H. Ast

Relativistic (e, 2e) collisions on atomic inner shells in symmetric geometry

We report here on an (e, 2e) experiment at relativistic electron energies (E0=300 keV and 500 keV) in coplanar symmetric geometry. Absolute triple differential cross section measurements forK-shell ionisation of gold, silver and copper are compared with a number of simple first order approximations. Appreciable discrepancies between theory and experiment are found, which reduce with decreasingZ and increasing primary energy. The theoretical calculations show that spin flip effects are important in symmetric geometry, in earlier works these had been neglected.

Influence of Coulomb boundary conditions for (e, 2e) processes on the K-shell of high- Z atoms

We study the relevance of physical boundary conditions for relativistic (e, 2e) processes on the K-shell of high-Z atoms. The relativistic distorted-wave Born approximation is extended to include the long-range Coulomb interaction in the final channel, allowing the two outgoing electrons to escape in the field of a singly charged positive ion. Besides the physical description we also construct the first fully relativistic Coulomb-Born approximation for (e, 2e) processes, which is the appropriate one to assess the validity of calculations based on semirelativistic Coulomb wavefunctions. The theoretical investigation is illustrated with calculated triple-differential cross sections for (e, 2e) processes on silver and gold, in both coplanar symmetric and asymmetric geometries. The comparison of the results obtained in the modified relativistic distorted-wave Born approximation with previous calculations indicates that the inclusion of asymptotic physical boundary conditions has only a limited effect. On the other hand, the fully relativistic Coulomb-Born approach is seen to yield results in very good agreement with the absolute experimental data, and demonstrates how the use of approximate semi-relativistic wavefunctions can be misleading.

Triple differential cross sections in energy-sharing symmetric geometry for gold and uranium at relativistic impact energies

We report the results of fully relativistic distorted-wave calculations for (e,2e) collisions at high energies on gold and uranium targets in a coplanar symmetric geometry. The results for gold are in excellent agreement with available absolute experimental data. We also observe a peak in the triple differential cross section at large angles which may be interpreted in terms of a multiple scattering mechanism. In the present case of large impact energies, the ratio of the large angle to the binary peak is several orders of magnitude larger than that previously observed at non-relativistic energies. Our calculations indicate that this peak should be accessible to experiment. We propose a new geometrical arrangement for experiments which we believe offers distinct advantages in the study of distortion effects in relativistic (e,2e) processes.

On the position of the binary peak in relativistic e,2e collisions

The triple differential cross section in coplanar asymmetric relativistic (e,2e) processes is not symmetric about the direction of momentum transfer. It is demonstrated that this symmetry, so familiar from the nonrelativistic first Born approximation, is in the relativistic case already broken at the first Born level due to the effect of retardation and magnetic contributions to the electron - electron interaction. A further shift away from the direction of momentum transfer is due to distortion effects in the incoming and outgoing channels. Similar effects are found in coplanar symmetric geometry.

(e, 2e) spectroscopy of atomic clusters

The potential of applying (e, 2e) spectroscopy to metallic clusters is discussed within the jellium model. It is shown that such experiments would allow the investigation of the analogy between cluster and nuclear structure. Distinct diffractive patterns in the state-selected triply differential ionization cross section as well as in the elastic channel reflect the effective cluster radius. Differences between the triply differential cross section for atomic systems and those for jellium spheres are expected even if the valence electron states are not energetically resolved.

Remark on the theory of three-body effects in relativistic (e,2e) processes

Recent theoretical results by Das and Dhar (1998 J. Phys. B: At. Mol. Opt. Phys. 31 2355) suggest a significant role of three-body effects in relativistic collisions. We point out a number of problematic assumptions in this work, and show that the measurements discussed in this work can be described quantitatively without reference to such effects.

Structure of the triply differential cross section in the recoil region in relativistic electron-impact ionization: II. Theoretical analysis

The experimentally observed double structure of the triply differential cross section in the recoil region of the ionization of the copper K-shell by relativistic electrons is analysed by calculations based on the relativistic distorted-wave Born approximation. We study separately the influence of the atomic potential on the incoming and outgoing electrons. Evidence is presented in support of the interpretation that different mechanisms account for the two maxima in the recoil regime.

Coulomb Boundary Conditions for Relativistic (e,2e) Processes

The relativistic (e,2e) experiments on high-Z atoms performed in the last years by the Tubingen group1,2 have stimulated theoreticians to provide an acceptable model to explain the ionization processes involved. The relativistic distorted wave Born approximation (rDWBA)3,4,5 seems the one which yields the best results and has produced data in qualitative, and in most cases quantitative, agreement with the absolute measurements1,2. In this contribution we study, theoretically, the relevance of Coulomb boundary conditions for (e,2e) processes on the K-shell of high-Z atoms. We consider several fully relativistic approximations and compare calculated triple differential cross sections (TDCSs) with the measurements1.

Progress Report on Relativistic (e,2e) Processes

In this rather compact summary we present an overview of the theoretical investigation of (e, 2e) processes that have been carried out by the Belfast-Cambridge-Frankfurt Collaboration during the last five years. This work has profited from close collaboration with the experimental group around W. Nakel in Tubingen.

Structure of the Triply Differential Cross Section in the Recoil Region in Relativistic Electron Impact Ionization

Electron impact ionization experiments in which the two outgoing electrons are detected in coincidence after angular and energy analysis have already provided a large body of information in the nonrelativistic energy region (see for instance Lahmam-Bennani 19911 and the articles in (e,2e) and related processes 2. In recent years progress has been made in extending the (e,2e) technique to relativistic impact energies and atomic inner shells using polarized3 and unpolarized electron beams4,5,6 Many of the longlasting discrepancies between experimental results and theoretical data (obtained in various calculations7,8) have been overcome by calculations carried out in the relativistic distorted wave Born approximation (RDWBA) (for a brief overview of the relevant publications see Dreizler et al, this volume9).