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Many-electron phenomena in the ionization of ions
Nuclear Instruments and Methods in Physics Research B 233 (2005) 141–150 www.elsevier.com/locate/nimb
Many-electron phenomena in the ionization of ions A. Mu¨ller
*
Institut fu¨r Atom- und Moleku¨lphysik, Justus-Liebig-Universita¨t Giessen, 35392 Giessen, Germany Available online 26 April 2005
Abstract This brief review of many-electron phenomena in the single and multiple ionization of ions tries to elucidate connections between ion–atom collisions and interactions of single free electrons and photons with neutral or charged atomic species. With the capability of using multiply charged ions in collisions with charged particles or photons, conventional studies on neutral targets can be extended to a new dimension: the target charge state. This is especially interesting for studies of selected effects along specific isoelectronic sequences, i.e. of n-electron atoms with variable nuclear charge. The necessary colliding-beams and merged-beams techniques are technically demanding but can provide access, for example, to electron correlation effects in collisions under the influence of increasingly strong electron–nucleus interactions. 2005 Published by Elsevier B.V. PACS: 34.80.Kw; 52.20.Fs; 33.20.Ni; 33.80.b; 36.40.Gk; 61.48.+c Keywords: Single ionization; Multiple ionization; Electron impact; Photoabsorption; Ion targets; Indirect processes; Many-electron transitions
1. Introduction For probing the structure and the dynamics of microscopic systems at the atomic or subatomic level, scattering experiments with energetic particles or photons are the generally accepted method of choice. Collisions involving molecular species
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Tel.: +49 641 99 15200; fax: +49 641 99 15009. E-mail address: [email protected] URL: http://www.strz.uni-giessen.de/k3/
0168-583X/$ - see front matter 2005 Published by Elsevier B.V. doi:10.1016/j.nimb.2005.03.096
for studying chemical reactions would typically require thermal energies of the collision partners while investigating the structure of nucleons requires the highest-energy accelerators presently available. The generic scattering scenario for binary collisions is sketched in Fig. 1. Particles A and B in given quantum mechanical states characterized by all their quantum numbers enter the interaction region with momenta ~ pA and ~ pB . From the interaction region, which is characterized by the black box, secondary particles emerge, for example C, D, and E, with their associated
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A pA
E pE
A
D pD
B pB
C pC
B
Fig. 1. Generic scattering scheme of collisions A + B ! C + D + E with the particles in states each characterized by a complete set of quantum numbers and by the particleÕs linear momentum.
momenta and quantum numbers. In kinematically complete experiments the momenta of the different outgoing particles are determined while it is often not possible to also identify all the quantum numbers. In ionizing ion–atom collisions frequently only the final state of the projectile, e.g. characterized by the emerging particle C, is observed, thus leaving ambiguity of what has really happened in the collision. In the theoretical treatment the time dependent Schro¨dinger equation has to be propagated in the box, and is projected afterwards to obtain observable quantities. For numerical calculations the black box may be represented by a grid composed of small volume elements that cover the interaction region. Single and multiple ionization processes in ion– atom collisions involve a multitude of complex interactions between the electrons and the nuclei of projectile and target. If we imagine just a collision of a one-electron atom (or ion) with a two-electron atom (or ion) there are already 10 different electromagnetic pair interactions to be considered (see Fig. 2). In an experiment that observes ionization of A, i.e. in the example of Fig. 2 the removal of the electron from A, there are several possible classes of processes and associated final states. The electron of A can be released to the continuum or it can be captured by particle B. At the same time, the two-electron atom B can loose one or both of its electrons to the continuum. A full theoretical treatment of this (still quite simple) example with all its electron-electron, electron–nucleus and nucleus-nucleus interactions is not possible. Approximations are required to make the problem tractable.
Fig. 2. Pair interactions and electron pathways to be considered in ionization processes where a one-electron atom A is ionized in a collision with a two-electron atom B.
Some of the complexity is avoided in studies of fast collisions when the impulse approximation can be applied and the electrons can be described as independent quasi-free particles with a known momentum distribution. Under such conditions investigations of electron–ion collision phenomena become possible. The resulting simplification of interpreting experiments has been exploited very successfully by a number of groups (e.g. [1,2] and references therein). For the detailed investigation of ionization mechanisms that can occur in fast ion–atom collisions, it is illuminating to consider collisions of ions (or atoms) with really free electrons or completely stripped nuclei. For that purpose, electron–ion and ion–ion experiments with well prepared beams of free particles provide favorable conditions. The resulting requirement of employing colliding-beams techniques is associated with low densities of the interacting particles and hence often poses problems with low signal and high background rates. The scheme shown in Fig. 1 can alternatively represent the principle arrangement of a crossed-beams experiment where beams of particle species A and B meet in the interaction region and the outgoing particles have to be analyzed. Different from the previous quantummechanical meaning, the black box plotted in Fig. 1 is now interpreted as a classical macroscopic interaction volume. The experimentalist has to enter this crossing region with his instrumentation and determine the overlap of the two intersecting
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beams. Besides the disadvantage of low beam densities these experiments provide unique access to absolute cross sections, a feature that is not generally available for investigating collisions of neutral species. An example is the measurement of absolute cross sections for ionization and fragmentation of fullerenes. Vapor densities of neutral complex molecules cannot easily be determined and therefore, measured cross sections for such species are only relative in most cases. With charged particles, however, and suitable assessment of beam overlaps and detector efficiencies, absolute cross sections can be obtained in interacting-beams experiments. Another advantage of such measurements is in the principle accessibility of very narrow collision energy distributions. Especially in electron–ion collision studies the resulting high energy resolution provides quantitative access to and characterization of individual, possibly even state-selective, reaction pathways. Even in the ‘‘simple’’ electron–ion and nucleus– ion collision systems (simple compared with the initial ion–atom problem) single and multiple ionization still involve a multitude of complex mechanisms. Besides the direct removal of one or several electrons from the target, resonant and non-resonant formation of intermediate multiply excited states which subsequently decay by electron emission is important in electron-impact single and multiple ionization of ions and atoms. The following sections will briefly illustrate the increasing complexity of charged-particle collisions with the number of electrons in the target atom (or ion).
2. Direct ionization Direct ionization proceeds via one-step or multi-step knock-off mechanisms which can partly be disentangled by studying effects of different projectile species. As a first step, the situation for ionization of hydrogenlike targets by structureless projectiles will be briefly reviewed. 2.1. Direct single ionization Naturally, direct ionization of a hydrogenlike atom T with atomic number ZT by a structureless
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projectile P with charge ZP can only be single ionization, i.e. promotion of the one and only available electron to the continuum by a knock-off process PZ P þ þ TðZ T 1Þþ ! PZ P þ þ TZ T þ þ e.
