Direct Double Ionization Research Articles

Two electron photoemission processes in the valence band of solids

We present experimental evidence on photo double ionization processes in the valence band of solids. Applying a 'Time-of-Flight' electron spectroscopy technique, we measured the energy distribution of pairs of correlated electrons emitted from clean Cu(001)- and Ni(001)- crystals upon absorption of linearly polarized photons of 45eV energy. Data were taken for normal and grazing orientation of the light wave vector with respect to the crystal surfaces. The energy sharing distributions of electron pairs emitted from the vicinity ofthe Fermi-level show significant differences for Cu and Ni. For interpretation of our data, we consider a direct double ionization mechanism in competition with a two step process involving single photoexcitation and a subsequent collision of the photoelectron with an additional band electron. A theoretical approach by J. Berakdar including both mechanisms is in good agreement with our data. In this theory the differences between Cu and Ni are traced back to distinct relative contributions of both mechanisms in the two metals due to the different average electron density.

Two-electron atoms in strong fields

Multiphoton excitation and ionization of two-electron atoms under strong laser pulses, with emphasis on double excitation, is reviewed. After an introduction to the basic concepts of traditional single-photon spectroscopy and methodology, the main phenomena and experimental observations under multiphoton excitation in the perturbative regime are summarized. That is followed by the discussion of the main ideas underlying various non-perturbative approaches, especially as they pertain to the two-electron problem. The present state of understanding non-perturbative time-dependent behavior, in that context and in relation to issues such as correlation, double excitation, sequential and direct double ionization, is then formulated and discussed. The article ends with a summary of effects relating to autoionizing states in strong fields and an outlook for future developments.

Measurement of the Initial Condition of Electrons Ionized by a Linearly Polarized, High-Intensity Laser

We have measured the angular spectrum of electrons born in a linearly polarized, high-intensity laser focus. The spectrum is directly related to the initial conditions of the ionized electrons in the plane perpendicular to the propagation direction. Our measurements for high charge states of neon are in good agreement with predictions of quasistatic tunneling models and limit the initial electron kinetic energy to approximately 0.5% of its average quiver energy. This measurement is important for studies of high-order harmonic generation and direct double ionization. [S0031-9007(96)02268-5] PACS numbers: 32.80.Fb, 32.80.Rm Over the past several years, a simple two-stage model of ionization, referred to as the “quasistatic” or “simpleman’s” model [1‐4], has succeeded in explaining a wide variety of experimental aspects of intense field-atom interactions in the tunneling regime. These include many characteristics of the electron energy spectra [5], direct double ionization in the tunneling regime [6], and the cutoff energy of the high-harmonic plateau [7]. The basic assumption of the model is that ionized electrons can return to collide with the nucleus with an energy that depends on both their initial momentum and the phase within the optical cycle at which they were born. The initial phase, in turn, depends on the ionization model. For classical ionization, or barrier-suppression ionization (BSI) [8], the electrons are born only at the peak of the field and hence have zero initial phase. In ac tunneling models [9,10], the electrons are born over a range in phase within the optical cycle near the peak of the field. After ionization, the trajectory is calculated classically, neglecting the Coulomb force of the residual ions, as it is much weaker than the force due to the laser field [3]. The distributions of electrons as a function of their initial momentum and initial phase determine the rates of several of the abovementioned processes. This Letter reports a measurement of the initial conditions of electrons ionized in the long-pulse tunneling regime. The Keldysh adiabaticity parameter [11] g ; sIpy2Upd 1y2 , 0.1, where Ip is the ionization potential of the atom and Up is the ponderomotive energy [12]. Unlike some previous studies of above-threshold ionization electrons [5,13] in which the effect of the ponderomotive potential was minimized, our intent was for the freed electrons to gain the full energy provided by the field gradient. For electrons born at the peak of the field and with zero initial momentum perpendicular to the propagation direction, the ponderomotive potential leads to an axisymmetric electron distribution in the plane perpendicular to the propagation direction [14]. A small initial momentum perpendicular to the propagation direction or ionization of the electron at an off-peak phase of the optical cycle breaks the symmetry of the ponderomotive potential. We used a high-intensity laser to ionize electrons from neon gas at low density and measured the electron spectra as a function of the forward angle u (relative to k) and the azimuthal angle w (relative to the polarization direction in the plane perpendicular to the propagation direction). We observed a significant asymmetry in the electron number distribution in the plane perpendicular to the direction of propagation, with more electrons detected along the direction of polarization than perpendicular to it. The observed asymmetry is due to the nonzero initial conditions and is consistent with quasistatic tunneling models. Earlier work utilizing the retarding-potential grids attempted to measure the initial drift momentum by calculating the difference between the electron energy spectra parallel and perpendicular to the polarization direction [3,15]. The direction of the initial momentum along the polarization direction implies that the number, as well as the energy, of electrons seen along the polarization direction will be larger than the number seen perpendicular to it. The azimuthal distribution of the number of electrons is a more sensitive measure of the initial conditions than the azimuthal distribution of the energy of the electrons. In addition, at high electron energies, the forward electron momentum [16] complicates the retarding potential method.

