B. Najjari

Two-Center Resonant Photoionization

Photoionization of an atom A, in the presence of a neighboring atom B, can proceed via resonant excitation of B with subsequent energy transfer to A through two-center electron-electron correlation. We demonstrate that this two-center mechanism can strongly outperform direct photoionization at nanometer internuclear distances and possesses characteristic features in its time development and the spectrum of emitted electrons.

Inelastic Collisions of Relativistic Electrons with Atomic Targets in a Laser Field

We consider inelastic collisions between relativistic electrons and atomic targets assisted by a low-frequency laser field in the case when this field is still much weaker than the typical internal fields in the target. Concentrating on target transitions we show that they can be substantially affected by the presence of the laser field. This may occur either via strong modifications in the motion of the relativistic electrons caused by the electron-laser interaction or via the Compton effect when the incident electrons convert laser photon(s) into photons with frequencies equal to target transition frequencies. PACS numbers: 34.10+x, 34.50.Rk, 34.80.Qb The theoretical studies of electron-atom collisions in the presence of an intense laser field have already quite a long history. Starting with the sixties, the different aspects of scattering of a non-relativistic electron moving in a laser field on an external potential had been considered in numerous papers, later on these studies were extended to field-assisted inelastic electron-atom collisions in which atomic internal degrees of freedom are excited (for a review see [1]). More recently much attention has been paid to processes involving relativistic electrons in strong laser fields (for a recent review see [2]) including field-assisted collisions between relativistic electrons and atomic targets (see [3]-[4] and references therein). To our knowledge, however, in all the studies of such collisions the target was regarded merely as a source of an external potential acting on the electrons whose internal structure is not influenced by the collision process. In this communication we report first theoretical results for field-assisted collisions of relativistic electrons with atomic (ionic) targets which explicitly take into account the internal degrees of freedom of the target. Inelastic laser-field-free collisions of relativistic electrons with atoms have been extensively studied in the past (see for a review [5]). The addition of a laser field into such collisions could substantially modify the states of the electron and/or the atom that in general may lead to various effects. For instance, if the laser field is strong enough it can, even without any collision, cause ionization of an atomic target. In what follows, however, we shall focus on a different situation. Namely, one can choose the parameters of the laser field in such a way that the field per se does not affect the target directly but can very effectively interact with the incident electrons. Then, solely via this interaction, the field may modify inelastic target cross sections compared to the case of the field-free collisions. Atomic units are used throughout unless otherwise stated. Let at the remote past (t → −∞) and future (t → +∞), when the interactions between the projectileelectron and the atomic target and the laser field are supposed not to occur, the states of this electron are given, respectively, by

Single ionization of helium by 102 eV electron impact: three-dimensional images for electron emission

Single ionization of helium by 102 eV electron impact has been studied by measuring the momentum vectors of all final-state particles, i.e., two electrons and the He + ion, with an advanced reaction microscope. Fully differential cross sections for asymmetric scattering geometry, which have been normalized to an absolute scale, have been obtained covering a large range of emission angles for the emitted low-energy (E ≤ 15 eV) electron and different scattering angles for the fast electron. Strong electron emission out of the projectile scattering plane is confirmed for electron impact, as was observed before for heavy-ion impact ionization. The data are compared with theoretical predictions from a three-Coulomb wavefunction model, first-order and second-order distorted-wave approaches, as well as a convergent close-coupling calculation.

Resonantly enhanced photoionization in correlated three-atomic systems

Modifications of photoionization arising from resonant electron–electron correlations between neighbouring atoms in an atomic sample are studied. The sample contains atomic species A and B, with the ionization potential of A being smaller than the energy of a dipole-allowed transition in B. The atoms are subject to an external radiation field which is near resonant with the dipole transition in B. Photoionization of an atom A may thus proceed via a two-step mechanism: photoexcitation in the subsystem of species B, followed by interatomic Coulombic decay. As a basic atomic configuration, we investigate resonant photoionization in a three-atomic system A–B–B consisting of an atom A and two neighbouring atoms B. It is found that, under suitable conditions, the presence of neighbouring atoms can strongly affect the photoionization process, including its total probability, time development and photoelectron spectra. In particular, comparing our results with those for photoionization of an isolated atom A and a two-atomic system A–B, respectively, we reveal the characteristic impact made by the third atom.

Tuning the internuclear distance in ionization of H2

The dependence of triply differential cross sections on the internuclear distance R is explored for ionization of molecular hydrogen by 200 eV electrons for two distinct values R = 1.1 and 1.4 au in comparison with helium as an isoelectronic system with a single nucleus (R = 0). A clear and systematic trend is observed with an increasing recoil-peak contribution with decreasing R. BBK-type model calculations indicate that the inclusion of the passive electron in the target wavefunction is the key ingredient for explaining the data rather than the two-centre character of the system.