ð1Þ
This process has first been treated theoretically by Thomson [3] for projectile electrons and hydrogen target atoms. In that basic approach, the impact-parameter dependent energy transfer DE to the target electron is calculated assuming classical Coulomb scattering of the projectile from a quasifree electron initially at rest. The presence of the target nucleus is essentially neglected and only the binding energy I of the target electron is considered. For all impact parameters where DE P I the ionization probability is 1 and in all other cases it is 0. Thus, the total ionization cross section can be determined. One can extend this concept to arbitrary structureless charged projectiles and arbitrary hydrogenlike systems as described by Eq. (1). For the laboratory situation (non-relativistic treatment), we find the energy transfer DE to the target electron in relation to the impact parameter b (see e.g. [4] p. 423) " # 2 2 2 4 Z Z e m 1 ðm þ m Þ P P e b2 ¼ P T 2 . ð2Þ 4mP me E2 ð4p0 Þ me EDE Here, e is the charge of an electron, 0 the electric constant, mP the projectile mass, me the mass of the electron, and E the laboratory energy of the projectile assuming that the target particle T is at rest. From this equation and the concept introduced by Thomson, the cross section for all ionization processes described by Eq. (1) can be derived " # 2 pZ 2P e4 mP 1 ðmP þ me Þ 1 r¼ . ð3Þ 4mP me E2 ð4p0 Þ2 me EI The simple classical treatment outlined above can only provide qualitative results but has been developed to an extremely successfull tool helping to understand multi-electron processes in atomic collisions [5]. Already from the simple result represented by Eq. (3) one can draw important conclusions on the scaling behaviour of single ionization processes. At sufficiently high energies E the
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second term in the square brackets can be neglected. Then the scaled ionization cross section R ¼ rI 2 =Z 2P is a universal function of the scaled energy u = Eme/(ImP), i.e. for any combination of a projectile such as e, p, He2+, . . . and a target such as H, He+, Li2+, . . . identical functions R(u) have to be expected for large values of u. If the projectile is kept fixed, then the scaling should even be valid for the whole range of non-relativistic projectile energies. In particular, scaled cross sections R(u) for electron-impact ionization of hydrogenlike targets should be identical for each ZT. There is a limited number of experimental results for projectile–target combinations in ionization processes as described by Eq. (1). Consistent data sets are available for ionization of H by e, p, and He2+ [6,7] as well as for electron-impact ionization of He+ [8], Li2+ [9], B4+, C5+, N6+, O7+ [10] and some scattered results are even available up to U91+ [11,12], where, however, relativistic effects have to be considered that go well beyond the classical formula Eq. (3). Measuring direct ionization in ion–ion collisions is very difficult. The only data available over an extended energy range are on the p + He+ system [13–15]. The experimental cross sections of three separate experiments differ from one another and have large uncertainties precluding a convincing comparison on the basis of Eq. (3). The predicted scaling behaviour is investigated in Fig. 3 where scaled cross sections are shown for the ionization of hydrogen by electrons, protons and a-particles, and for the ionization of He+ and B4+ by electrons. While the original projectile energies cover ranges between approximately 10 eV and 2 MeV and the original cross section maxima span a range from about 1019 cm2 to 4 · 1016 cm2, the maxima of the scaled cross sections show little difference for different projectile-target combinations. This is especially true for all available data on electronimpact ionization of H-like ions with 3 6 ZT 6 26 out of which only the measurement on B4+ is shown in Fig. 3 to avoid an overcrowded display of data points. All of the scaled cross section functions for that range of ZT fall on top of the B4+ data within their error bars. The maximum of the original cross section for Fe25+ is even as low as 1022 cm2 [11] and yet, the classical scaling fully
Fig. 3. Scaled cross sections R for ionization of hydrogen atoms and hydrogenlike ions by structureless charged projectiles as a function of scaled projectile energy u. The data are from work of Shah et al., Peart et al. and Aichele et al. (see text).
accounts for the differences. It has to be mentioned, though, that the classical cross sections obtained from Eq. (3) only qualitatively agree with the measurements. In particular, the high-energy behaviour of the calculated cross section misses the ln(E) term that is found in quantum mechanical treatments and already shows up in first order perturbation theory. The simple scaling found for single ionization of hydrogenlike systems can easily be extended to many-electron atoms and ions. Then, however, only direct knock-off processes can be accounted for, whereas complex indirect ionization phenomena require much more sophisticated theoretical treatment. In the direct contributions to the total single ionization cross section one just has to distinguish between the different subshells of the target atom with their specific ionization potentials. The number of (equivalent) electrons in each subshell linearly enhances the cross section calculated for the one-electron case. 2.2. Direct double ionization While direct single ionization appears to be understood quite well on the level of total cross sections the situation becomes very much more
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involved for direct double ionization processes. Accordingly, double ionization of helium has been an object of tremendous efforts in the atomic collisions research of the last two decades. A general scaling behaviour describing PZ P þ þ TðZ T 2Þþ ! PZ P þ þ TZ T þ þ 2e.
ð4Þ
for any given projectile-target combination over the whole energy range is not readily obtained. Nor can theory provide reliable cross sections for the direct processes described by Eq. (4), not to speak of more complex projectiles. Mechanisms that can be responsible for double ionization have been identified early on [16,17]. The incident electron can undergo two sequential ionizing collisions with the two target electrons, a process that has been termed TS2 (two-step 2) in the literature (for a review see [18]). Alternatively TS1 (two-step 1) describes a mechanism where the projectile knocks off a target electron which, on its way out, ionizes the second target electron. Both processes have been treated theoretically by Gryzin´ski on the basis of classical Coulomb scattering [16]. More realistic quantum mechanical treatments followed later (see [18]). The third mechanism results from the sudden change of charge when an electron is removed from the He atom. By the resulting change of screening the second electron may be shaken off to the continuum [17]. The SO (shake off) mechanism is also considered to be the main contribution in particle-impact double ionization at the limit of high velocities and low projectile charge states ([19] and references therein). An empirical scaling for double ionization by heavy-particles Aq+ colliding with He atoms is shown in Fig. 4. Cross section ratios R = r++/r+ obtained in numerous different experiments are plotted as a function of vP/q where vP is the projectile velocity and q the projectile charge state. The background behind this plot is the prediction of a (q/vP)2 dependence of R at low and intermediate projectile velocities [20] and the convergence of R to the shake-off limit at high velocities. On a logarithmic scale the predicted scaling behaviour becomes visible also, of course, when R is plotted against vP/q. The present plot follows the style that has been previously used in the literature by many other authors. The data cover a very wide range of
Fig. 4. Ratios r++/r+ of experimental cross sections for direct double and direct single ionization of He atoms. Data from different experiments are plotted as a function of vP/q where vP is the projectile velocity and q the projectile charge state. The data were adopted from [21–23]. They are not meant to cover every single published result on ion impact double ionization of helium. Ion species investigated are indicated in the figure.
ion charge states from q = 1 to q = 90 and ion energies between about 50 keV and 100 GeV. Considering the different electronic structures of the projectiles as well as the vastly different charge states and velocities, the cross section ratios line up remarkably well with one another. As already shown for single ionization, also double ionization studies can be extended to charged target particles following along the lines of Eq. (4). There are published data for the twoelectron targets H [24], He [25–29], and Li+ [30]. More results e.g. for He-like boron and carbon are becoming available in the near future [31]. All available cross sections r++ for electronimpact direct double ionization of two-electron targets can be scaled in a satisfactory manner by 2.6 plotting the product r++I th as a function of E=I th (see Fig. 5) where E is the electron energy and I th the combined binding energy of both electrons in the target, i.e. the threshold energy for the double ionization process. The scaling differs from a recent suggestion by Shevelko et al. [32] that uses a I 3 th dependence of double ionization cross sections for a wide range of light ions. In the present
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Fig. 5. Scaled cross sections r++I 2th.6 for electron-impact direct double ionization of He-like atoms (and ions) as a function of E=I th where I th is the threshold energy. The solid line is based on a rescaled version of a semi-empirical formula suggested by Shevelko et al. [32]. The data are from experiments by Yu et al, Schram et al., Gaudin and Hagemann, Nagy et al., Stephan et al. and Shah et al. (see text). 2.6 context, the I th scaling was found to give a better fit of the available data for two-electron targets.
zation channels. The simplest possible system for the observation of effects of intermediate excited states in an experiment is a metastable He-like parent ion in a 1s2s configuration. By exciting the 1s electron to the L- or M-shell a doubly excited state is formed that can eject an electron and thus finally bring the ion into its final H-like state. The K-shell can also be excited in a resonant manner, i.e. the incident electron is captured by a dielectronic process and the intermediate triply excited state can eject two electrons either sequentially or simultaneously. In both processes the intermediate product of the excitation is a hollow state with no electrons in the K-shell. First results have been obtained with metastable B3+ and C4+ ions [33]. R-matrix calculations can reproduce several of the main features of the measured cross sections, however, further theoretical work will be necessary to come to a conclusive and convincing result. Indirect processes can also occur in electron-impact ionization of He-like ions with both electrons in the K-shell. The results of a previous measurement [34] and a more recent R-matrix calculation [35] are shown in Fig. 6. From the measured total
3. Indirect ionization processes Besides direct knock-off ionization of an atom or ion that has at least two electrons, the production of intermediate highly excited states that can decay by electron emission provides intricate additional pathways towards the final release of one or more electrons from the target. Intermediate states with sufficient excitation energy can be formed by production of one or more vacancies in inner shells. The resulting product can possibly undergo cascades of Auger-processes and thus the final result of the initial interaction is a net single or multiple ionization of the parent target atom or ion. The final charge state depends on the specific case of the collision and the electronic states involved. 3.1. Indirect single ionization No more than two bound electrons in the initial target state are necessary to open up indirect ioni-
Fig. 6. Measured and calculated cross sections for indirect ionization of Li+ [35]. The contribution of direct ionization has been subtracted with the idea to obtain the isolated cross section for indirect ionization (see text). The window resonances are due to simultaneous excitation of both K-shell electrons and subsequent simultaneous ejection of two electrons.
