Electron emission from highly charged ions: signatures of magnetic interactions and retardation in strong fields

The electron emission of highly charged ions has been reanalyzed with the goal of separating the magnetic and retardation contributions to the electron–electron (e–e) interaction from the static Coulomb repulsion in strong fields. A remarkable change in the electron angular distribution due to the relativistic terms in the e–e interaction is found, especially for the autoionization of beryllium-like projectiles, following a 1s → 2p3/2 Coulomb excitation in collision with some target nuclei. For low-energetic, high-Z projectiles with Tp ≲ 10 MeV u−1, a diminished (electron) emission in the forward direction as well as oscillations in the electron angular distribution due to the magnetic and retarded interactions are predicted for the autoionization of the 1s2s22p3/2 3P2 resonance into the 1s22s 2S1/2 ground and the 1s22p 2P1/2 excited levels of the finally lithium-like ions, and in contrast to a pure Coulomb repulsion between the bound and emitted electrons. The proposed excitation–autoionization process can be observed at existing storage rings and will provide a novel insight into the dynamics of electrons in strong fields.


Introduction
The electron-electron (e-e) interaction in (strong) Coulomb fields has attracted much interest since the early days of quantum mechanics [1,2]. Relativistic calculations for neutral atoms and highly charged ions (HCI) soon showed that accurate level energies and fine-structure splittings can be obtained only if, in addition to the static Coulomb repulsion among the electrons, the magnetic and retardation contributions to the e-e interaction, also known as the Breit interaction in atomic physics, as well as the self-energy and vacuum polarization of (at least) the inner-shell electrons, are also taken into account ( [3,4] and references therein). Many computations on the electronic structure of few-electron HCI have been carried out since then, which helped advance atomic many-body techniques into the best-approved theories of physics today. More recently, the e-e interaction has been explored in different collision [5,6], autoionization [7] and ion recombination processes [8][9][10][11][12][13]. In the dielectronic recombination of HCI, in particular, it was shown that the Breit interaction can modify individual (capture) cross sections and rates by 50% or more [14][15][16][17][18], or may even dominate the Coulomb repulsion and finally lead to a qualitative change in the expected x-ray emission pattern [19,20]. These investigations demonstrated that ion and x-ray spectroscopies of HCI now provide a unique tool for improving our understanding of the e-e and electron-photon interactions in the presence of strong fields [21].
Until now, however, very little has been known about how the magnetic and retarded interactions among electrons affect the electron emission and hence the dynamics of electrons in strong fields. While shifts in the transition energies [22] and cross sections [23] of the recorded ion and x-ray spectra clearly illustrate the importance of the relativistic contributions to e-e interaction, when averaged over space and time, further insight into the dynamics of electrons in strong Coulomb fields can be obtained only by measuring the angular and spin properties of the emitted electrons. Indeed, angle-resolved measurements on the electron emission from few-electron ions may help explore how electron dynamics is affected by the relativistic motion of electrons and the presence of a negative continuum. Such measurements can be seen as complementary to accurate hyperfine and g-factor experiments [24] that explore the magnetic interaction among the bound electrons and their interplay with the charge and magnetization distribution of the nucleus.
In this paper, we analyze the electron emission from HCI following the Coulomb excitation of (lithium-and) beryllium-like ions. For the 1s 2 2s 2 1 S 0 + Z T → 1s2s 2 2p 3 P 2 excitation of beryllium-like projectiles and their subsequent autoionization into the 1s 2 2s 2 S 1/2 and 1s 2 2p 2 P 1/2, 3/2 levels especially (figure 1), an unexpected strong variation in the angular distribution  (1). The Coulomb excitation of initially beryllium-like projectiles in the 1s 2 2s 2 1 S 0 ground state gives rise to ions in the 1s2s 2 2p 3/2 3 P 2 resonant state that may autoionize into the 1s 2 2s 2 S 1/2 and 1s 2 2p 2 P 1/2, 3/2 levels of the finally lithium-like projectiles. The resonant and final levels of this process can be easily identified by the kinetic energy of the emitted electrons as well as their relative intensity, if necessary.