Direct and indirect dissociative double photoionization of diatomic molecules

An enhanced photoelectron - ion - ion triple coincidence technique eliminates the effect of target molecule thermal velocity on measured ion pair kinetic energy releases. Kinetic energy release distributions at photon energies of 40.8 and 48.4 eV are reported for diatomic molecules and are compared with calculated distributions for direct vertical transitions to theoretically known dication states. Good agreement in the case of indicates that double photoionization of this molecule at 8 eV above threshold is mainly direct. Double photoionization of CO, and NO is purely indirect at the lowest photon energies and has both indirect and direct components at higher energies in this range. The indirect processes give a wide range of final product energies and often involve atomic autoionization. Selectivity in the direct double ionization processes is consistent with the application of symmetry-based propensity rules.

Electronic Structure Information from Electron Impact Ionisation Experiments

Electron impact ionisation with full determination of the kinematics (measurement of energies and momenta of the incident, scattered and ejected electrons) has proven to be useful for investigating both the electronic structure of atoms and molecules and the mechanism of ionisation. These experiments are, by definition, coincidence experiments since it is necessary to be sure that all the detected electrons originate from the same collision. For single-electron ionisation, (e, 2e), the emphasis has been on momentum densities and spectroscopic factors–see for example Coplan et al. (1994), McCarthy and Weigold (1976, 1988, 1991) and Leung (1991). For double ionisation, (e,3e), data are just beginning to emerge, with early results on the Auger process and direct double ionisation (Duguet and Lahmam-Bennani 1992). Both (e, 2e) and (e, 3e) experiments are technically challenging because the signals are small and there is usually a large background. In the last few years, electrostatic spectrographs and position sensitive detectors have improved the resolution and precision of (e, 2e) measurements and have made (e,3e) measurements a practical reality.

Electron impact ionization of krypton ions ( q = 8–13)

Absolute cross sections for electron impact single ionization of Kr 10+ and Kr 11+ ions and double ionization of Kr q+ ( q = 8–13) have been measured in an animated crossed-electron ion beam experiment. Ionization thresholds corresponding to particular electron pairs and inner-shell electron ejection are estimated from a structure Hartree-Fock calculation. For double ionization, results show that, along the homonuclear sequence, direct double ionization is progressively overcome due to the increasing relative importance of direct L-shell ionization followed by autoionization. The presence of ions in metastable states is observed for Kr 8+ and Kr 9+ contributing to direct and indirect processes.

Laser-assisted inelastic rescattering during above-threshold ionization.

As an electron is freed from an atom by an intense laser it is accelerated by the oscillating field. Before escaping entirely, it may recollide with its parent ion. During this rescattering, the remaining electrons of the ion might be excited or ionized. The influence of the laser field on these impact excitation and ionization processes is investigated. Model calculations for helium at 780 nm and intensities near ${10}^{15}$ W/${\mathrm{cm}}^{2}$ show that the effect of the field on the total probability of promoting an electron from the ionic ground state is small. However, the laser alters the final excited-state populations, rapidly ionizing any excited bound states. We discuss the importance of these results in the search for the mechanism responsible for direct double ionization in the tunneling regime.

Electron impact double ionization of singly charged ions C+, N+, O+, F+ and Ne+

The first absolute cross section measurements For double ionization of C+, N+, O+ and Ne+ ions by electron impact are reported. The animated crossed beams method has been employed in the energy range from below ionization thresholds to approximately 2500 eV. The classical binary encounter approximation overestimates measured cross sections by almost two orders of magnitude. Along the sequence, the cross section maximum does not follow classical scaling laws. A simple scaling law based on an electron pair ejection model is proposed for the prediction of direct double ionization. Inner-shell ionization followed by autoionization is seen to play a dominant role for C+ only.

Electron-ion coincidence spectroscopy on atomic barium in the excitation range of the 4d giant resonance.

