Post-collision Interaction Research Articles

Coplanar symmetric (e, 2e) cross sections for krypton 4s ionization

The triple-differential cross section for electron impact ionization of the 4sorbital of krypton (binding energy 27.5 eV) has been measured in coplanarsymmetric kinematics. The experimental results are presented for outgoingelectron energies of 85, 50, 20, 10 and 4 eV. The results are comparedwith two distorted wave Born approximation calculations; the influenceof post-collision interaction (PCI) on the cross sections is investigatedby incorporating correct final state boundary conditions in one of thecalculations. The influence of PCI is found to be very important at thelower energies. Inclusion of the three-body final state boundary conditionsimproves the agreement between theory and experiment, but there are stillsignificant discrepancies, indicating that additional physical effects (suchas higher-order interactions) are important at lower energies.

Perturbation theory for (e, 3e)on helium

The contributions of order e4to the Tmatrix for electron impact double ionization of atomic helium have beenevaluated. The resulting fivefold differential cross sections are characterizedby the interference of the amplitudes associated with the differentcombinations of binary interactions of the active electrons. They showstrong artefacts due to neglect of high-order post-collisional interactions,but also remarkable agreement with current experimental data if oneof the atomic electrons is ejected into the forward half-plane. Theresults allow a discussion of the validity of the ‘reaction mechanism’ and‘photoionization limit’ approaches to the interpretation of experimental (e, 3e)data.

Shifts in electron capture to the continuum at low collision energies: Enhanced role of target postcollision interactions

Measurements of electron velocity distributions emitted at $0\ifmmode^\circ\else\textdegree\fi{}$ for collisions of 10- and 20-keV ${\mathrm{H}}^{+}$ incident ions on ${\mathrm{H}}_{2}$ and He show that the electron capture to the continuum cusp formation, which is still possible at these low impact energies, is shifted to lower momenta than its standard position (centered on the projectile velocity), as recently predicted. Classical trajectory Monte Carlo calculations reproduce the observations remarkably well, and indicate that a long-range residual interaction of the electron with the target ion after ionization is responsible for the shifts, which is a general effect that is enhanced at low nuclear velocities.

Angle-dependent postcollisional interaction and interference effects in resonant double photoionization of neon

The resonant double photoionization of Ne has been studied via an electron-electron coincidence experiment. A complete set of measurements was performed at different mutual angles when the photoelectron and Auger-electronpairs have nearly equal energy. The overall experimental energy resolution, narrower than the natural linewidth of the intermediate state, has allowed us to observe interference effects due to the indistinguishability of the two electrons. The observed energy and angular distribution exhibit a strong interplay of postcollisional interaction and interference effects. Calculations based on the model developed by Sheinerman and Schmidt [J. Phys. B 30, 1677 (1997)] describe the main trend of the experimental observations.

Final-state interaction description of the autoionization of atoms by ion impact in the velocity matching regime

The line profile of the electron emitted in the autoionization of an atom by ion impact is strongly affected by the post-collision interaction (PCI) with the outgoing projectile. Here we analyze how these PCI effects are modified when the projectile velocity is in the close vicinity of the resonant electron velocity. In this energy range, the analysis of the resonance contribution is hindered by the characteristic ‘electron capture to the continuum’ divergence in the direct term. Here we present a theoretical study of the interplay between both contributions, based on a generalization of the final-state interaction model.