of the electrons is found, caused by the magnetic interaction among the electrons. In addition to the details of the e-e interaction, the predicted change in angular distribution depends sensitively also on the velocity of the projectile ions, thus enabling one to 'tune' the (relativistic) interaction for every ion along the isoelectronic sequence separately. Angle-resolved measurements for different ions therefore provide quite a sensitive tool for analyzing the electron dynamics in strong fields, complementary to the well-established spectroscopy of hard x-rays.
While the Coulomb excitation of HCI and their subsequent electron emission can be readily described by the density matrix theory [25], care has to be taken to select an excitation-autoionization process for which the electron angular emission is affected by the mixing between different partial waves of the outgoing electrons, thus enabling one to separate the magnetic and retarded interactions from the instantaneous Coulomb repulsion. For HCI, in fact, the effects of multipole mixing on the (Auger) electron emission are most pronounced for the (single-electron) excitation of beryllium-like ions, while helium-like ions cannot autoionize after a single 1s → 2l j excitation and lithium-like ions autoionize into the 1s 2 1 S 0 ground state (of the finally helium-like ion) via a single partial wave. Since the e-e interaction operator is scalar, it cannot affect the (shape of the) angular distribution of the electrons emitted for a single partial wave, irrespective of all the details of the relativistic terms. This remains true even for the Auger decay of the meta-stable 1s2s2p 4 P 5/2 level, which is forbidden in the non-relativistic limit and has thus been used widely as a test bed for studying magnetic and retardation effects over the last few decades [26][27][28]. The electron angular distribution for the autoionization of the 1s2s2p 4 P 5/2 level into the 1s 2 1 S 0 ground state is defined entirely by geometrical factors that depend on the parities and total angular momenta of the initial and final ionic states, but is independent of the transition amplitude; see equations (3.1.15)-(3.1.16) of [25].
To work out further details of the electron emission of HCI, let us consider the excitation-autoionization process of a q-fold charged projectile in collision with some target atom with nuclear charge Z T . In this process, the projectile is initially assumed to be in its ground state |α 0 J 0 M 0 with welldefined total angular momentum J 0 , M 0 and parity, and is excited by the target (nucleus) into some state |α r J r M r that is embedded within the continuum of the next higher charge state of the ion, A (q+1)+ . Thus, the projectiles can also autoionize under emission of an electron to some final state |α f J f M f , in addition to the typical photon emission of inner-shell excited HCI. In the notation of the atomic states, α 0 , α r , . . . hereby denote all additional quantum numbers needed for a unique specification of these states. The autoionization of ions in the resonant state |α r J r M r is caused by e-e coupling to the continuum [29] and leads to electrons with well-defined kinetic energy = E r − E f as obtained from the total energies of the resonance and final ionic states, respectively.

Theory and computations
A (time-independent) density operator can be assigned to the ion at each step of process (1), by taking into account the finally emitted electron by this operator. In first-order perturbation theory, these density operators before and after a given 'interaction' are related to each other by ρ k = R k ρ k−1 R + k , where R k refers to the transition operator of the kth step and ρ k to the corresponding density operator just after the interaction has occurred. Complete transformation of the density operators for both steps of process (1), the initial excitation and the subsequent (auto-)ionization, therefore enables one to explore how the angular distribution (and polarization) of the emitted electrons is affected by the various interactions that occur during the time evolution of the system. Here, we shall not provide a detailed derivation of the finalstate density operator that is presented elsewhere [30], but display only those formulae that are needed for the further discussion below. For the Coulomb excitation of an initially unpolarized ion in level (α 0 J 0 ) into some magnetic substate |α r J r M r with a specified projection M r , the partial cross section is given by where is the transition amplitude in first-order perturbation theory [31,32]. These formulae for the projectile excitation in relativistic ion-atom collisions are displayed in natural units (h = m e = c = 1), and here b denotes the impact parameter,α 3 (i) ≡α z (i) the Dirac matrix for the ith particle and E 0 and E r refer to the total energies of the projectile ion in its initial and intermediate resonance states, respectively. Furthermore, integration over time and the impact parameter b can be carried out analytically in momentum space, and this helps simplify the computation of the amplitudes (3).

