Post-collision Interaction Research Articles

Triple-differential cross sections for (e,2e) electron-impact ionization dynamics of tetrahydrofuran at low projectile energy

We study the triple-differential cross section (TDCS) for the electron-impact ionization of the highest occupied molecular orbital of tetrahydrofuran at a projectile energy ${E}_{0}=91\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$. The experimental data were measured using a reaction microscope, which covers a large part of the full solid angle for the secondary electron emission with energies ranging from 6 to 15 eV, and projectile scattering angles ranging from $\ensuremath{-}{10}^{\ensuremath{\circ}}$ to $\ensuremath{-}{20}^{\ensuremath{\circ}}$. The experimental TDCSs are internormalized across all measured scattering angles and ejected energies. They are compared with predictions from the multicenter distorted-wave (MCDW) approximation and a modified MCDW-Nee method which includes the postcollision interaction (PCI) using the Ward-Macek factor. Additional calculations were obtained using a molecular three-body distorted-wave (M3DW) approach which accounts for PCI in an exact treatment. Generally, the MCDW-Nee and M3DW models show better agreement with experiment than the MCDW calculations. This shows the importance of accounting for PCI for low-energy outgoing electrons in electron-impact ionization processes.

Ejected-electron-energy and angular dependence of fully differential ionization cross sections in medium-velocity proton collisions with He and H2

We have measured fully momentum-analyzed recoiling target ions and scattered projectiles, produced in ionization of He and ${\mathrm{H}}_{2}$ by 75 keV proton impact, in coincidence. The momentum of the ejected electrons was deduced from momentum conservation. From the data we extracted fully differential ionization cross sections as a function of the polar electron emission angle (for fixed electron energies) and as a function of the electron energy (for fixed electron emission angles). Comparison between experiment and various distorted wave calculations confirms that under kinematic conditions where the post-collision interaction plays an important role, the few-body dynamics underlying the ionization process are still poorly understood.

Conjugate photoelectron recapture peaks in the high resolution Auger electron spectra following near-threshold Ar 2p photoionization

We have observed formation of Rydberg series superimposed on the Ar (L3M2,3M2,3) Auger electron spectral profile with photoexcitation just above the 2p−13/2 photoionization threshold. This is due to the recapture of photoelectrons induced by post-collision interaction between the Auger electron and photoelectron: Ar+ 2p−13/2 + e− → Ar+ 3p−2ml + e−. The intensity distribution of the angular momentum state resolved Rydberg peaks revealed prominent conjugate peaks due to angular momentum exchange between photoelectrons and Auger electrons in the process. In addition, we measured the 2p−13/2nl → 3p−2ml + e− resonant Auger spectra with high resolution below the 2p−13/2 threshold. Our results showed that conjugate shake-up/down 2p−13/2nd → 3p−2mp + e− processes are stronger than the direct 2p−13/2nd → 3p−2ms, (m−1)d + e− processes in the spectator Auger processes, implying a strong angular momentum exchange effect between photoelectron and Auger electron.

Fluorescence Time Delay in Multistep Auger Decay as an Internal Clock.

Differences in postcollision interaction (PCI) effects on Kr L_{3}M_{4,5}M_{4,5} Auger electron spectra were observed, depending on whether the initial photoionization occurred slightly above the K threshold or slightly above the L_{3} threshold. For the former, KL fluorescence emission most likely happens and then Auger processes due to the L_{3} hole follow. The time delay due to fluorescence causes a reduced shift of the Auger peak and tailing toward lower energy, since the Auger overtaking of the photoelectron happens later in time and at a location farther away from the ionic core, compared to the case for the simple one-step L_{3}M_{4,5}M_{4,5} Auger decay after L-shell photoionization. Time-dependent theory for PCI in multistep processes agrees well with experiment, illustrating the effect as an internal clock for the time-sequence of the dynamical process.