Ab initio calculation of angular distribution patterns of resonant photodouble-ionization in neon

Angle-resolved patterns of the differential cross section for resonance-affectedphoto double-ionization in neon under the conditions of equal and slightlyunequal energies of the ejected electrons are calculated using ab initioN-electronscattering wavefunctions that take into account interference, exchange andcorrelation effects. Post-collisional interactions are included a posteriori,correcting the direct and resonant amplitudes in the scattering wavefunctions bymeans of separate correlation factors taken from the literature. The method usedfor constructing scattering wavefunctions with two electrons in the continuum isdescribed in detail. Comparison between theoretical cross sections convoluted withapparatus functions and available experimental data (Schaphorst S J, Jean A,Schwarzkopft O, Lablanquie P, Andric L, Huetz A, Mazeau J and Schmidt V 1996J. Phys. B: At. Mol. Opt. Phys. 29 1901; Rioual S, Rouvellou B, Avaldi L, BatteraG, Camilloni R, Stefani G and Turri G 2000 Phys. Rev. A 61 044702and Rioual S, Rouvellou B, Avaldi L, Battera G, Camilloni R, StefaniG and Turri G 2001 Phys. Rev. Lett. 86 1470) shows close agreement.Resonant, direct and interference contributions to the differential cross sectionsand geometrical features of the electron emission are analysed in detail.

The shift of L 2 level photoelectron line of Cu metal measured in coincidence with the L 2–L 3V–VVV Auger-electron line

The L 2 photoelectron line of Cu metal measured in coincidence with the L 2–L 3V–VVV Auger line, moves to lower kinetic energies when the Auger analyzer moves to lower kinetic energy tail of the L 3–VV ( 1G) Auger line. Creagh et al. [Surf. Sci. 432 (1999) 297] proposed the possibility that the shift is due to the post-collision interaction (PCI). However, the present many-body theory shows that even without the presence of the PCI, the L 2 coincidence-photoelectron line shifts from the XPS spectral peak position towards the lower kinetic energy side, irrespective of the Auger-electron analyzer’s positions. The energy shift depends on the Auger-electron analyzer’s position. The coincidence-photoelectron line is asymmetrical. The present theory predicts the shift which agrees with the observed energy shift. The shift is due to the change in the partial L 2–L 3V CK transition rate which depends critically on the CK-electron energy. We comment on the PCI effect in the light of the recent experimental study of the L 2–L 3V CK transition rate near the L 2 ionization threshold.

Multielectron excitations in x-ray absorption spectra of Rb and Kr

In the K-edge x-ray absorption of rubidium vapour and gaseous krypton,comprehensive spectra of collective excitations down to the relative probability of 5 ×10−5 are extracted. After removal of the asymptotic Victoreen trend, the region ∼ 100eV above the edge exhibits a steep decrease of the absorption coefficientattributed to core relaxation and post-collision interaction in the Auger decay.With an exponential model for the decrease, the entire spectrum of multielectronexcitations is recognized as a succession of consecutive resonant, shake-up andshake-off channels. They can be identified as coexcitations of electrons fromsuccessively deeper subshells, from 5s down to 3s. The identification of excitedstates is aided by a quantitative modelling of subshell contributions and bynatural-width deconvolution. The valence and subvalence coexcitations are shownto follow the pattern of the lighter homologues potassium and argon.

Cascade processes after 3p-shellthreshold photoionization of Kr

Yield spectra of the multiply charged ions Kr2+, Kr3+, Kr4+ and Kr5+ in coincidence with thresholdelectrons (Ek⩽0.03 eV) have been measured near the3p-shell ionization region of Kr. Profiles of post-collisioninteraction (PCI) effects induced by Auger cascades following3p-shell threshold ionization are derived from these coincidence spectra. On the basis of the PCI profiles, the number ofAuger cascade steps for each of the decay channels leading tothe formation of the multiply charged ions in 3p3/2- and3p1/2-shell threshold ionization of Kr was determined,and the branching ratios of the decay channels were estimated.

Postcollision interaction and two-center effects in ionizing collisions

Momentum distributions of the recoil target ion and the ejected electron have been calculated for 75-keV ${\mathrm{H}}_{2}^{+}+\mathrm{He}$ collisions by applying the classical trajectory Monte Carlo (CTMC) and the continuum-distorted-wave-eikonal-initial-state (CDW-EIS) theory. A qualitative agreement was found between the calculated centroid values of the momentum distributions and the corresponding experimental data published recently by An et al. [Phys. Rev. A 63, 030703 (2001)]. The presence of postcollision interaction effects in the momentum distributions was analyzed repeating the CTMC calculations with a short-range model potential between the electron and the projectile ion as a function of the interaction length. The role of two-center effects was investigated by comparing the CDW-EIS results with those obtained in the first-Born approximation.