For the first time a free metal atom has been investigated by analyzed electron-ion coincidence spectroscopy after inner-shell excitation with synchrotron radiation. Probabilities of the decay from different ${\mathrm{Ba}}^{+}$ inner-hole states (4${\mathit{d}}^{\mathrm{\ensuremath{-}}1}$, 5${\mathit{s}}^{\mathrm{\ensuremath{-}}1}$, 5${\mathit{p}}^{\mathrm{\ensuremath{-}}1}$) to higher charged ions (${\mathrm{Ba}}^{2+}$, ${\mathrm{Ba}}^{3+}$, ${\mathrm{Ba}}^{4+}$) have been determined, which allows a direct link between electron and ion spectroscopy results. Comparison between the different data sets and Hartree-Fock calculations for ${\mathit{N}}_{45}$ Auger transitions yields new knowledge about direct double ionization processes, e.g., their dominance on 4${\mathit{d}}^{\mathrm{\ensuremath{-}}1}$ Auger decay.

Resonant double multiphoton ionization via planetary states

The authors have studied double ionization of Ba 6snl Rydberg states through resonant two-photon excitation of 8snl double-Rydberg states with n=13 and 14 and different l. The laser intensity dependence of Ba2+ yield measured for l>or=8, when the electrons suffer long-range dipole interaction, shows a decrease from four-photon for l=8 to less than three for l=11. The four-photon dependence is due to autoionization decay populating the Ba+(7p) levels which gives an indirect signature to the Ba2+ production. By increasing l this decay vanishes and the data show evidence of a direct double-ionization process via planetary-electron states for l>or=10. Additional intensity measurements performed for low l=6 states strongly mixed with 5fn'l' ones by short-range multipole interaction, reveal indirect Ba2+ production and an individual case of partial stabilization due to destructive interference leading to direct double ionization.

First observation of a Fano profile following one step autoionization into a double photoionization continuum

We have measured the double photoionization cross section of sodium atoms between the first 2s 2 p 5 2 P double photoionization (52.4 eV) and 2s-single 1.3 S photoionization thresholds (71.0 eV). We have also observed a Fano profile into the double ionization continuum resulting from the interference between the one-step direct double ionization process and the resonant double Auger decay of core-excited neutral sodium in the 2s→3p resonance region. Profiles of absolute partial and total cross sections have been obtained in all important channels. The Fano and Starace parameters, in particular a width of 0.23 eV, have been determined, allowing full characterization of the resonance

Multiphoton ionization of magnesium and calcium atoms by short and intense laser pulses

Single and double ionization of magnesium and calcium atoms following Nd: YAG laser multiphoton excitation at 1064 and 532 nm have been studied by employing pulses of 35 ps and 200 ps duration at intensities of the order of 1010–2×1013 W/cm2. The dependence of ion formation on the laser intensity has been measured and the slopes of the linear parts of the log-log plots and the ratios of saturation intensities for two pulse durations have been compared with the predictions of the scaling law. No evidence for a pure direct double ionization process has been obtained.

Angular distribution of positive photofragments following dissociative double ionization in the HBr molecule

Dissociative rates from the five doubly ionized states in the HBr molecule associated with the first two dissociation limits have been measured by recording the kinetic energy spectra of the H+ signal using monochromatic as well as white synchrotron radiation. The direct double ionization of the 4p pi valence electrons is found to be only weakly affected by electron interactions. Photoabsorption in the region of the 3d excitation in Br is highly anisotropic, as reflected by the angular dependence of the photofragment distributions. Comparisons with results based on potential energy curves for HBr2+ calculated employing multi-reference configuration interaction (MRD-CI) are presented and a good agreement between theory and experiment is found.

Relaxation processes following excitation and ionization of SiF4 in the vicinity of the silicon 2p threshold. II. Dissociation of the molecular ions

Partial ion yields from photoionization of SiF4 have been measured with time-of-flight mass spectrometry, photoion–photoion coincidence and triple photoion coincidence techniques using synchrotron radiation from 100 to 136 eV, in the region of the silicon 2p edge where strong resonances are found. From the photon energy dependence of positive ion pairs and of doubly charged fragment intensities, with a suitable normalization procedure, we have estimated the total double photoionization cross section. Below the Si2p edge, the double to single dissociative ionization branching ratio follows the resonance behavior, and is consistent with the photoelectron results of de Souza et al. (Paper I) and discussed in terms of multibond breaking dissociation pathways of residual excited ions (singly and doubly charged) produced by resonant Auger decay processes. Above the Si2p edge, the fragmentation is found to originate from dissociative double ionization occurring after normal Auger processes. The small additional contribution of triple dissociative ionization is consistent with a second order Auger process. In contrast, the underlying valence ionization continuum is responsible for all parent intensity and most of the SiF+3 fragment expected from the normal dissociative ionization channels. The measurement of appearance energies of fragment ion pairs by the photoion–photoion coincidence method, offers a direct measurement of the first direct double ionization onset in SiF4 and new values for other dissociative SiF2+4 states which complement those found by Auger spectroscopy.