Charge states and effective loss cross sections for 33 TeV lead ions penetrating aluminum and gold foils

We consider the penetration of incident 33 TeV Pb81+(1s) and Pb82+ ions through thin foils of aluminium and gold. We show that, due to the relativistic time dilatation, collision-induced excitations of the hydrogen-like lead ions inside the foils very substantially affect the projectile-electron loss process. Because of this the procedure of extracting loss cross sections from measured data on the fraction of hydrogen-like ions, which works quite well for modest relativistic impact energies, becomes questionable and, in particular, makes it impossible to extract accurate information about these sections from an experiment (Krause et al 1998 Phys. Rev. Lett. 80 1190) in which the penetration of 33 TeV Pb81+(1s) and Pb82+ ions through foils was investigated.

On the Higher-Order Effects in Target Single Ionization by Bare Ions in the Perturbative Regime

We consider hydrogen and helium ionization with emission of soft electrons in high-velocity collisions with bare ions in the perturbative regime |Zp|/vp 0.1, where Zp is the projectile charge and vp the collision velocity. For such collisions it is usually assumed that the first-order approximation in the projectile–target interaction yields good results for single ionization. However, by performing calculations in the first and second Born, Glauber and CDW–EIS approximations, we show that higher-order effects can considerably influence electron emission already in the collision plane where the main part of the emission occurs. Moreover, the deviations from the first-order results become even stronger if the electron emission is analysed in the plane perpendicular to the momentum transfer. In this plane a pronounced structure appears in the fully differential cross section. This structure is different for collisions with Zp > 0 and Zp < 0 and the difference remains noticeable even for collisions with protons and anti-protons moving at velocities approaching the speed of light. It is also found that, on average, the higher-order effects are relatively more important for collisions with negatively charged projectiles. The deviations from first-order results for emission from hydrogen in the perturbative regime are attributed mainly to the projectile interaction with the hydrogen nucleus. In case of helium single ionization, our calculations suggest that a proper description of electron emission in the perpendicular plane may be very demanding with respect to the quality of the approximations for the initial and final helium states.

Relativistic time dilation and the spectrum of electrons emitted by 33-TeV lead ions penetrating thin foils

We study the energy distribution of ultrarelativistic electrons produced when a beam of 33 TeV Pb(1s) ions penetrates a thin Al foil. We show that, because of a prominent role of the excitations of the ions inside the foil which becomes possible due to the relativistic time dilatation, the width of this distribution can be much narrower compared to the case when the ions interact with rarefied gaseous targets. We also show that a very similar shape of the energy distribution may arise when 33 TeV Pb ions penetrate a thin Au foil. These results shed some light on the origin of the very narrow electron energy distributions observed experimentally about a decade ago. PACS numbers: 34.10+x, 34.50.Fa Atomic physics normally does not deal with objects exposed to extreme conditions. One of the interesting and important exceptions of this rule is represented by the studies of various phenomena accompanying the penetration of targets by highly charged projectile ions moving with velocities very close to the speed of light. During the interaction between the ion and a target atom both of these particles are exposed to extremely intense and extraordinarily short pulses of the electromagnetic fields. For instance, in collisions of 33 TeV hydrogen-like Pb(1s) ions with Al (which will be considered below) the typical durations of the electromagnetic pulses acting on the electron bound in the ion are < ∼ 10 sec (in the rest frame of the ion). The peak pulse intensities in this frame can reach ∼ 10-10 W/cm which enables, despite the very short interaction time, to induce transitions of the very tightly bound electron of the ion with a noticeable probability [1]. First experimental results on the total cross section for the electron loss from 33 TeV Pb(1s) were reported in [2] together with data for the electron capture by 33 TeV bare Pb ions [3]. Compared to the study of the total cross sections much more information can be obtained when differential cross sections are explored. The first experimental results on the differential cross sections for such collisions were reported in [4]. In that experiment the incident beams of 33 TeV Pb(1s) and 33 TeV Pb were penetrating Al and Au foils, respectively. In both cases it was found that the penetration is accompanied by the emission of ultrarelativistic electrons whose energy distributions have the form of a cusp with a maximum at an energy corresponding to the electrons moving in the laboratory frame with velocities equal to that of the ions. One of unexpected results reported in [4] was that the measured distribution of the high-energy electrons produced under the bombardment of a thin Al foil was found to be much narrower than one could expect based on the consideration of the width of the Compton profile of the electron state in the incident Pb(1s) ions [4]. Moreover, in a more rigorous calculation performed in [5] for the energy spectrum of electrons emitted from a 33 TeV Pb(1s) ion colliding with an Al atom it was confirmed that such a spectrum is indeed much broader than that observed in the experiment [4]. Another intriguing finding of [4] was that for 33 TeV Pb ions incident on a thin Au foil the shape of the measured energy distributions of high-energy electrons emerged from the foil was very similar to that obtained for the beam of 33 TeV Pb(1s) ions incident on the Al foil. It is known that the total and differential loss cross sections depend on a bound state from which the electron leaves the ion (see e.g. [6], [7] and references therein). Therefore, it was speculated in [4] that in the case of the incident 33 TeV Pb ions the very narrow shape of the electron cusp might be a signature of the electron capture into excited states. However, for the Pb(1s) ions incident on the Al foil the possible influence of excited states of these ions on the electron cusp was not considered seriously because of the common experience that excitations of very heavy hydrogen-like ions inside thin foils of relatively light elements do not have a noticeable impact on the electron loss process. For instance, in the recent experimental-theoretical study [8] on 200 MeV/u Ni(1s) ions incident on gaseous and solid targets it was found that the fraction of the ions excited inside the solids does not exceed 5-6%. Moreover, even such rather modest values seem to be hardly reachable for very heavy hydrogen-like ions since, compared to the case of relatively light ions, the penetration of matter by the very heavy ions possesses the following two important differences. First, because of a very tight binding of the electron in such ions cross sections for collision-induced electron transitions are much smaller. Therefore, for highly charged ions, like Pb, moving inside solids the mean free path with respect to the collision-induced transitions will be much larger. Second, the lifetimes of the excited states with respect to the spontaneous radiative decay in such ions are much shorter. The above two points mean that there will be much