Quantum theory of the effect of post-collision interaction on the absorption of X-ray photons by a deep atomic shell

A fundamental problem for modern atomic physics, the theoretical description of the many-particle effects of post-collision interactions in the photoionization of deep atomic shells outside the framework of quantum-mechanical perturbation theory is considered. The analytical solution of the stationary many-particle Schrödinger equation for the non-relativistic wavefunction of the system of interacting continuous spectra of atomic states is obtained using a class of weight-functions of Cauchy–Lorentz type. States considered are those resulting from: (i) direct photoionization of a deep shell of a free atom and (ii) Auger-decay of a deep vacancy with two (photo- and Auger-) electrons in the continuous spectrum. The solution takes into account: (a) the rearrangement of the continuum photoelectron wavefunction in the changing field of the atomic residue, and (b) the electrostatic interaction of photo- and Auger-electrons resulting from the Auger-decay of the vacancy. The corresponding analytical structure of the photoionization cross section of the deep atomic shell is derived. A generalization is proposed for: (a) two or more channels of Auger-decay of the deep vacancy, and (b) direct photoexcitation of the deep atomic shell.

(e,2e)triple-differential cross sections of helium and argon at 64.6 eV

The distorted-wave Born approximation with spin averaged static exchange potential and modified semiclassical exchange potential has been used to calculate the triple-differential cross section of He (1s 2 ) and Ar (3p 6 ) in the coplanar to perpendicular plane geometry. Similar to helium a strong interference minima in the cross section has been observed for the argon atom for all the incident electron angles. The triple-differential cross section in the case of argon at low- and high-scattering angles is in very good agreement with the present experiment. Inclusion of postcollision interaction gives a dip at 45° (characteristic feature of p-orbital targets), which has not been observed exactly at 45° by the experiment and calculations without postcollision interaction. The agreement with experiment in case of helium is quite good, but in the case of argon, some discrepancies are still there.

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.

Post-collision interaction effects following4p-shell ionization of Xe

Yield spectra of multiply charged ions in coincidence withthreshold electrons (Ekin⩽0.03 eV) have beenmeasured near the 4p-shell ionization region of Xe. Thecoincidence spectra of Xe3+ and Xe4+ ions as afunction of photon energy exhibit characteristic profiles induced by post-collision interactions in Auger cascadesfollowing 4p-shell threshold ionization of Xe. Peaks of theprofiles shift from the nominal 4p-shell threshold, and thoseshapes are asymmetric and broadened. The profiles have the samepeak-shifts and the same peak-widths in both Xe3+ andXe4+ coincidence spectra. Based on the properties of the profiles, it is concluded that both of these ions result fromtwo-step Auger cascades. Furthermore, it is found that Augershake-off (i.e. double Auger) decays play a significant role inthe cascades following 4p-shell ionization of Xe.

The triple differentialcross sections of ionic targets in the coplanar to perpendicularplane geometry

The distorted wave Born approximation with spin averaged staticexchange potential has been used to calculate the tripledifferential cross sections of Li+(1s2),Rb+(4p6), Cs+(5p6), Cu+(3d10)and Ag+(4d10) ions in the coplanar to perpendicularplane geometry. The incident electron energy has been chosen at40 eV above the ionization potential. The calculations have beencarried out with three sets of detection energies for theoutgoing electrons, namely (20, 20 eV) symmetric, (15, 25 eV)asymmetric and (5, 35 eV) highly asymmetric. The incidentelectron angle has been varied from 0° (coplanarsymmetric geometry) to 90° (perpendicular plane geometry)with angular increments of 22.5°. The effect of post-collision interaction has also been studied. An interferencedip in the cross section has been noticed for each target. Inthe perpendicular plane geometry it has been seen that Zhanget al's model is applicable only to the targets with s- andp-orbital electrons.