Electron-impact-ionization cross sections of the Ga and In atoms.

Absolute electron-impact cross sections for single, double, and triple ionization of gallium and indium have been measured from 0 to 200 eV. Beams of Ga and In atoms are formed by charge-transfer neutralization of 3-keV-ion beams with triethylamine or xenon. The cross sections are considerably larger than previous measurements and are also larger than the predictions of various empirical formulas and classical and quantum-mechanical theories, due in part to significant contributions from autoionization. The double-ionization cross sections appear to be dominated by ionization of a d electron followed by autoionization, rather than by direct double ionization.

Electron-impact double-ionization cross sections for Xe8+

Absolute cross-section measurements are presented for the double ionization of ${\mathrm{Xe}}^{8+}$ by electron impact from below threshold to 1500 eV. A search for direct double ionization indicates that this process is small or negligible compared to the single-electron processes which contribute to double ionization. The presence of a high percentage of metastable target ions in the interaction region of this experiment significantly affects the interpretation of the measured cross sections and indicates the potential importance of selected metastable ions in plasmas.

Multiphoton dissociative ionization of molecular deuterium.

The kinetic energy spectra of deuterium ions produced from ${\mathrm{D}}_{2}$ arising from collision-free subpicosecond irradiation at 248 nm with intensities spanning the ${10}^{13}$--${10}^{16}$-W/${\mathrm{cm}}^{2}$ range have been measured by time-of-flight analysis. The behaviors of the kinetic energy distributions of the fragments and the relative abundances of atomic (${\mathrm{D}}^{+}$) and molecular (${\mathrm{D}}_{2}^{+}$) ions reveal the presence of two mechanisms of multiphoton dissociative ionization. Calibration of the energy scale for ${\mathrm{D}}^{+}$ is facilitated by comparison with ${\mathrm{He}}^{2+}$. For intensities in the ${10}^{13}$--${10}^{15}$-W/${\mathrm{cm}}^{2}$ region, intermediate three-photon resonances and the optical Stark shift play important roles. At an intensity \ensuremath{\sim}${10}^{16}$ W/${\mathrm{cm}}^{2}$, a direct transition from the molecular ground state to the dissociative ionic level appears as a significant channel. No evidence of direct double ionization was observed.

Single and double ionization of helium by neutral-particle to fully stripped ion impact.

New measurements of direct single and double ionization of helium by hydrogen, helium, carbon, nitrogen, and oxygen ions are presented for projectile charge states ranging from 0 to 3+. These data are combined with previously published values to provide a detailed description of direct double ionization of helium for a wide range of experimental parameters, i.e., projectile ions include protons through oxygen, impact energies from 25 to 5000 keV/u, and projectile charge states ranging from neutral to fully stripped. The charge-state and impact-velocity dependencies of the measured cross sections are compared with the dependencies predicted by an independent electron multiple-ionization model. It is found that a multistep mechanism (i.e., the independent ionization of both target electrons) is the dominant direct double-ionization mechanism for charged-particle impact energies above 100 keV/u. This mechanism dominates until some maximum impact velocity, which depends on the projectile charge, is reached. For higher velocities a single-step ionization mechanism becomes important. The limited neutral-particle impact data indicate that the single-step mechanism becomes dominant at much lower impact velocities and there is no evidence of the multistep mechanism in the neutral-particle impact energy range investigated.

Many-body approach to two- and three-photon double ionization and excitation of xenon.

We investigate different processes which may be responsible for ejection of two electrons from the external shell of xenon through the absorption of two and three photons, namely two-photon direct double ionization and three-photon sequential double ionization via the ion in an excited state or in the ground state. We calculate the cross sections of the ionization processes involved, using many-body perturbation theory. These cross sections are then used within a rate equation model for comparing the relative efficiencies of the different double-ionization mechanisms.

Satellites and double ionization continua in the CS2 photoelectron spectrum

The CS+2 valence satellites have been studied with photoelectron spectroscopy using synchrotron radiation in the 35–75 eV photon energy range. Partial cross sections (σ) and asymmetry parameters (β) for most bands have been measured as a function of photon energy. Below 28 eV binding energy, the symmetry of satellite bands has been identified on the basis of their β value and a comparison between experimental photoelectron spectra and new ab initio SCF-CI calculations of CS+2 corrected for transition moments. For the bands with binding energies above 28 eV no configuration interactions states of CS+2 are predicted with significant intensity. We suggest that they originate from the opening of direct double ionization continua. This is supported by the similarity of their cross sections with the total double ionization one.