Features of the Excitation of Principal Series Lines of Atoms of the Zinc Subgroup by an Electron Impact: I. Cadmium

Using the technique of intersecting beams of slow electrons and atoms of zinc, excitation functions of four spectral lines of Zn I principal series corresponding to the 4snp $${}^{1}P_{1}^{^\circ }$$ → 4s2 1S0 transitions for n = 4, 5, 6, and 7 are measured. Their wavelengths are 213.9, 158.9, 145.8, and 140.4 nm, respectively. Within the energy range of 11–18 eV, the effect of postcollision interaction of electrons (slow scattered and fast ejected ones) has been revealed on these functions with the decay of the autoionizing state. At incident electron energies of ∼11–13 and ∼15–18 eV, such interaction leads to an additional population of the initial levels for these lines and, correspondingly, to the formation of maximum on their excitation functions due to the capture of a scattered electron into these excited levels. The terms of atomic autoionizing states responsible for the observed maximums are determined. The combined influence of the decay of these autoionizing states and postcollision interaction is expressed in the energy shift of the maximums on the excitation functions relative to positions of the corresponding autoionizing states. Using a straightforward calculation in the classical approximation, effective widths of the electron decay of the autoionizing states are estimated. The estimates involve an exact formula and approximation formulas. The latter are valid for different relations between the value of the postcollision shift of maximums on the excitation functions and electron bonding energy at the atomic level. They are used for the determination of effective widths when approximating experimental shifts by the least squares method.

Post-collision interaction in sequential double-ionization of helium

SynopsisWe investigate the post-collision interaction between a slow electron released by a pump pulse from the neutral helium atom and a fast electron released by a time-delayed probe pulse from the created ion. To this end, we numerically solve the time-dependent Schrödinger equation in the basis of the essential eigenstates of the unperturbed Hamiltonian. We demonstrate that the energy exchange between the slow and the fast electrons and the recapture of slow photoelectrons can be controlled by the properties of the pulse-sequence.

Особенности возбуждения линий главной серии атомов подгруппы цинка электронным ударом. II. Цинк

Using the technique of crossed beams of slow electrons and zinc atoms, the excitation functions of four spectral lines of Zn I principal series corresponding to the 4snp 1Po1  4s2 1S0 transitions for n = 4, 5, 6, 7 are measured. Their wavelengths are 213.9, 158.9, 145.8, 140.4 nm, respectively. In the energy range 11–18 eV, these functions revealed the manifestation of the effect of collision interaction of electrons (slow scattered and fast emitted) during the decay of the autoionization state. At incident electron energies of 11–13 and 15–18 eV, this interaction leads to an additional population of the initial levels for these lines and, correspondingly, to the formation of maxima on their excitation functions due to the capture of the scattered electron at the indicated excited levels. The terms of autoionizing states of the atom responsible for the observed maxima are established. The combined effect of the decay of these autoionizing states and the post-collision interaction is expressed in the energy shift of the maxima on the excitation functions relative to the positions of the corresponding autoionizing states. In the classical approximation, the effective widths of the electronic decay of autoionizing states are estimated by direct calculations. For the estimations, exact and approximate formulas are used. The latter are valid for various relations between the magnitude of the post-collision shift of the maxima on the excitation functions and the electron binding energy at the atomic level. They are used to determine the effective widths when the experimental shifts are approximated by the least squares method.

Особенности возбуждения линий главной серии атомов подгруппы цинка электронным ударом. I. Кадмий

Using the technique of crossed beams of slow electrons and cadmium atoms, the excitation functions of three spectral lines of its principal series (166.9, 152.7, 146.9 nm) outgoing from the 5snp 1Po1 levels were measured (n = 6, 7, 8, respectively). In the range of electron energies 12–18 eV, a manifestation of the post-collision interaction of slow scattered electrons and fast electrons ejected during the decay of autoionizing states was found in these functions. This process, at incident electron energies of 11.8, 12.4, and 16.6 eV, leads to additional population of the initial levels of spectral transitions and, correspondingly, to maxima on the excitation functions due to the capture of a scattered electron to these excited levels. The terms of autoionizing states of the atom responsible for the observed maxima on the excitation functions of spectral lines are established. In the classical approximation, by two methods – direct calculation and least squares approximation – estimate the effective widths of the electronic decay of autoionizing states, the combined action of which leads to an energy shift of the maxima. Approximate calculation formulas are used, which are valid for various relations between the post-collision shift of the maxima on the excitation functions and the binding energy of atomic levels.