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single ionization cross section a smooth curve representing direct single ionization was subtracted to obtain indirect ionization contributions. Apparently, the cross section difference is negative at some energies, indicating that direct and indirect ionization channels destructively interfere and the additional channel leads to a reduction of the cross section. Again, all the processes involved in indirect ionization produce intermediate hollow states of the Li+ ion or the Li atom. 3.2. Indirect multiple ionization When the number of electrons bound in the target atom is increased to 3 or beyond, indirect contributions to multiple ionization become possible. In the ionization of a Li-like system, one of the K-shell electrons may be excited while the other one is released to the continuum. Again, a doubly excited intermediate state is formed which ends up in a final charge state with two electrons removed. Contributions of this type to the total net double ionization have to be expected to be small because two tightly bound electrons have to be moved at a time (which is possible, as the previous sections of this paper have demonstrated). Usually, double ionization shows substantial contributions from single ionization of an innershell of the target atom or ion. If an inner-shell electron is released to the continuum the resulting ion can undergo an Auger-process and thus the final result of the process is a net double ionization. Such processes become possible with four or more target electrons. Triple ionization of berylliumlike ions with configurations 1s22s2 can proceed via direct removal of two L-shell electrons plus one K-shell electron, for example by electron impact e + (1s22s2) ! (1s) + 4e. The cross section is small due to the required interaction of 4 electrons. An alternative route from 1s22s2 to 1s is double-Kshell ionization with subsequent autoionization: e þ ð1s2 2s2 Þ ! ð2s2 Þ þ 3e ! ð1sÞ þ e þ 3e.
ð5Þ
In this scheme an intermediate hollow 2s2 ion is formed which subsequently decays by an Auger process. Since the indirect process involves double rather than triple ionization it can be expected to
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have a larger cross section than the direct process (Eq. (5)). The decay of the intermediate state proceeds with a branching ratio of almost 100% which guarantees the final triple-ionization step. The initial double ionization removes a pair of tightly bound but correlated electrons and thus it is of a nature similar to the well studied double ionization of He atoms. If this concept is valid, the cross section for indirect triple ionization of a berylliumlike ion by electron impact should scale in the same manner as that for processes described by Eq. (4). Indeed, measurements for B+ and C2+ [36] in the threshold region for double K-shell ionization perfectly follow the scaling displayed in Fig. 5. More complex mechanisms with cascades of radiative and Auger decays are also possible and can produce signal in multiple-ionization channels. This was demonstrated in a comprehensive study on electron-impact single and multiple ionization of Baq+ ions in charge states from q = 1 to q = 13 [37]. e þ Baqþ ! BaðqþnÞþ þ ðn þ 1Þe.
ð6Þ
Depending on the charge state q of the parent ion the number n of electrons removed in a single collision ranged from n = 1 up to n = 7. Absolute cross sections were measured in the energy range where the 3d-subshell can be opened. This range changes with the parent ion charge state and is covered by collision energies in the experiment between 600 eV and 1050 eV. As one example for the measurements, the experimental cross sections for n-fold ionization of Ba4+ ions are shown in Fig. 7 with n ranging from 1 to 6. At energies between 750 eV and 770 eV a pair of peaks is found in each cross section, apparently due to resonant capture of the incident electron by the Ba4+ parent ion. The resonance energy and the double-peak nature indicate the involvement of a 3d electron in the collision leaving a deep-core 2D vacancy behind in an intermediate short-lived Ba3+ ion which subsequently decays by the emission of (n + 1), i.e. up to 7 electrons. In the cross section for single ionization the resonances are hardly visible on top of the strong non-resonant ionization. By subtracting a smooth curve from the measured cross section, however, the resonance contributions can be extracted.
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[39]. Other rare-earth elements show similar effects [40]. 3.3. Photoionization
Fig. 7. Measured cross sections for n-fold ionization of Ba4+ ions (n = 1,2, . . . , 6) [38].
On an absolute scale the strongest peak features are found for net double and triple ionization. On a relative scale, however, in comparison with the non-resonant ‘‘background’’ the resonances are strongest in 6-fold ionization. Here, 7 electrons are ejected from the deep-core excited intermediate Ba3+ ion whose excitation energy barely exceeds the threshold for 6-fold ionization. Therefore the phase space for 6-fold ionization is greatly reduced and the cross section for non-resonant processes becomes small. As a consequence the resonance contributions near the threshold of 6-fold ionization dominate the related cross section. Observations like the ones described here for Ba4+ have been made for all investigated Baq+ ions. The ions Ba1+ and Ba2+ had already previously been studied, though in a much narrower energy range
The role of multiply excited states in ionization processes can be experimentally studied in great detail by a further reduction of the initial ion– atom problem. In the previous sections the target atom was essentially decomposed into its constituents, electrons and fully stripped nuclei, and interactions of the free structureless charged particles with the projectile ion were investigated in detail. Indirect processes involving multiply excited intermediate states are found to be important and can be made visible by spectroscopy-type measurements with low energy-spread electrons by looking for structures in the total partial cross sections. Fig. 6 shows one of the most striking examples for the capability of crossed-beams energy-scanning techniques. Similar multiply excited states of atoms and ions can be selectively populated by photon interactions making use of the potential for extreme energy resolution available at modern synchrotron radiation sources [41,42]. Accordingly, many-electron phenomena can also be observed in photoionization studies. Recent photoionization and photofragmentation measurements with singly and multiply charged fullerene ions have provided quantitative information on the excitation and the decay of collective resonances. A large fraction of the delocalized electrons oscillate as a whole relative to the ionic background of the fullerene cage. Giant resonance features have been observed in various decay channels leading to ionization and fragmentation of parent neutral fullerenes [43–46] and also of parent fullerene ions in different charge states [47]. The dominant collective resonance phenomena observed in the photoionization experiments have recently been identified as the result of surface- and volume-plasmon excitations [47]. 3.4. Summary Ionization of atoms and ions has been discussed in the light of classical Coulomb interaction
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between charged particles. Many-electron effects occur both in single and multiple ionization. The most obvious multi-electron processes are those of direct multiple ionization. Scaling behaviour of direct double ionization is documented for many different ionic projectiles colliding with helium atoms and for electron-impact on different heliumlike atoms and ions. Direct single ionization by an electron requires an interaction between just two electrons. More than two electrons may be involved in a single-ionization process both in the formation and in the decay of intermediate multiply excited states which contribute to ionization by electron ejection processes. Clear evidence has been found for resonant excitation of two K-shell electrons in He-like Li+ which requires the interaction of all three electrons in the system. Some of the excited states can only contribute to net single ionization if two electrons are ejected in a doubleAuger process while simultaneously the third electron falls down to a more tightly bound state. With the number of target electrons the possibilities for many-electron effects vastly increase. Triple ionization after direct double-K-shell ionization has been observed in Be-like ions. Even direct 7fold ionization was observed in electron-impact measurements on multiply charged barium ions. The ultimate many-electron effect was studied in photoionization experiments with fullerene ions, where the incoming photon is absorbed and by that excites collective oscillations of delocalized electrons against the positive charge of the carbon cage. The plasmon states are extremely short lived and can decay via fragmentation and ionization channels.