5
The partial cross section (2) describes the excitation of the projectile electrons into some (magnetic) substate |α r J r M r and, if the cascade processes due to the excitation of high-lying levels can be neglected, therefore also defines the relative population of the substates after Coulomb excitation has taken place. For a fixed direction of the ion beam, however, this population is in general not statistically distributed but typically aligned, i.e. with an equal population only of just the magnetic substates with the same modulus |M r |. In atomic theory, this alignment of the projectile ions can be described most conveniently in terms of one (or just a very few) parameters [25,33] that are directly related to the partial cross sections (2), and where σ ( is the total excitation cross section and J r M r J r − M r |k0 a Clebsch-Gordan coefficient. For a beam of initially unpolarized ions, as can be seen from expression (4) and the symmetry of the Clebsch-Gordan coefficients, the alignment parameters A k (α r J r ) are non-zero only for even values of k 2J i . In the second step of process (1), the ion does stabilize itself under the emission of an (Auger) electron with characteristic angular distribution and polarization. Of course, both these properties are related to the (sublevel) population of the excited ion and hence to the alignment parameters A k (α r J r ). For example, the angular distribution of the emitted electron is given by where θ is the polar angle with regard to the beam direction and are characteristic functions that describe the dynamics of the autoionization, and including the normalization factor Indeed, the angular distribution (5) nicely reflects the two steps of process (1): the excitation of the ions, characterized by the alignment parameters A k (α r J r ), and the subsequent autoionization as described by . The function f k in equation (6) merely depends on the (reduced) matrix elements ( f J f , κ)J r V r J r of the e-e interaction V , where and κ = ±( j + 1/2) for l = j ± 1/2 describe the energy, angular momentum and parity of the emitted electrons, and κ denotes the total phase of the outgoing electron.
In the relativistic atomic theory, as appropriate for medium and heavy elements, the (frequency-dependent) e-e interaction comprises both, the instantaneous Coulomb repulsion (the first term) and the Breit interaction, i.e. the magnetic and retardation contributions (the second and third terms). In this 6 representation of the interaction operator, moreover, ω denotes the frequency of the virtual photon and α i the vector of Dirac matrices associated with the ith particle. The e-e interaction operator (7) has been derived rigorously within the framework of quantum electrodynamics [3] and applied to a large number of electronic structure calculations in recent years [34,35].
To analyze the angular distribution (5) of the emitted electrons in further detail, the Coulomb excitation amplitudes (3) and alignment parameters (4) as well as the characteristic functions (6) for the autoionization of the inner-shell excited projectiles have been calculated with multiconfiguration Dirac-Fock wave functions [36,37]. Wave function expansions of increasing size were tested in order to ensure that the calculated transition amplitudes and alignment parameters converge within 5%. This level of convergence is sufficient to reveal and demonstrate the influence of the (frequency-dependent) Breit interaction on the angular distribution (and polarization) of emitted electrons.