Exchange interference inthe angular correlation between magnesium photo- andCoster-Kronig electrons

For the well defined process of 2s photoionization in atomicmagnesium with subsequent L1-L2,3M1 1P or 3PCoster-Kronig decay, exchange interference effects are studiedfor coincident two-electron emission. Both electrons areobserved for back-to-back emission in a plane perpendicular tothe photon-beam direction, changing the photon energy so thatthe photoelectron line is moved, from below to above, throughthe state-selected Coster-Kronig line. The coincidence signalof the singlet Coster-Kronig channel shows the expectedconstructive interference effect leading to an increase by afactor of 4. However, in the coincidence signal of thetriplet Coster-Kronig channel the expected destructiveinterference appears to be hidden due to (1P1-3P1)spin-orbit induced J-mixing. Implementing this complicationinto the theory which includes electron exchange and theinfluence of post-collision interaction, very good agreement isachieved between theoretical and experimental data. This givesquantitative confirmation of the selected process of sequentialtwo-electron emission described in a one-step formulation.

Inherent post-collision interaction in spectator

Abstract The inherent post-collision interaction (PCI) between an Auger-electron and a spectator electron in core-hole decay in metals and charge-transfer systems is described in a systematic maimer by a many-body theory. The inherent PCI effect on spectator Auger-transition spectral lineshapes of metals and charge-transfer systems is discussed. The spectator Auger-transition energy shift due to a change of chemical environment is discussed in the light of the inherent PCI.

Auger-electron lineshapes in electron impactionization: a calculation for non-coincidence experiments

The distortion effects of the post-collision interaction onargon L2,3M2,3M2,3 Auger-electron lineshapeshave been calculated for 300 eV, 500 eV and 2 keV electronimpact inner-shell ionization. The calculations were based onthe model of Kuchiev and Sheinerman (Kuchiev M Yu andSheinerman S A 1987 Sov. Phys.-Tech. Phys. 32 879)applying our cross section data for secondary electrons,determined by a classical trajectory Monte Carlo method and inaddition a continuum distorted wave method for 2 keV. Theasymmetry parameters of the calculated peak shapes have beenexamined as a function of the projectile energy and the Augeremission angle and for some cases compared with our previousexperimental results.

Dynamics and post-collision interaction effects in two electron decay from the Xenon 4d hole.

Two Auger electrons, one very slow, one fast, have been detected in coincidence following near threshold 4d photoionization of the Xe atom. The distribution in the energy the two electrons share has been measured for the first time revealing the presence of post-collision interaction effects that provide unique information on the decay dynamics of the 4d hole. Analysis of the distorted line shapes indicates that the dominant process is decay of Xe+(4d(-1)) to Xe3+ through cascade emission of a zero kinetic energy Auger electron followed by a fast Auger electron. The widths of the intermediate Xe2+* states are estimated to be about 60 meV.

Post-collisioninteraction after inner-shell ionization by electronimpact: the shape of Auger lines

We measured the lineshapes of Ne K-L2,3L2,3and Ar L2,3-M2,3M2,3 Auger electronsdistorted by post-collision interaction (PCI) forelectron-impact ionization. The excessenergies E1 = E0-I(nlj) (E0 and I(nlj) are the incident andtheionization energies) were 27-427 eV for Ne K ionization and12-750 eV for Ar L3 ionization. For comparison we calculatedtheoretical Auger spectra where the PCI-distorted lineshape, obtainedineikonal theory (Sheinerman et al 1994 J. Phys. B:At. Mol. Opt. Phys. 27 5681), was convolvedwith the experimentally known spectrometer function and aGaussian function for the Doppler effect of the thermallymoving target atoms. The agreement of experimental andtheoretical spectra is excellent in all cases. Thisdemonstrates the quality of eikonal theory in calculatingthe PCI-distorted Auger lineshapes.