Acknowledgement The author thanks all his coworkers and collaborators who have contributed to the instrumentation and the research program behind the physics reviewed in this paper. In particular, the ionization measurements and the understanding of the results reported here, have been made possible by the work of W. Arnold, C. Becker, C. Bo¨hme, A. Frank, K. Huber, J. Jacobi, H. Knopp, R.A. Phaneuf, S. Ricz, V.P. Shevelko, S. Schippers,
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W. Shi, H. Teng, F. Timphus, and T.v. Zoest. We are grateful for support by Deutsche Forschungsgemeinschaft, Bonn Bad Godesberg, and by Bundesministerium fu¨r Bildung und Forschung, Berlin. References [1] H. Kollmus, R. Moshammer, R.E. Olson, S. Hagmann, M. Schulz, J. Ullrich, Phys. Rev. Lett. 88 (2002) 103202. [2] E.P. Benis, T.J.M. Zouros, T.W. Gorczyca, A.D. Gonza´lez, P. Richard, Phys. Rev. A 69 (2004) 052718. [3] J.J. Thomson, Phil. Mag. 23 (1912) 449. [4] E.W. McDaniel, Atomic Collisions: Electron and Photon Projectiles, John Wiley & Sons, New York, 1989. [5] R.E. Olson, Nucl. Instr. and Meth. B, these Proceedings. doi:10.1016/j.nimb.2005.03.080. [6] M.B. Shah, H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys. 14 (1981) 2361. [7] M.B. Shah, D.S. Elliott, H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys. 20 (1987) 2481, 3501. [8] B. Peart, D.S. Walton, K.T. Dolder, J. Phys. B: At. Mol. Opt. Phys. 2 (1969) 1347. [9] K. Tinschert, A. Mu¨ller, G. Hofmann, K. Huber, E. Salzborn, R. Becker, D.C. Gregory, J. Phys. B: At. Mol. Phys. 22 (1989) 531. [10] K. Aichele, U. Hartenfeller, D. Hathiramani, G. Hofmann, V. Scha¨fer, M. Steidl, M. Stenke, E. Salzborn, T. Pattard, J.M. Rost, J. Phys. B: At. Mol. Opt. Phys. 31 (1998) 2369. [11] B. OÕRourke, F.J. Currell, H. Kuramoto, Y.M. Li, S. Ohtani, X.M. Tong, H. Watanabe, J. Phys. B: At. Mol. Opt. Phys. 34 (2001) 4003. [12] R.E. Marrs, S.R. Elliott, D.A. Knapp, Phys. Rev. Lett. 72 (1994) 4082. [13] B. Peart, K. Rinn, K.T. Dolder, J. Phys. B: At. Mol. Opt. Phys. 16 (1983) 1461. [14] M.F. Watts, K.F. Dunn, H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys. 19 (1986) L355. [15] K. Rinn, F. Melchert, K. Rink, E. Salzborn, J. Phys. B: At. Mol. Opt. Phys. 19 (1986) 3717. [16] M. Gryzin´ski, Phys. Rev. 138 (1965) A336. [17] M.H. Mittleman, Phys. Rev. Lett. 16 (1966) 498. [18] J.H. McGuire, Electron Correlation Dynamics in Atomic Collisions, Cambridge University Press, Cambridge, 1997. [19] R. Do¨rner, H. Schmidt-Bo¨cking, T. Weber, T. Jahnke, M. Scho¨ffler, A. Knapp, M. Hattass, A. Czasch, L.P.H. Schmidt, O. Jagutzki, Rad. Phys. Chem. 70 (2004) 191. [20] J.H. McGuire, Phys. Rev. Lett. 49 (1982) 1153. [21] J.H. McGuire, A. Mu¨ller, B. Schuch, W. Groh, E. Salzborn, Phys. Rev. A 35 (1987) 2479. [22] A.S. Schlachter, J.A. Tanis, Phys. Rev. Lett. 73 (1994) 3596. [23] P. Jardin, A. Cassimi, J.P. Grandin, H. Rothard, J.P. Lemoigne, D. Hennecart, X. Husson, A. Lepoutre, Nucl. Instr. and Meth. B 98 (1995) 363.
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[24] D.J. Yu, S. Rachafi, J. Jureta, P. Defrance, J. Phys. B: At. Mol. Opt. Phys. 25 (1992) 4593. [25] B.L. Schram, A.J.H. Boerboom, J. Kistemaker, Physica 32 (1966) 185. [26] A. Gaudin, R. Hagemann, J. Chim. Phys. 64 (1967) 1209. [27] P. Nagy, A. Skutlartz, V. Schmidt, J. Phys. B: At. Mol. Opt. Phys. 13 (1980) 1249. [28] K. Stephan, H. Helm, T.D. Ma¨rk, J. Chem. Phys. 73 (1980) 3763. [29] M.B. Shah, D.S. Elliott, P. McCallion, H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys. 21 (1988) 2751. [30] B. Peart, K.T. Dolder, J. Phys. B: At. Mol. Opt. Phys. 2 (1969) 1169. [31] A. Mu¨ller, C. Bo¨hme, J. Jacobi, H. Knopp, K. Ariki, S. Schippers, in: S. Datz et al. (Eds.), XXII International Conference on Photonic, Electronic and Atomic Collisions, Santa Fe, New Mexico, USA, Abstracts of Contributed Papers, Rinton Press, Princeton, New Jersey, USA, 2001, p. 321. [32] V.P. Shevelko, H. Tawara, F. Scheuermann, B. Fabian, A. Mu¨ller, E. Salzborn, J. Phys. B 38 (2005) 525. [33] H. Knopp, J. Jacobi, S. Schippers, A. Mu¨ller, in: J. Anton, H. Cederquist, M. Larsson, E. Lindroth, S. Mannervik, H. Schmidt, R. Schuch (Eds.), XXIII International Conference on Photonic, Electronic and Atomic Collisions, Stockholm, Sweden, Abstracts of Contributed Papers, Stockholm University, 2003, Fr083. [34] A. Mu¨ller, G. Hofmann, B. Weißbecker, M. Stenke, K. Tinschert, M. Wagner, E. Salzborn, Phys. Rev. Lett. 63 (1989) 758. [35] H. Teng, J. Phys. B: At. Mol. Opt. Phys. 33 (2000) L227. [36] J. Jacobi, H. Knopp, S. Schippers, A. Mu¨ller, in: J. Anton, H. Cederquist, M. Larsson, E. Lindroth, S. Mannervik, H. Schmidt, R. Schuch (Eds.), XXIII International Conference on Photonic, Electronic and Atomic Collisions, Stockholm, Sweden, Abstracts of Contributed Papers, Stockholm University, 2003, Fr086.
[37] H. Knopp, C. Bo¨hme, J. Jacobi, S. Ricz, S. Schippers, A. Mu¨ller, Nucl. Instr. and Meth. B 205 (2003) 433. [38] H. Knopp, C. Bo¨hme, J. Jacobi, S. Ricz, S. Schippers, A. Mu¨ller, in: S. Datz et al. (Eds.), XXII International Conference on Photonic, Electronic and Atomic Collisions, Santa Fe, New Mexico, USA, Abstracts of Contributed Papers, Rinton Press, Princeton, New Jersey, USA, 2001, p. 318. [39] G. Hofmann, A. Mu¨ller, B. Weißbecker, M. Stenke, K. Tinschert, E. Salzborn, Z. Phys. D: At. Mol. Clusters 21 (suppl.) (1991) 189. [40] K. Aichele, D. Hathiramani, F. Scheuermann, A. Mu¨ller, E. Salzborn, D. Mitnik, J. Colgan, M.S. Pindzola, Phys. Rev. Lett. 86 (2001) 620. [41] S. Schippers, A. Mu¨ller, S. Ricz, M.E. Bannister, G.H. Dunn, A.S. Schlachter, G. Hinojosa, C. Cisneros, A. Aguilar, A.M. Covington, M.F. Gharaibeh, R.A. Phaneuf, Phys. Rev. A 67 (2003) 032702. [42] S. Schippers, A. Mu¨ller, R.A. Phaneuf, T. van Zoest, I. Alvarez, C. Cisneros, E.D. Emmons, M.F. Gharaibeh, G. Hinojosa, A.S. Schlachter, S.W.J. Scully, J. Phys. B: At. Mol. Opt. Phys. 37 (2004) L209. [43] I.V. Hertel, H. Steger, J. de Vries, B. Weisser, C. Menzel, B. Kamke, W. Kamke, Phys. Rev. Lett. 68 (1992) 784. [44] J. Kou, T. Mori, M. Ono, Y. Haruyama, Y. Kubozono, K. Mitsuke, Chem. Phys. Lett. 374 (2003) 1. [45] J. Kou, T. Mori, S.V.K. Kumar, Y. Haruyama, Y. Kubozono, K. Mitsuke, J. Chem. Phys. 120 (2004) 6005. [46] A. Reinko¨ster, S. Korica, G. Pru¨mper, J. Viefhaus, K. Godehusen, O. Schwarzkopf, M. Mast, U. Becker, J. Phys. B 37 (2004) 2135. [47] S.W.J. Scully, E.D. Emmons, M.F. Gharaibeh, R.A. Phaneuf, A.L.D. Kilcoyne, A.S. Schlachter, S. Schippers, A. Mu¨ller, H.S. Chakraborty, M.E. Madjet, J.M. Rost, Phys. Rev. Lett. 94 (2005) 065503.