Results and discussion
Lithium-like ions are probably the simplest systems in which a 1s → 2l j (single-electron) excitation leads to the emission of electrons. In particular, the 1s2s2p 4 P term has received much interest in the literature [26,38,39] for the study of spin-orbit and relativistic interactions in (spin-) forbidden transitions, both by photon and electron spectroscopy. Even for lithiumlike uranium, for example, the 1s2s2p 4 P 5/2 level has a lifetime that is roughly two orders of magnitude larger than that for the 2,4 P 1/2, 3/2 levels from the same configuration. Nonetheless, the electron emission from all 2,4 P J levels of 1s → 2p inner-shell excited lithium-like ions does not enable one (so easily) to distinguish different contributions to the e-e interaction since the 1s 2 1 S 0 ground state of the (finally) helium-like ion only allows emission of a single partial wave, i.e. κ = κ in equation (6). For this reason, no interferences of different amplitudes due to the relativistic e-e interaction may arise in the angular distribution of the emitted electrons. This can be seen, for instance, from the properties of the 6 j symbols in equation (6) which, for J f = 0, are non-zero only for j = j = J r and l = l and this reduces the characteristic function f k to a purely geometrical factor, independent of any further detail with regard to the e-e interaction operator (7).
Inner-shell 1s → 2p excited beryllium-like ions still have a reasonably simple level structure (figure 1) that helps distinguish individual Auger lines rather readily. For these ions, the 1s(2s 2 2p + 2s2p 2 + 2p 3 ) configurations with a single hole in the K -shell comprise in total 30 finestructure levels 2S+1 L J with J = 0, . . . , 3. For medium-and high-Z ions along the beryllium sequence, all these levels have a comparable excitation energy that is well separated from the 1s → 3l j excitations. Moreover, since the Coulomb excitation is caused by the one-electron operator i 1/r i (t) in equation (3), mainly the 1s2s 2 2p levels are excited, while the population of the 1s(2s2p 2 + 2p 3 ) levels is clearly suppressed or even negligible. In the following, we are especially interested in the Coulomb excitation and subsequent autoionization of the 1s2s 2 2p 3/2 3 P 2 level, which does not decay by E1 dipole emission into the 1s 2 2s 2 1 S 0 ground level but only by magnetic quadrupole (M2) radiation. For the Coulomb excitation of this J = 2 level, figure 2 displays the cross sections σ and alignment parameters A 2 and A 4 from equation (4) as a function of the projectile energy between 5 and 100 MeV u −1 and for the three beryllium-like ions with Z = 54,79 and 92, respectively.
In fact, the strong energy dependence of both the cross sections and the alignment parameters, already enables one to 'tune' the importance of different terms in the angular distribution (5) for a single ion and autoionization transition, and even with enlarged flexibility if several decay lines and/or ions along the beryllium isoelectronic sequence are taken into account. For example, we shall see below that the two characteristic functions f 2 and f 4 are affected very differently by the Breit interaction and that a large contribution of the product A 4 · f 4 in equation (5) is particularly desirable in order to unravel relativistic effects. As seen from figure 2, the alignment parameter A 2 vanishes almost completely for low collision energies, while A 4 is large in magnitude, and this behavior is in clear contrast to the alignment at higher projectile energies T p 50 MeV u −1 . For a proper choice of the projectile energy, we can therefore enhance or diminish the (relative) contributions of the magnetic and retarded interactions, while the strength of the electron signal (cross section) can be kept feasible.