Triple differential cross-section measurements for electron-impact ionization of methane from a coplanar geometry to the perpendicular plane.

A new study of electron-impact single ionization of the HOMO 1t2 state of CH4 has been conducted at incident electron energies 20 eV and 40 eV above the ionization energy of the state. Triple differential cross sections were measured from a coplanar symmetric geometry, where scattered and ionized electrons were detected at equal angles, through to the perpendicular geometry where the outgoing electrons emerged orthogonal to the incident electron beam. At the lower energy, the electrons were detected with equal energies of 10 eV, whereas at the higher energy, data were obtained for equal energies of 20 eV and for unequal energies of 5 eV and 35 eV. The results are compared to a molecular 3-body distorted wave approximation that used a full averaging procedure to allow for the random orientation of the target, an orientation averaged molecular orbital model that averages the target wavefunction over all orientations prior to the collision, and a distorted wave Born approximation that does not include postcollisional interactions.

Dominance of angular momentum exchange in the PCI recapture of photoelectrons revealed by high resolution Auger electron measurements of Kr

An unexpectedly prominent angular momentum exchange effect in the double photoionization continuum was identified through the photoelectron recapture process induced by post-collision interaction (PCI). The Kr (M5N2,3N2,3) Auger electron spectrum originating from 3d−15/2 photoionization was measured with the photon energy tuned very close above the ionization threshold. As the photon energy approached the 3d−15/2 photoionization threshold, Rydberg series structures including several angular momentum components were formed within the Auger peak profile by the recapture of the photoelectrons into high-lying final ion orbitals. Our spectrum with line-width much narrower than the lifetime width of the corresponding core excited state allowed us to resolve detailed structures due to the orbital angular momentum states very clearly. Unexpectedly, conjugate peaks originating from the exchange of angular momentum between the photoelectron and the Auger electron through PCI were found to dominate the spectrum. Comparison with valence photoelectron spectrum of Kr via direct photoionization confirms the new assignment. Conjugate peaks were also found to be in accord with the quantum defect values obtained for the high Rydberg series Kr+4p−2(1S0, 1D2)ml. Extension of the new assignments to photon energies below threshold may call for the revision of previous interpretations of resonance Auger processes.

Theoretical study of the collision dynamics in (e,2e) reactions

A new theoretical approach is used to calculate the triple differential ionization cross-sections for atoms and molecules by electron impact. In a former study by Houamer et al (2017 Eur. Phys. J. D 71 17), which accounted for the post-collision interaction, the short-range potential and the distortion effects of the ejected electron were separately considered. Here, we present an improved description regarding the dynamics of the (e,2e) reaction, where the distortion effects and the short-range potential are simultaneously taken into account. The method is applied for specific atoms and molecules, and the results are compared to available experiments and other theories performed in coplanar asymmetric geometries.

Target dependence of postcollision interaction effects on fully differential ionization cross sections

We have measured and calculated fully differential cross sections (FDCS) for ionization of helium by 75-keV proton impact. Ejected electrons with a speed close to and above the projectile speed were investigated. This range of kinematics represents a largely unexplored regime. A high sensitivity of the FDCS to the details of the description of the few-body dynamics, reported earlier for ionization of ${\mathrm{H}}_{2}$, was confirmed. A peak structure was found in an electron angular range between the regions where the so-called binary and recoil peaks are usually observed. The need for nonperturbative calculations using a two-center basis set is demonstrated.

Single ionization of helium by fast proton impact in different kinematical regimes

We present ultrahigh-resolution data on fully differential cross sections for single ionization of helium induced by 1 MeV proton impact. In the present work we explore a different regime of kinematic conditions in terms of momentum transfer and electron energies than previously published data. These data are compared with different theoretical calculations. Reasonable agreement between the first Born approximation and experiment is obtained in the kinematic regime close to the Bethe ridge. Far from this region the calculated binary peak is shifted with respect to experiment. In order to resolve this problem, we analyze several theoretical mechanisms beyond the customary first Born approximation theory. These mechanisms include the 3C model (three Coulomb functions), effective charges, off-shell pair $T$ matrices instead of pair potentials, and semiclassical postcollision interaction. We find that a combination of the 3C model with a semiclassical postcollision interaction effect may explain the observed discrepancy.