Many-electron phenomena in the ionization of ions A. Mu¨ller
*
Institut fu¨r Atom- und Moleku¨lphysik, Justus-Liebig-Universita¨t Giessen, 35392 Giessen, Germany Available online 26 April 2005
Abstract This brief review of many-electron phenomena in the single and multiple ionization of ions tries to elucidate connections between ion–atom collisions and interactions of single free electrons and photons with neutral or charged atomic species. With the capability of using multiply charged ions in collisions with charged particles or photons, conventional studies on neutral targets can be extended to a new dimension: the target charge state. This is especially interesting for studies of selected effects along specific isoelectronic sequences, i.e. of n-electron atoms with variable nuclear charge. The necessary colliding-beams and merged-beams techniques are technically demanding but can provide access, for example, to electron correlation effects in collisions under the influence of increasingly strong electron–nucleus interactions. 2005 Published by Elsevier B.V. PACS: 34.80.Kw; 52.20.Fs; 33.20.Ni; 33.80.b; 36.40.Gk; 61.48.+c Keywords: Single ionization; Multiple ionization; Electron impact; Photoabsorption; Ion targets; Indirect processes; Many-electron transitions
1. Introduction For probing the structure and the dynamics of microscopic systems at the atomic or subatomic level, scattering experiments with energetic particles or photons are the generally accepted method of choice. Collisions involving molecular species
*
Tel.: +49 641 99 15200; fax: +49 641 99 15009. E-mail address: [email protected] URL: http://www.strz.uni-giessen.de/k3/
0168-583X/$ - see front matter 2005 Published by Elsevier B.V. doi:10.1016/j.nimb.2005.03.096
for studying chemical reactions would typically require thermal energies of the collision partners while investigating the structure of nucleons requires the highest-energy accelerators presently available. The generic scattering scenario for binary collisions is sketched in Fig. 1. Particles A and B in given quantum mechanical states characterized by all their quantum numbers enter the interaction region with momenta ~ pA and ~ pB . From the interaction region, which is characterized by the black box, secondary particles emerge, for example C, D, and E, with their associated
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A pA
E pE
A
D pD
B pB
C pC
B
Fig. 1. Generic scattering scheme of collisions A + B ! C + D + E with the particles in states each characterized by a complete set of quantum numbers and by the particleÕs linear momentum.
momenta and quantum numbers. In kinematically complete experiments the momenta of the different outgoing particles are determined while it is often not possible to also identify all the quantum numbers. In ionizing ion–atom collisions frequently only the final state of the projectile, e.g. characterized by the emerging particle C, is observed, thus leaving ambiguity of what has really happened in the collision. In the theoretical treatment the time dependent Schro¨dinger equation has to be propagated in the box, and is projected afterwards to obtain observable quantities. For numerical calculations the black box may be represented by a grid composed of small volume elements that cover the interaction region. Single and multiple ionization processes in ion– atom collisions involve a multitude of complex interactions between the electrons and the nuclei of projectile and target. If we imagine just a collision of a one-electron atom (or ion) with a two-electron atom (or ion) there are already 10 different electromagnetic pair interactions to be considered (see Fig. 2). In an experiment that observes ionization of A, i.e. in the example of Fig. 2 the removal of the electron from A, there are several possible classes of processes and associated final states. The electron of A can be released to the continuum or it can be captured by particle B. At the same time, the two-electron atom B can loose one or both of its electrons to the continuum. A full theoretical treatment of this (still quite simple) example with all its electron-electron, electron–nucleus and nucleus-nucleus interactions is not possible. Approximations are required to make the problem tractable.
Fig. 2. Pair interactions and electron pathways to be considered in ionization processes where a one-electron atom A is ionized in a collision with a two-electron atom B.
Some of the complexity is avoided in studies of fast collisions when the impulse approximation can be applied and the electrons can be described as independent quasi-free particles with a known momentum distribution. Under such conditions investigations of electron–ion collision phenomena become possible. The resulting simplification of interpreting experiments has been exploited very successfully by a number of groups (e.g. [1,2] and references therein). For the detailed investigation of ionization mechanisms that can occur in fast ion–atom collisions, it is illuminating to consider collisions of ions (or atoms) with really free electrons or completely stripped nuclei. For that purpose, electron–ion and ion–ion experiments with well prepared beams of free particles provide favorable conditions. The resulting requirement of employing colliding-beams techniques is associated with low densities of the interacting particles and hence often poses problems with low signal and high background rates. The scheme shown in Fig. 1 can alternatively represent the principle arrangement of a crossed-beams experiment where beams of particle species A and B meet in the interaction region and the outgoing particles have to be analyzed. Different from the previous quantummechanical meaning, the black box plotted in Fig. 1 is now interpreted as a classical macroscopic interaction volume. The experimentalist has to enter this crossing region with his instrumentation and determine the overlap of the two intersecting
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beams. Besides the disadvantage of low beam densities these experiments provide unique access to absolute cross sections, a feature that is not generally available for investigating collisions of neutral species. An example is the measurement of absolute cross sections for ionization and fragmentation of fullerenes. Vapor densities of neutral complex molecules cannot easily be determined and therefore, measured cross sections for such species are only relative in most cases. With charged particles, however, and suitable assessment of beam overlaps and detector efficiencies, absolute cross sections can be obtained in interacting-beams experiments. Another advantage of such measurements is in the principle accessibility of very narrow collision energy distributions. Especially in electron–ion collision studies the resulting high energy resolution provides quantitative access to and characterization of individual, possibly even state-selective, reaction pathways. Even in the ‘‘simple’’ electron–ion and nucleus– ion collision systems (simple compared with the initial ion–atom problem) single and multiple ionization still involve a multitude of complex mechanisms. Besides the direct removal of one or several electrons from the target, resonant and non-resonant formation of intermediate multiply excited states which subsequently decay by electron emission is important in electron-impact single and multiple ionization of ions and atoms. The following sections will briefly illustrate the increasing complexity of charged-particle collisions with the number of electrons in the target atom (or ion).
2. Direct ionization Direct ionization proceeds via one-step or multi-step knock-off mechanisms which can partly be disentangled by studying effects of different projectile species. As a first step, the situation for ionization of hydrogenlike targets by structureless projectiles will be briefly reviewed. 2.1. Direct single ionization Naturally, direct ionization of a hydrogenlike atom T with atomic number ZT by a structureless
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projectile P with charge ZP can only be single ionization, i.e. promotion of the one and only available electron to the continuum by a knock-off process PZ P þ þ TðZ T 1Þþ ! PZ P þ þ TZ T þ þ e.