Apart from the Coulomb excitation, the shape of the observed angular distribution of the emitted electron also depends on the competition between the (subsequent) autoionization and photon emission of the intermediate state |α r J r M r . For the 1s2s 2 2p 3/2 3 P 2 level, the dipoleforbidden (M2) decay gives rise to a much larger branching fraction for the emission of electrons, compared with the dipole-allowed 1,3 P 1 levels, see table 1. This fraction for the autoionization into the 1s 2 2s 2 S 1/2 ground state is about 24% for Xe 50+ and still 7% for U 88+ beryllium-like ions. For the 3 P 2 resonance, moreover, there are two terms with k = 2 and k = 4 that contribute to the angular distribution of the emitted electrons and enable one to explore deviations from a W (θ ) ∝ 1 + β P 2 (cos θ) standard pattern. In order to display how the magnetic and retardation contributions affect the autoionization of the 3 P 2 resonance, table 1 lists the characteristic functions f 2 and f 4 as well as the branching fraction for the autoionization into the two lowest 1s 2 2s 2 S 1/2 and 1s 2 2p 2 P 1/2 levels of the finally lithium-like ion. Results with and without including the magnetic and retardation terms into the Auger amplitudes are tabulated for the same ions as above. While the (dipole) function f 2 is affected only weakly by the relativistic contributions to the e-e interaction, even for beryllium-like U 88+ ions, the f 4 values change significantly. Indeed, the characteristic function f 4 is completely dominated by the Breit interaction in the autoionization amplitudes, a behavior that can be understood by analyzing expression (6). For the strong autoionization into the 1s 2 2s 2 S 1/2 ground level of the Table 1. Characteristic functions f 2 , f 4 and branching fraction (bf) for the autoionization of the 1s2s 2 2p 3/2 J = 2 resonance into the 1s 2 2s 2 S 1/2 ground and 1s 2 2p 2 P 1/2 first excited levels of lithium-like ions. Results are displayed without (Coulomb only) and with including the magnetic and retardation contributions (Coulomb + Breit) in the Auger amplitudes. See text for a further discussion. lithium-like ion, for example, the outgoing electron leaves the ion predominantly in a p 3/2 partial wave with the amplitude a p 3/2 ≡ ( 2 S 1/2 , p 3/2 ) J = 2 V 1s2s 2 2p 3/2 3 P 2 that is two orders of magnitude larger than the Auger amplitude a f 5/2 ≡ ( 2 S 1/2 , f 5/2 ) J = 2 ||V || 1s2s 2 2p 3/2 3 P 2 for an f 5/2 partial wave. The amplitude a f 5/2 even vanishes to a very good approximation for a pure Coulomb repulsion among the electrons, a f 5/2 0, owing to the tensorial structure of this operator that requires a bound f-orbital to admix into the expansion of the 1s2s 2 2p 3/2 3 P 2 wave function. With these definitions of a p 3/2 and a f 5/2 , the characteristic functions for the autoionization into the 1s 2 2s 2 S 1/2 ground level can be simplified to where κ refers again to the phase of the outgoing electron. In single-configuration approximation and for a pure Coulomb interaction, a f 5/2 = 0, we therefore obtain f 2 = − √ 7/10 = −0.837 and f 4 = 0 for all ions along the beryllium isoelectronic sequence, as seen from table 1. If a f 5/2 becomes non-zero because of the magnetic and retardation contributions to the e-e interaction, the two characteristic functions f 2 and f 4 then depend not only on the ratio between the a f 5/2 and the (dominant) a p 3/2 amplitudes but also on the phase difference of the involved partial waves, cos( f 5/2 − p 3/2 ). For the autoionization into the 1s 2 2s 2 S 1/2 ground state, the relativistic interactions lead to a 3% reduction of f 2 for Z = 92, while f 4 changes from nearly zero (for a pure Coulomb interaction) to about 0.11 if the complete e-e interaction is taken into account.