Controlling Dynamics of Postcollision Interaction.

A general scheme to get insight and to control postcollision interaction (PCI) by means of sequential double ionization with two high-frequency pulses is discussed. In particular, we propose to consider PCI of a slow photoelectron released by the pump pulse from a neutral atom with a fast photoelectron released by the time-delayed probe pulse from the created ion. This scheme is exemplified by the abinitio calculations performed for the prototypical helium atom. In order to visualize PCI effects in real time and real space, the corresponding time-dependent Schrödinger equation is solved by propagating two-electron wave packets in terms of essential stationary eigenstates of the unperturbed Hamiltonian. It is demonstrated that the exchange of energy between the slow and fast photoelectron wave packets in continuum, as well as the recapture of threshold photoelectrons owing to the PCI, can be controlled by the properties of the ionizing pulses and the time delay between them.

Angular interferences of sequentially ionized double-continuum wave packets

Following the recent report of energy and angle interferences in below-threshold photoexcitation Auger processes due to postcollision interactions [Wang and Robicheaux, Phys. Rev. A 98, 013421 (2018)], similar interferences are also found in double-continuum wave packets from a two-step time-delayed photoionization of a two-electron atom. Properties of the interferences are studied in detail with respect to laser pulse time widths, laser frequency chirping, and ionization time delay. The effects of these physical quantities on the resulting interferences are discussed.

Triple-differential cross sections for single ionization of CO2 by 100 eV electron impact

We present a combined experimental and theoretical study for electron-impact ionization of carbon dioxide (CO2) for the projectile energy E0 = 100 eV. Experimental triple-differential cross sections (TDCS) are obtained using a multi-particle momentum spectrometer (reaction microscope). For projectile scattering angles between −5° and −20° a large part of the full solid angle is covered for the slow ejected electron with energies between 5 and 15 eV. The experimental data are measured for the ionization of the three outer valence molecular orbitals 1πg, 1πu, and 3σu which lead to a non-dissociating ion. The measured TDCS summed over all three orbitals are internormalized across the scattering angles and ejected electron energies. They are compared to the theoretical results from the multi-center distorted wave (MCDW) approximation, and from the MCDW-WM approximation which includes post-collision interaction using the Ward–Macek factor (WM). Reasonable good agreement is found between the experiment and the MCDW-WM calculations for the angular dependence and the relative magnitude of the cross sections in the coplanar plane, while for the perpendicular and full perpendicular planes larger discrepancies exist. Since post-collision interaction is not considered the MCDW method shows strong discrepancies with experiment for small mutual angles of the two outgoing electrons in the final state.

Photoionization of the iodine 3d, 4s, and 4p orbitals in methyl iodide.

Ionization of the I 3d, 4s, and 4p orbitals in methyl iodide (CH3I) has been studied by using synchrotron radiation to measure the total ion yield and by recording photoelectron spectra with linearly polarized radiation in two polarization orientations. The complete photoelectron spectrum of CH3I has been recorded at several photon energies, and bands due to the C 1s, I 3d, 4s, 4p, and 4d atomic-like orbitals, as well as the molecular orbitals, have been observed and assigned. In the vicinity of the I 3d5/2 and 3d3/2 ionization thresholds at 626.8 and 638.3 eV, respectively, the ion yield displays weak structure in the pre-edge region due to transitions into valence or Rydberg states, and, at higher energies, a shoulder and a broad maximum attributed to the I 3d5/2 → εf and the I 3d3/2 → εf shape resonances, respectively. The absorption spectrum calculated using time-dependent density functional theory, within the Tamm-Dancoff approximation, has allowed assignments to be proposed for the valence and Rydberg states. The Stieltjes imaging technique has been used to simulate the absorption spectrum above the ionization threshold and indicates that transitions into the f(l = 3) continuum channel dominate. This conclusion has been corroborated by a Continuum Multiple Scattering-Xα (CMS-Xα) calculation. The asymmetric broadening of the photoelectron bands associated with the I 3d orbital, due to post collision interaction, is taken into account in our experimental analysis. Experimentally derived photoelectron anisotropy parameters for the I 3d orbital are in good agreement with the theoretical predictions obtained with the CMS-Xα approach. The I 3d shake-up/shake-off photoelectron spectrum has been recorded, and assignments have been proposed for several of the satellites. The M4N45N45 and M5N45N45 Auger electron yields have been measured, and that for the M5N45N45 decay exhibits a maximum due to interchannel coupling between the 3d5/2 and 3d3/2 continua. The photoelectron band associated with the I 4p orbital has an unusual appearance. Based upon previous theoretical work for the analogous Xe 4p orbital, it appears that the initial I 4p-1 hole state decays rapidly through Coster-Kronig and super-Coster-Kronig transitions. This leads to a redistribution of the spectral intensity associated with the I 4p orbital and results in a photoelectron spectrum containing a single structured band together with an extended continuum. Another continuum is observed on the high binding energy side of the peak due to the 4s orbital, and we assign this to super-Coster-Kronig transitions into the 4p-14d-1 continuum.

