteringanalysis of triply differential cross sections forelectron emission in energetic ion-atom collisions

The role of multiple-scattering events has beeninvestigated in single ionization of atoms induced byenergetic ion impact. The triply differential crosssections have been evaluated as a function ofthe projectile scattering angle for fixed values of theemitted electron energy and angle within the framework ofthe distorted-wave Born approximation (DWB). It has beenshown that the double-scattering mechanism, which(sometimes) results in a characteristic double-scatteringpeak at a definite projectile scattering angle, provides asatisfactory description of the process over a wideregion of electron ejection energies and angles. Forlow-energy electron emission the role of higher orders isnot negligible, and the quantum mechanical nature of theprocess is more emphasized. At an electron velocity equalto the projectile velocity the analogy with the mechanismof electron capture into bound states has also beeninvestigated. In this region the DWB theory forionization corresponds to theOppenheimer-Brinkman-Kramers model for electron capture.

On the angular distributions of electrons photoejected from fixed-in-space and randomly oriented molecules

Abstract New theoretical expressions are devised from a dynamical perspective for molecular photoionization cross sections differential in electron ejection angles which facilitate comparisons between theory and experiment and provide a convenient basis for ab initio calculations. The cross sections obtained for fixed-in-space molecules, including the lowest-order (nondipole) effects of retardation, are given in terms of invariant molecular body-frame transition moments and related normalized angular-distribution amplitudes which can be calculated employing interaction-prepared states without reference to specific scattering boundary conditions. Corresponding expressions for molecular dipole and nondipole anisotropy factors appropriate for randomly oriented molecules are obtained in closed forms involving expectation values of harmonic polynomials over the fixed-in-space body-frame angular-distribution amplitudes. The expressions are seen to be in the spirit of corresponding results for atomic photoionization anisotropy factors, to which they reduce in appropriate limits. Interpretations of recently measured angular distributions of photoelectrons from the K-shell of molecular nitrogen illustrate how the development relates measurements on randomly oriented molecules to those performed on fixed-in-space molecules. The theoretical formalism provides results in excellent accord with measurements of the molecular nitrogen K-shell dipole anisotropy factor, and accounts for the origins of large nondipole effects observed at relatively low photon energies (ℏω≤500 eV) in the measured angular distributions.

Asymmetric(e,2e)measurement of vibrational intensities in the 100-eV electron-impact ionization ofN2to theN2+X2Σg+andA2Πustates

Asymmetric $(e,2e)$ experiments have been carried out on ${\mathrm{N}}_{2}$ for incident energy 100 eV, incident electron scattering angle 4\ifmmode^\circ\else\textdegree\fi{}, secondary-electron energy 5 eV, and secondary-electron ejection angles from -32\ifmmode^\circ\else\textdegree\fi{} to 100\ifmmode^\circ\else\textdegree\fi{}. The experiments have sufficient energy resolution (\ensuremath{\sim}0.13 eV) to resolve the vibrational structure in the coincidence energy-loss spectrum. Ionization transitions to the $X{}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ and $A{}^{2}{\ensuremath{\Pi}}_{u}^{+}$ states were observed. When the final state of the product ion was $X{}^{2}{\ensuremath{\Sigma}}_{g}^{+},$ no vibrational excitation was observed at secondary electron ejection angles of 100\ifmmode^\circ\else\textdegree\fi{} (recoil) or -80\ifmmode^\circ\else\textdegree\fi{} (binary). However, at -32\ifmmode^\circ\else\textdegree\fi{}, near the peak of the binary lobe of the cross section, a strong increase in the production of the ${v}^{\ensuremath{'}}=1$ state was observed. In contrast, production of the $A{}^{2}{\ensuremath{\Pi}}_{u}^{+}$ state was characterized by the expected Frank-Condon vibrational intensities at 100\ifmmode^\circ\else\textdegree\fi{} and 80\ifmmode^\circ\else\textdegree\fi{} on the recoil side but a decrease in the relative intensities of the ${v}^{\ensuremath{'}}=1,$ 2, and 3 vibrational states at -32\ifmmode^\circ\else\textdegree\fi{}. The A state deviations occur where the cross section is small, so we conclude that 100-eV electron impact does not produce significant vibrational excitation in the $A{}^{2}{\ensuremath{\Pi}}_{u}^{+}$ state. On the other hand, the $X{}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ state is produced with significant vibrational excitation in the binary lobe where the cross section is large. This excitation is important for both a theoretical understanding of the ionization process as well as plasma and atmospheric phenomena.

Differential cross sections for ionization of atmospheric gases by electron impact

Absolute values of doubly differential cross sections for electron ejection in collisions of fast electrons with , , CO and molecules have been measured at the electron ejection angle of , in the incident electron energy range 100-1000 eV and in the ejected electron energy range 5-50 eV. Singly differential cross sections are also determined using a normalization procedure. The measured cross sections agree well with available data of other authors, except for those on at 1000 eV, where a disagreement of up to a factor of 3 is observed. However, a rather good agreement is found between experimental data of this work at high energies and calculations using the Born approximation.

Excitation of autoionizing states of helium by 100 keV proton impact: theory and experiment

A joint theoretical and experimental study of the excitation of the autoionizing and states of helium by 100 keV proton impact is presented for the first time. The role of the three-body Coulomb interaction in the final state between the ejected electron, the scattered proton and the recoil helium ion is emphasized. Calculations have been carried out with inclusion of the three-body Coulomb interaction and within an expansion of a two-electron excitation amplitude in powers of projectile - target interaction up to the second order. A new parametrization is proposed to describe resonance profiles distorted by the Coulomb interaction in the final state (CIFS). New high-resolution (up to 68 meV) measurements of electron emission spectra made it possible to resolve the near-lying and resonances and reveal an evident distortion of the resonance profiles by CIFS for forward electron ejection angles below . Processing of the experimental spectra has been done both with the new parametrization, with allowance for CIFS, and with the Shore formula. Considering the complexity of the problem, reasonable agreement is achieved between experiment and theory.