Young-type interference in projectile-electron loss in energetic ion-molecule collisions.

Under certain conditions an electron bound in a fast projectile-ion, colliding with a molecule, interacts mainly with the nuclei and inner shell electrons of atoms forming the molecule. Due to their compact localization in space and distinct separation from each other these molecular centers play in such collisions a role similar to that of optical slits in light scattering leading to pronounced interference in the spectra of the electron emitted from the projectile. PACS numbers: PACS:34.10.+x, 34.50.Fa The wave–particle duality, which states that all atomic objects exhibit particle as well as wave properties, is one of the basic concepts of quantum mechanics. Proposed initially by Louis de Broglie [1] in 1923, this concept has been confirmed few years later in the electron diffraction experiments [2, 3]. Since then, a large number of investigations have been performed in order to observe the wave nature of not only electrons but also heavier particles such as, for example, neutrons, atoms, dimers and even fullerenes C60 [4]. Most of these measurements were aimed at a demonstration of Young’s double–slit phenomena, in which the coherent addition of the amplitudes of two (or many) paths, leading to interference, is related to the wave–like particle behavior. In the atomic world the natural analog of the Young’s slits is represented by diatomic molecules. Starting with the works [5]-[6], especially significant interest has been focused on studying interference phenomena involving homo-nuclear molecules [7]-[22]. These studies were dealing with two principally different interference scenarios. In one of them the attention was focused on interference in the spectra of electrons emitted from the molecule in the course of photoionization [6] [13] and consequent Auger decay [14], as well as in ionization by electrons [15] and heavy ions [16]-[18]. Note that in such a scenario, unlike the Young’s experiment, the wave is not diffracted by the ”slits” but rather emerges from them. In the second scenario, which was realized in [19]-[22] for electron capture and proton scattering and is a more direct analog of the Young’s optical experiment, interference is caused by coherent scattering of the incident projectile on the atomic centers of the molecule. In this letter we propose yet another way to collisioninduced interference. It falls into the second scenario but, similarly to [16]-[18], deals with interference in electron emission spectra. It is realized in collisions of molecules with partially stripped multiply-charged projectile-ions, in which the electron(s) of the projectile is emitted. Compared to the electron emission, studied in [16][18], the present case possesses important differences. In particular, in the situation, considered in [16]-[18], the electron wave is launched from the ”slits”, which are not really separated and well localized since the electrons of molecules like H2 occupy the whole volume of the molecule and are mainly located not on the atomic nuclei but rather between them. As a result, the corresponding interference pattern is rather smooth. In contrast, as will be shown below, the emission from the projectile occurs due to a coherent scattering of the electron of the projectile on the nuclei of the molecule (partially screened by the inner shell electrons) and, therefore, the ”slits” are very well separated and localized in space that can lead to very pronounced interference effects in the emission pattern. Below, based on the relativistic time–dependent perturbation approach, we shall derive the cross section for electron loss in collisions with homo-nuclear dimers. The possibility of interference effects will be demonstrated by calculating the cross section for fast hydrogen–like magnesium Mg(1s) and S(1s) ions colliding with N2 dimers. Atomic units are used throughout except where otherwise stated. Since the collision between an ion carrying an electron and a molecule in general represents a very complex many-body problem, our consideration will be based on a simplified model which, however, takes into account all essential physics of the collision process in question. Within this model, in order to describe electron transitions in the projectile we shall use the first order perturbation theory in the interaction between this electron and the molecule. Such an approximation is a good one, provided Zp > ∼ ZA, where Zp and ZA are, respec-

Two-center dielectronic recombination and resonant photoionization

We consider radiative recombination and photoionization in an atomic system, which consists of two subsystems A and B. These subsystems are well separated in space and it is supposed that A has a lower ionization potential. In such a case photoionization of A and recombination of an incident electron with A{sup +} can be strongly influenced, via two-center electron-electron correlations, by resonant electron dipole transitions induced in B. A theoretical description of these two-center resonant dielectronic processes is presented.