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

Abstract

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.