ð1Þ
This process has first been treated theoretically by Thomson [3] for projectile electrons and hydrogen target atoms. In that basic approach, the impact-parameter dependent energy transfer DE to the target electron is calculated assuming classical Coulomb scattering of the projectile from a quasifree electron initially at rest. The presence of the target nucleus is essentially neglected and only the binding energy I of the target electron is considered. For all impact parameters where DE P I the ionization probability is 1 and in all other cases it is 0. Thus, the total ionization cross section can be determined. One can extend this concept to arbitrary structureless charged projectiles and arbitrary hydrogenlike systems as described by Eq. (1). For the laboratory situation (non-relativistic treatment), we find the energy transfer DE to the target electron in relation to the impact parameter b (see e.g. [4] p. 423) " # 2 2 2 4 Z Z e m 1 ðm þ m Þ P P e b2 ¼ P T 2 . ð2Þ 4mP me E2 ð4p0 Þ me EDE Here, e is the charge of an electron, 0 the electric constant, mP the projectile mass, me the mass of the electron, and E the laboratory energy of the projectile assuming that the target particle T is at rest. From this equation and the concept introduced by Thomson, the cross section for all ionization processes described by Eq. (1) can be derived " # 2 pZ 2P e4 mP 1 ðmP þ me Þ 1 r¼ . ð3Þ 4mP me E2 ð4p0 Þ2 me EI The simple classical treatment outlined above can only provide qualitative results but has been developed to an extremely successfull tool helping to understand multi-electron processes in atomic collisions [5]. Already from the simple result represented by Eq. (3) one can draw important conclusions on the scaling behaviour of single ionization processes. At sufficiently high energies E the
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second term in the square brackets can be neglected. Then the scaled ionization cross section R ¼ rI 2 =Z 2P is a universal function of the scaled energy u = Eme/(ImP), i.e. for any combination of a projectile such as e, p, He2+, . . . and a target such as H, He+, Li2+, . . . identical functions R(u) have to be expected for large values of u. If the projectile is kept fixed, then the scaling should even be valid for the whole range of non-relativistic projectile energies. In particular, scaled cross sections R(u) for electron-impact ionization of hydrogenlike targets should be identical for each ZT. There is a limited number of experimental results for projectile–target combinations in ionization processes as described by Eq. (1). Consistent data sets are available for ionization of H by e, p, and He2+ [6,7] as well as for electron-impact ionization of He+ [8], Li2+ [9], B4+, C5+, N6+, O7+ [10] and some scattered results are even available up to U91+ [11,12], where, however, relativistic effects have to be considered that go well beyond the classical formula Eq. (3). Measuring direct ionization in ion–ion collisions is very difficult. The only data available over an extended energy range are on the p + He+ system [13–15]. The experimental cross sections of three separate experiments differ from one another and have large uncertainties precluding a convincing comparison on the basis of Eq. (3). The predicted scaling behaviour is investigated in Fig. 3 where scaled cross sections are shown for the ionization of hydrogen by electrons, protons and a-particles, and for the ionization of He+ and B4+ by electrons. While the original projectile energies cover ranges between approximately 10 eV and 2 MeV and the original cross section maxima span a range from about 1019 cm2 to 4 · 1016 cm2, the maxima of the scaled cross sections show little difference for different projectile-target combinations. This is especially true for all available data on electronimpact ionization of H-like ions with 3 6 ZT 6 26 out of which only the measurement on B4+ is shown in Fig. 3 to avoid an overcrowded display of data points. All of the scaled cross section functions for that range of ZT fall on top of the B4+ data within their error bars. The maximum of the original cross section for Fe25+ is even as low as 1022 cm2 [11] and yet, the classical scaling fully
Fig. 3. Scaled cross sections R for ionization of hydrogen atoms and hydrogenlike ions by structureless charged projectiles as a function of scaled projectile energy u. The data are from work of Shah et al., Peart et al. and Aichele et al. (see text).
accounts for the differences. It has to be mentioned, though, that the classical cross sections obtained from Eq. (3) only qualitatively agree with the measurements. In particular, the high-energy behaviour of the calculated cross section misses the ln(E) term that is found in quantum mechanical treatments and already shows up in first order perturbation theory. The simple scaling found for single ionization of hydrogenlike systems can easily be extended to many-electron atoms and ions. Then, however, only direct knock-off processes can be accounted for, whereas complex indirect ionization phenomena require much more sophisticated theoretical treatment. In the direct contributions to the total single ionization cross section one just has to distinguish between the different subshells of the target atom with their specific ionization potentials. The number of (equivalent) electrons in each subshell linearly enhances the cross section calculated for the one-electron case. 2.2. Direct double ionization While direct single ionization appears to be understood quite well on the level of total cross sections the situation becomes very much more
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involved for direct double ionization processes. Accordingly, double ionization of helium has been an object of tremendous efforts in the atomic collisions research of the last two decades. A general scaling behaviour describing PZ P þ þ TðZ T 2Þþ ! PZ P þ þ TZ T þ þ 2e.
ð4Þ
for any given projectile-target combination over the whole energy range is not readily obtained. Nor can theory provide reliable cross sections for the direct processes described by Eq. (4), not to speak of more complex projectiles. Mechanisms that can be responsible for double ionization have been identified early on [16,17]. The incident electron can undergo two sequential ionizing collisions with the two target electrons, a process that has been termed TS2 (two-step 2) in the literature (for a review see [18]). Alternatively TS1 (two-step 1) describes a mechanism where the projectile knocks off a target electron which, on its way out, ionizes the second target electron. Both processes have been treated theoretically by Gryzin´ski on the basis of classical Coulomb scattering [16]. More realistic quantum mechanical treatments followed later (see [18]). The third mechanism results from the sudden change of charge when an electron is removed from the He atom. By the resulting change of screening the second electron may be shaken off to the continuum [17]. The SO (shake off) mechanism is also considered to be the main contribution in particle-impact double ionization at the limit of high velocities and low projectile charge states ([19] and references therein). An empirical scaling for double ionization by heavy-particles Aq+ colliding with He atoms is shown in Fig. 4. Cross section ratios R = r++/r+ obtained in numerous different experiments are plotted as a function of vP/q where vP is the projectile velocity and q the projectile charge state. The background behind this plot is the prediction of a (q/vP)2 dependence of R at low and intermediate projectile velocities [20] and the convergence of R to the shake-off limit at high velocities. On a logarithmic scale the predicted scaling behaviour becomes visible also, of course, when R is plotted against vP/q. The present plot follows the style that has been previously used in the literature by many other authors. The data cover a very wide range of
Fig. 4. Ratios r++/r+ of experimental cross sections for direct double and direct single ionization of He atoms. Data from different experiments are plotted as a function of vP/q where vP is the projectile velocity and q the projectile charge state. The data were adopted from [21–23]. They are not meant to cover every single published result on ion impact double ionization of helium. Ion species investigated are indicated in the figure.
ion charge states from q = 1 to q = 90 and ion energies between about 50 keV and 100 GeV. Considering the different electronic structures of the projectiles as well as the vastly different charge states and velocities, the cross section ratios line up remarkably well with one another. As already shown for single ionization, also double ionization studies can be extended to charged target particles following along the lines of Eq. (4). There are published data for the twoelectron targets H [24], He [25–29], and Li+ [30]. More results e.g. for He-like boron and carbon are becoming available in the near future [31]. All available cross sections r++ for electronimpact direct double ionization of two-electron targets can be scaled in a satisfactory manner by 2.6 plotting the product r++I th as a function of E=I th (see Fig. 5) where E is the electron energy and I th the combined binding energy of both electrons in the target, i.e. the threshold energy for the double ionization process. The scaling differs from a recent suggestion by Shevelko et al. [32] that uses a I 3 th dependence of double ionization cross sections for a wide range of light ions. In the present
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Fig. 5. Scaled cross sections r++I 2th.6 for electron-impact direct double ionization of He-like atoms (and ions) as a function of E=I th where I th is the threshold energy. The solid line is based on a rescaled version of a semi-empirical formula suggested by Shevelko et al. [32]. The data are from experiments by Yu et al, Schram et al., Gaudin and Hagemann, Nagy et al., Stephan et al. and Shah et al. (see text). 2.6 context, the I th scaling was found to give a better fit of the available data for two-electron targets.
zation channels. The simplest possible system for the observation of effects of intermediate excited states in an experiment is a metastable He-like parent ion in a 1s2s configuration. By exciting the 1s electron to the L- or M-shell a doubly excited state is formed that can eject an electron and thus finally bring the ion into its final H-like state. The K-shell can also be excited in a resonant manner, i.e. the incident electron is captured by a dielectronic process and the intermediate triply excited state can eject two electrons either sequentially or simultaneously. In both processes the intermediate product of the excitation is a hollow state with no electrons in the K-shell. First results have been obtained with metastable B3+ and C4+ ions [33]. R-matrix calculations can reproduce several of the main features of the measured cross sections, however, further theoretical work will be necessary to come to a conclusive and convincing result. Indirect processes can also occur in electron-impact ionization of He-like ions with both electrons in the K-shell. The results of a previous measurement [34] and a more recent R-matrix calculation [35] are shown in Fig. 6. From the measured total
3. Indirect ionization processes Besides direct knock-off ionization of an atom or ion that has at least two electrons, the production of intermediate highly excited states that can decay by electron emission provides intricate additional pathways towards the final release of one or more electrons from the target. Intermediate states with sufficient excitation energy can be formed by production of one or more vacancies in inner shells. The resulting product can possibly undergo cascades of Auger-processes and thus the final result of the initial interaction is a net single or multiple ionization of the parent target atom or ion. The final charge state depends on the specific case of the collision and the electronic states involved. 3.1. Indirect single ionization No more than two bound electrons in the initial target state are necessary to open up indirect ioni-
Fig. 6. Measured and calculated cross sections for indirect ionization of Li+ [35]. The contribution of direct ionization has been subtracted with the idea to obtain the isolated cross section for indirect ionization (see text). The window resonances are due to simultaneous excitation of both K-shell electrons and subsequent simultaneous ejection of two electrons.