Selectivity of the Br 3d−1 Auger decays in HBr

The Auger decay of the spin-orbit and molecular-field split Br $3{d}^{\ensuremath{-}1}$ core holes in HBr is investigated, both by a photoelectron--Auger-electron coincidence experiment and by ab initio calculations based on the one-center approximation. The branching ratios for the Auger decay of the five different core-hole states to the $4p{(\ensuremath{\sigma},\ensuremath{\pi})}^{\ensuremath{-}2}$ dicationic final states are determined. Experimental and theoretical data are in good agreement and conform to results for the $4p{\ensuremath{\pi}}^{\ensuremath{-}2}$ final states from a previous analysis of the high-resolution conventional Auger-electron spectrum. The branching ratios for the Br $3{d}^{\ensuremath{-}1}$ Auger decay to the $4p{(\ensuremath{\sigma},\ensuremath{\pi})}^{\ensuremath{-}2}$ with \ensuremath{\Sigma} symmetry follow the propensity rule of ${L}_{2,3}VV$ Auger decay [S. Svensson, A. Ausmees, S. J. Osborne, G. Bray, F. Gel'mukhanov, H. \AA{}gren, A. Naves de Brito, O.-P. Sairanen, A. Kivim\aki, E. N\~ommiste, H. Aksela, and S. Aksela, Phys. Rev. Lett. 72, 3021 (1994)] stating that the oriented core holes decay preferentially by involving a valence electron from an orbital with the same spatial orientation. For the ${M}_{4,5}VV$ decay in HBr this propensity rule has to be supplemented by the requirement that the Auger-electron channel and the other valence orbital have the same preferential orientation. We also probe the influence of the Auger kinetic energy on the distortion of the photoline caused by the postcollision interaction effect. For small kinetic energies, differences between experimental results and theoretical predictions are identified.

Revealing excitonic processes and chemical bonding in MoS2 by x-ray spectroscopy

Electron core-hole processes at absorption edges sport several signatures, primarily in the form of bound states and/or excitonic enhancement. Through analysis of the resonant-Raman Auger effect for the two-dimensional transition-metal dichalcogenide $\mathrm{Mo}{\mathrm{S}}_{2}$, we demonstrate that these effects have significant manifestations at the S $K$ edge. We characterize two asymmetric excitonically enhanced edges: one at the fundamental band edge and one several electron volts above it following a second band gap that lies entirely within the unoccupied states, with the latter revealing an anomalous postcollision interaction effect. Our interpretation is supported by comparison of both the photoemission valence-band spectrum and the S $K$-edge x-ray-absorption spectrum with electronic structure calculations and an ab initio solution of the Bethe-Salpeter equation that accurately accounts for the electron-core-hole interaction.

Interference patterns from post-collision interaction in below-threshold photoexcitation Auger processes

We focus on the post-collision interaction in Auger processes where the photoelectron energy is near or below the ionization threshold. Time-dependent quantum and classical calculations are performed. When the photoelectron is more deeply bound, interference patterns can be seen in the angular and photoelectron energy distributions. These interference patterns are visible in quantum calculations, but not in purely classical calculations. A semiclassical analysis using actions from two-path trajectories gives the relative locations of the interference maxima very close to those from the full quantum calculations.