Since mainly the characteristic function f 4 is affected by the magnetic and retardation contributions to the e-e interaction, we need to choose projectile energies for which a sufficiently large product A 4 · f 4 is predicted. A sizeable alignment parameter A 4 (in magnitude)  Figure 3. Angle-differential cross section for the electron emission of the 1s2s 2 2p 3/2 3 P 2 − 1s 2 2s 2 S 1/2 autoionization of beryllium-like ions with projectile energies T p = 5, 10 and 100 MeV u −1 , following the Coulomb excitation from their 1s 2 2s 2 1 S 0 ground state. Results are shown in the rest frame of three beryllium-like projectiles with charges Z = 54, 79 and 92 and in two approximations. Angular distributions with only the Coulomb repulsion incorporated into the Auger amplitudes (blue dashed lines) in expression (6) are compared with those where the complete e-e interaction is taken into account (black solid lines). arises especially at low projectile energies and may then alter the angular distribution of the emitted electrons. Figure 3 displays the angular distribution for the autoionization of the 1s2s 2 2p 3/2 3 P 2 resonance into the 1s 2 2s 2 S 1/2 ground state of the lithium-like ion for three projectile energies T p = 5, 10 and 100 MeV u −1 and for beryllium-like ions with nuclear charge Z = 54, 79 and 92. The angular distributions of the corresponding electron lines is calculated in two approximations with regard to how the e-e interaction is included in the characteristic functions f k . Apart from a pure Coulomb repulsion between the bound and outgoing electrons (blue dashed lines), we consider here the full relativistic e-e interaction (7) in this figure (black solid lines). A rather strong interference between the Coulomb and the magnetic terms in the e-e interaction arises especially at low projectile energies, T p 10 MeV u −1 , and gives rise to a double-peak structure in the angular distributions as well as to a 10% reduction of the electron yield in the forward direction if the nuclear charge of the projectiles is increased from Z = 54 to 92. This lowering of the electron emission in the forward direction (θ ≈ 0 • ) is significant and further enhanced in the laboratory frame due to the Lorentz transformation of the energetic electrons (see below). At higher projectile energies, the anisotropy of the electron emission increases steadily, owing to enhancement of the alignment parameter A 2 , but with less effect than from the magnetic and retardation contributions to the e-e interaction, see figure 2.
A similar analysis as for the autoionization of the 1s2s 2 2p 3/2 3 P 2 level into the 1s 2 2s 2 S 1/2 ground level of the lithium-like ion can be performed for its autoionization into the 1s 2 2p 2 P 1/2 lowest excited level of these ions. In this decay mode, the outgoing electron leaves the ion in either a d 3/2 or d 5/2 partial wave, with preference for a d 5/2 emission. In contrast to the autoionization into the 1s 2 2s 2 S 1/2 ground level, however, a non-zero f 4 value arises here already for a pure Coulomb repulsion owing to the spin-orbit splitting of the relativistic 2p orbital. 8 Nevertheless, the magnetic contributions to the e-e interaction have a remarkable effect on this electron line and enlarge the f 4 function by more than a factor of ten for all beryllium-like projectiles with nuclear charge Z 67 (table 1). This enhancement in the function f 4 gives rise, together with a small change of the f 2 function, to a strong alteration of the electron angular distribution, as shown in figure 4. Again, a double-peak structure and a reduced electron yield in the forward direction by up to a factor of 2 is predicted due to the magnetic and retarded interactions among the electrons. Let us note here, however, that autoionization into the 1s 2 2p 2 P 1/2 lowest-excited level is likely more difficult to observe because the branching fraction (relative intensity) of the 1s2s 2 2p 3/2 3 P 2 → 1s 2 2p 2 P 1/2 line is much smaller than for the autoionization into the 1s 2 2s 2 S 1/2 ground level, see table 1.
The proposed excitation-autoionization scheme (1) facilitates, in contrast to electron capture, a clear distinction of the emitted electrons from the initial (Coulomb) excitation process. This scheme can be realized most easily at ion storage rings such as the experimental storage ring (ESR) in Darmstadt. The electrons from the projectiles are then measured in the laboratory frame and thus the predicted angular distributions need to be Lorentz transformed first before they can be compared with experiment. For example, figure 5 displays the angular distribution of the electrons emitted from beryllium-like U 88+ projectiles at 5 MeV u −1 in the 1s2s 2 2p 3/2 3 P 2 − 1s 2 2s 2 S 1/2 (left panel) and 1s2s 2 2p 3/2 3 P 2 − 1s 2 2p 2 P 1/2 (right panel) autoionization. As seen from this figure, in particular the electron emission in the forward direction appears to be very sensitive with regard to relativistic contributions to the e-e interaction. Here, zero-angle electron spectrometry has been found sensitive in electron-photon coincidence measurements to resolve details at the high-energetic end of the bremsstrahlung spectrum [40]. Therefore, measurements of the electron emission in the forward direction, say between 0 < θ 30 • in the laboratory frame, will enable one to resolve the predicted decrease in electron yield at low angles. As seen from figure 5, already a peak structure in the forward direction would provide a clear signature of the Breit interaction, and further details will be revealed if the range of measured angles is enlarged towards 90 • or even beyond.