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single ionization cross section a smooth curve representing direct single ionization was subtracted to obtain indirect ionization contributions. Apparently, the cross section difference is negative at some energies, indicating that direct and indirect ionization channels destructively interfere and the additional channel leads to a reduction of the cross section. Again, all the processes involved in indirect ionization produce intermediate hollow states of the Li+ ion or the Li atom. 3.2. Indirect multiple ionization When the number of electrons bound in the target atom is increased to 3 or beyond, indirect contributions to multiple ionization become possible. In the ionization of a Li-like system, one of the K-shell electrons may be excited while the other one is released to the continuum. Again, a doubly excited intermediate state is formed which ends up in a final charge state with two electrons removed. Contributions of this type to the total net double ionization have to be expected to be small because two tightly bound electrons have to be moved at a time (which is possible, as the previous sections of this paper have demonstrated). Usually, double ionization shows substantial contributions from single ionization of an innershell of the target atom or ion. If an inner-shell electron is released to the continuum the resulting ion can undergo an Auger-process and thus the final result of the process is a net double ionization. Such processes become possible with four or more target electrons. Triple ionization of berylliumlike ions with configurations 1s22s2 can proceed via direct removal of two L-shell electrons plus one K-shell electron, for example by electron impact e + (1s22s2) ! (1s) + 4e. The cross section is small due to the required interaction of 4 electrons. An alternative route from 1s22s2 to 1s is double-Kshell ionization with subsequent autoionization: e þ ð1s2 2s2 Þ ! ð2s2 Þ þ 3e ! ð1sÞ þ e þ 3e.
ð5Þ
In this scheme an intermediate hollow 2s2 ion is formed which subsequently decays by an Auger process. Since the indirect process involves double rather than triple ionization it can be expected to
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have a larger cross section than the direct process (Eq. (5)). The decay of the intermediate state proceeds with a branching ratio of almost 100% which guarantees the final triple-ionization step. The initial double ionization removes a pair of tightly bound but correlated electrons and thus it is of a nature similar to the well studied double ionization of He atoms. If this concept is valid, the cross section for indirect triple ionization of a berylliumlike ion by electron impact should scale in the same manner as that for processes described by Eq. (4). Indeed, measurements for B+ and C2+ [36] in the threshold region for double K-shell ionization perfectly follow the scaling displayed in Fig. 5. More complex mechanisms with cascades of radiative and Auger decays are also possible and can produce signal in multiple-ionization channels. This was demonstrated in a comprehensive study on electron-impact single and multiple ionization of Baq+ ions in charge states from q = 1 to q = 13 [37]. e þ Baqþ ! BaðqþnÞþ þ ðn þ 1Þe.
ð6Þ
Depending on the charge state q of the parent ion the number n of electrons removed in a single collision ranged from n = 1 up to n = 7. Absolute cross sections were measured in the energy range where the 3d-subshell can be opened. This range changes with the parent ion charge state and is covered by collision energies in the experiment between 600 eV and 1050 eV. As one example for the measurements, the experimental cross sections for n-fold ionization of Ba4+ ions are shown in Fig. 7 with n ranging from 1 to 6. At energies between 750 eV and 770 eV a pair of peaks is found in each cross section, apparently due to resonant capture of the incident electron by the Ba4+ parent ion. The resonance energy and the double-peak nature indicate the involvement of a 3d electron in the collision leaving a deep-core 2D vacancy behind in an intermediate short-lived Ba3+ ion which subsequently decays by the emission of (n + 1), i.e. up to 7 electrons. In the cross section for single ionization the resonances are hardly visible on top of the strong non-resonant ionization. By subtracting a smooth curve from the measured cross section, however, the resonance contributions can be extracted.
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[39]. Other rare-earth elements show similar effects [40]. 3.3. Photoionization
Fig. 7. Measured cross sections for n-fold ionization of Ba4+ ions (n = 1,2, . . . , 6) [38].
On an absolute scale the strongest peak features are found for net double and triple ionization. On a relative scale, however, in comparison with the non-resonant ‘‘background’’ the resonances are strongest in 6-fold ionization. Here, 7 electrons are ejected from the deep-core excited intermediate Ba3+ ion whose excitation energy barely exceeds the threshold for 6-fold ionization. Therefore the phase space for 6-fold ionization is greatly reduced and the cross section for non-resonant processes becomes small. As a consequence the resonance contributions near the threshold of 6-fold ionization dominate the related cross section. Observations like the ones described here for Ba4+ have been made for all investigated Baq+ ions. The ions Ba1+ and Ba2+ had already previously been studied, though in a much narrower energy range
The role of multiply excited states in ionization processes can be experimentally studied in great detail by a further reduction of the initial ion– atom problem. In the previous sections the target atom was essentially decomposed into its constituents, electrons and fully stripped nuclei, and interactions of the free structureless charged particles with the projectile ion were investigated in detail. Indirect processes involving multiply excited intermediate states are found to be important and can be made visible by spectroscopy-type measurements with low energy-spread electrons by looking for structures in the total partial cross sections. Fig. 6 shows one of the most striking examples for the capability of crossed-beams energy-scanning techniques. Similar multiply excited states of atoms and ions can be selectively populated by photon interactions making use of the potential for extreme energy resolution available at modern synchrotron radiation sources [41,42]. Accordingly, many-electron phenomena can also be observed in photoionization studies. Recent photoionization and photofragmentation measurements with singly and multiply charged fullerene ions have provided quantitative information on the excitation and the decay of collective resonances. A large fraction of the delocalized electrons oscillate as a whole relative to the ionic background of the fullerene cage. Giant resonance features have been observed in various decay channels leading to ionization and fragmentation of parent neutral fullerenes [43–46] and also of parent fullerene ions in different charge states [47]. The dominant collective resonance phenomena observed in the photoionization experiments have recently been identified as the result of surface- and volume-plasmon excitations [47]. 3.4. Summary Ionization of atoms and ions has been discussed in the light of classical Coulomb interaction
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between charged particles. Many-electron effects occur both in single and multiple ionization. The most obvious multi-electron processes are those of direct multiple ionization. Scaling behaviour of direct double ionization is documented for many different ionic projectiles colliding with helium atoms and for electron-impact on different heliumlike atoms and ions. Direct single ionization by an electron requires an interaction between just two electrons. More than two electrons may be involved in a single-ionization process both in the formation and in the decay of intermediate multiply excited states which contribute to ionization by electron ejection processes. Clear evidence has been found for resonant excitation of two K-shell electrons in He-like Li+ which requires the interaction of all three electrons in the system. Some of the excited states can only contribute to net single ionization if two electrons are ejected in a doubleAuger process while simultaneously the third electron falls down to a more tightly bound state. With the number of target electrons the possibilities for many-electron effects vastly increase. Triple ionization after direct double-K-shell ionization has been observed in Be-like ions. Even direct 7fold ionization was observed in electron-impact measurements on multiply charged barium ions. The ultimate many-electron effect was studied in photoionization experiments with fullerene ions, where the incoming photon is absorbed and by that excites collective oscillations of delocalized electrons against the positive charge of the carbon cage. The plasmon states are extremely short lived and can decay via fragmentation and ionization channels.
Acknowledgement The author thanks all his coworkers and collaborators who have contributed to the instrumentation and the research program behind the physics reviewed in this paper. In particular, the ionization measurements and the understanding of the results reported here, have been made possible by the work of W. Arnold, C. Becker, C. Bo¨hme, A. Frank, K. Huber, J. Jacobi, H. Knopp, R.A. Phaneuf, S. Ricz, V.P. Shevelko, S. Schippers,
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W. Shi, H. Teng, F. Timphus, and T.v. Zoest. We are grateful for support by Deutsche Forschungsgemeinschaft, Bonn Bad Godesberg, and by Bundesministerium fu¨r Bildung und Forschung, Berlin. References [1] H. Kollmus, R. Moshammer, R.E. Olson, S. Hagmann, M. Schulz, J. Ullrich, Phys. Rev. Lett. 88 (2002) 103202. [2] E.P. Benis, T.J.M. Zouros, T.W. Gorczyca, A.D. Gonza´lez, P. Richard, Phys. Rev. A 69 (2004) 052718. [3] J.J. Thomson, Phil. Mag. 23 (1912) 449. [4] E.W. McDaniel, Atomic Collisions: Electron and Photon Projectiles, John Wiley & Sons, New York, 1989. [5] R.E. Olson, Nucl. Instr. and Meth. B, these Proceedings. doi:10.1016/j.nimb.2005.03.080. [6] M.B. Shah, H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys. 14 (1981) 2361. [7] M.B. Shah, D.S. Elliott, H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys. 20 (1987) 2481, 3501. [8] B. Peart, D.S. Walton, K.T. Dolder, J. Phys. B: At. Mol. Opt. Phys. 2 (1969) 1347. [9] K. Tinschert, A. Mu¨ller, G. Hofmann, K. Huber, E. Salzborn, R. Becker, D.C. Gregory, J. Phys. B: At. Mol. Phys. 22 (1989) 531. [10] K. Aichele, U. Hartenfeller, D. Hathiramani, G. Hofmann, V. Scha¨fer, M. Steidl, M. Stenke, E. Salzborn, T. Pattard, J.M. Rost, J. Phys. B: At. Mol. Opt. Phys. 31 (1998) 2369. [11] B. OÕRourke, F.J. Currell, H. Kuramoto, Y.M. Li, S. Ohtani, X.M. Tong, H. Watanabe, J. Phys. B: At. Mol. Opt. Phys. 34 (2001) 4003. [12] R.E. Marrs, S.R. Elliott, D.A. Knapp, Phys. Rev. Lett. 72 (1994) 4082. [13] B. Peart, K. Rinn, K.T. Dolder, J. Phys. B: At. Mol. Opt. Phys. 16 (1983) 1461. [14] M.F. Watts, K.F. Dunn, H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys. 19 (1986) L355. [15] K. Rinn, F. Melchert, K. Rink, E. Salzborn, J. Phys. B: At. Mol. Opt. Phys. 19 (1986) 3717. [16] M. Gryzin´ski, Phys. Rev. 138 (1965) A336. [17] M.H. Mittleman, Phys. Rev. Lett. 16 (1966) 498. [18] J.H. McGuire, Electron Correlation Dynamics in Atomic Collisions, Cambridge University Press, Cambridge, 1997. [19] R. Do¨rner, H. Schmidt-Bo¨cking, T. Weber, T. Jahnke, M. Scho¨ffler, A. Knapp, M. Hattass, A. Czasch, L.P.H. Schmidt, O. Jagutzki, Rad. Phys. Chem. 70 (2004) 191. [20] J.H. McGuire, Phys. Rev. Lett. 49 (1982) 1153. [21] J.H. McGuire, A. Mu¨ller, B. Schuch, W. Groh, E. Salzborn, Phys. Rev. A 35 (1987) 2479. [22] A.S. Schlachter, J.A. Tanis, Phys. Rev. Lett. 73 (1994) 3596. [23] P. Jardin, A. Cassimi, J.P. Grandin, H. Rothard, J.P. Lemoigne, D. Hennecart, X. Husson, A. Lepoutre, Nucl. Instr. and Meth. B 98 (1995) 363.
150
A. Mu¨ller / Nucl. Instr. and Meth. in Phys. Res. B 233 (2005) 141–150
[24] D.J. Yu, S. Rachafi, J. Jureta, P. Defrance, J. Phys. B: At. Mol. Opt. Phys. 25 (1992) 4593. [25] B.L. Schram, A.J.H. Boerboom, J. Kistemaker, Physica 32 (1966) 185. [26] A. Gaudin, R. Hagemann, J. Chim. Phys. 64 (1967) 1209. [27] P. Nagy, A. Skutlartz, V. Schmidt, J. Phys. B: At. Mol. Opt. Phys. 13 (1980) 1249. [28] K. Stephan, H. Helm, T.D. Ma¨rk, J. Chem. Phys. 73 (1980) 3763. [29] M.B. Shah, D.S. Elliott, P. McCallion, H.B. Gilbody, J. Phys. B: At. Mol. Opt. Phys. 21 (1988) 2751. [30] B. Peart, K.T. Dolder, J. Phys. B: At. Mol. Opt. Phys. 2 (1969) 1169. [31] A. Mu¨ller, C. Bo¨hme, J. Jacobi, H. Knopp, K. Ariki, S. Schippers, in: S. Datz et al. (Eds.), XXII International Conference on Photonic, Electronic and Atomic Collisions, Santa Fe, New Mexico, USA, Abstracts of Contributed Papers, Rinton Press, Princeton, New Jersey, USA, 2001, p. 321. [32] V.P. Shevelko, H. Tawara, F. Scheuermann, B. Fabian, A. Mu¨ller, E. Salzborn, J. Phys. B 38 (2005) 525. [33] H. Knopp, J. Jacobi, S. Schippers, A. Mu¨ller, in: J. Anton, H. Cederquist, M. Larsson, E. Lindroth, S. Mannervik, H. Schmidt, R. Schuch (Eds.), XXIII International Conference on Photonic, Electronic and Atomic Collisions, Stockholm, Sweden, Abstracts of Contributed Papers, Stockholm University, 2003, Fr083. [34] A. Mu¨ller, G. Hofmann, B. Weißbecker, M. Stenke, K. Tinschert, M. Wagner, E. Salzborn, Phys. Rev. Lett. 63 (1989) 758. [35] H. Teng, J. Phys. B: At. Mol. Opt. Phys. 33 (2000) L227. [36] J. Jacobi, H. Knopp, S. Schippers, A. Mu¨ller, in: J. Anton, H. Cederquist, M. Larsson, E. Lindroth, S. Mannervik, H. Schmidt, R. Schuch (Eds.), XXIII International Conference on Photonic, Electronic and Atomic Collisions, Stockholm, Sweden, Abstracts of Contributed Papers, Stockholm University, 2003, Fr086.
[37] H. Knopp, C. Bo¨hme, J. Jacobi, S. Ricz, S. Schippers, A. Mu¨ller, Nucl. Instr. and Meth. B 205 (2003) 433. [38] H. Knopp, C. Bo¨hme, J. Jacobi, S. Ricz, S. Schippers, A. Mu¨ller, in: S. Datz et al. (Eds.), XXII International Conference on Photonic, Electronic and Atomic Collisions, Santa Fe, New Mexico, USA, Abstracts of Contributed Papers, Rinton Press, Princeton, New Jersey, USA, 2001, p. 318. [39] G. Hofmann, A. Mu¨ller, B. Weißbecker, M. Stenke, K. Tinschert, E. Salzborn, Z. Phys. D: At. Mol. Clusters 21 (suppl.) (1991) 189. [40] K. Aichele, D. Hathiramani, F. Scheuermann, A. Mu¨ller, E. Salzborn, D. Mitnik, J. Colgan, M.S. Pindzola, Phys. Rev. Lett. 86 (2001) 620. [41] S. Schippers, A. Mu¨ller, S. Ricz, M.E. Bannister, G.H. Dunn, A.S. Schlachter, G. Hinojosa, C. Cisneros, A. Aguilar, A.M. Covington, M.F. Gharaibeh, R.A. Phaneuf, Phys. Rev. A 67 (2003) 032702. [42] S. Schippers, A. Mu¨ller, R.A. Phaneuf, T. van Zoest, I. Alvarez, C. Cisneros, E.D. Emmons, M.F. Gharaibeh, G. Hinojosa, A.S. Schlachter, S.W.J. Scully, J. Phys. B: At. Mol. Opt. Phys. 37 (2004) L209. [43] I.V. Hertel, H. Steger, J. de Vries, B. Weisser, C. Menzel, B. Kamke, W. Kamke, Phys. Rev. Lett. 68 (1992) 784. [44] J. Kou, T. Mori, M. Ono, Y. Haruyama, Y. Kubozono, K. Mitsuke, Chem. Phys. Lett. 374 (2003) 1. [45] J. Kou, T. Mori, S.V.K. Kumar, Y. Haruyama, Y. Kubozono, K. Mitsuke, J. Chem. Phys. 120 (2004) 6005. [46] A. Reinko¨ster, S. Korica, G. Pru¨mper, J. Viefhaus, K. Godehusen, O. Schwarzkopf, M. Mast, U. Becker, J. Phys. B 37 (2004) 2135. [47] S.W.J. Scully, E.D. Emmons, M.F. Gharaibeh, R.A. Phaneuf, A.L.D. Kilcoyne, A.S. Schlachter, S. Schippers, A. Mu¨ller, H.S. Chakraborty, M.E. Madjet, J.M. Rost, Phys. Rev. Lett. 94 (2005) 065503.