In fact, the proposed measurements appear to be feasible with present-day available spectrometers at heavy-ion storage rings or those, for instance, planned at the future FAIR facility. The Coulomb excitation of high-Z projectile ions has been explored in good detail for initially hydrogen-and helium-like ions [23,41]. In these measurements, it was found that the alignment of the inner-shell excited states itself is sensitive to magnetic interactions and, hence, to details of the Lienard-Wiechert potential. A relativistically modified alignment of such inner-shell excited states was also seen in the angular distribution of the emitted electrons, but these effects on the alignment can be separated (to a good extent) from the interaction of the emitted electrons and the bound-state density by varying the charge state of the projectiles. In beryllium-like ions, moreover, the 1s2s 2 2p 3/2 3 P 2 resonance is well separated in energy from the two 1s2s 2 2p 1/2 3 P 0,1 levels by about 370 eV for Xe 50+ and 4200 eV for U 88+ and therefore allows a clear distinction of the K − L 1 L 2 Auger lines in the corresponding electron spectrum. It is only the 1s2s 2 2p 3/2 1 P 1 resonance that lies quite close in energy to the 3 P 2 level (by about 12 32 eV for Xe 50+ and 60 eV for U 88+ ) and which also receives a substantial population due to the Coulomb excitation. The autoionization of the 1,3 P 1 levels into the 1s 2 2s 2 S 1/2 and 1s 2 2p 2 P 1/2 levels may therefore partially blend the electron emission from the 1s2s 2 2p 3/2 3 P 2 resonance. Owing to the E1 dipole decay into the 1s 2 2s 2 1 S 0 ground state, however, the 1 P 1 level has a 60 times shorter lifetime than 3 P 2 and only a very tiny branching fraction for autoionization. In addition, cascade contributions to the population of the 3 P 2 level mainly occur via the Coulomb excitations of the 1s2s 2 (3d + 4d + 4f) levels but were found negligible at the present level of accuracy.

Conclusion
The electron emission of HCI has been reconsidered for unraveling the influence of the magnetic and retarded interaction among the electrons on the electron dynamics in strong fields. A remarkable change in the predicted angular distribution of the electrons is found for the Coulomb excitation of beryllium-like ions in the 1s2s 2 2p 3/2 3 P 2 resonance and the subsequent autoionization into the 1s 2 2s 2 S 1/2 ground and 1s 2 2p 2 P 1/2 levels of the finally lithium-like ions. When compared with the radiative or dielectronic capture of electrons, the Coulomb excitation is particularly suitable for studying the electron emission in strong fields as it is not disturbed by free (incident) electrons. The present analysis of the relativistic contributions to e-e interaction extends a previous study of the photon emission of HCI in which the Breit terms also lead to a different behavior in the angular distribution and polarization of the emitted x-rays [19,42] when compared with the Dirac-Coulomb theory, which was recently confirmed by experiment [20]. In contrast to photon emission, which only exhibits the integral effect of the relativistic motion of electrons, electron spectrometry enables one to access further details of the electron dynamics in strong Coulomb fields.
The simplest signatures of the relativistic contributions to e-e interaction in high-Z ions are the reduced electron emission in the forward direction (θ 5 • ) as well as the doublepeak structure in the expected angular distribution; these signatures arise especially at low projectile energies 10 MeV u −1 and for beryllium-like ions with nuclear charge Z 70. The electron angular distribution from such projectiles can be analyzed with present-day electron spectrometers and provides complementary information about the electron dynamics in strong fields that is not accessible from x-ray spectra alone.