The energy dependence of relativistic nonradiative electron capture

The energy dependence of the nonradiative electron capture cross-section is discussed in the relativistic domain. A simple analytic expression is obtained for inner-shell transitions using second-order perturbation theory. We have confirmed that the leading-order term is found to have the following energy dependence: σ ∼ E −1 ln 2 E. This is attributed to a combination of kinematic features of the process and retardation effects. Electron capture without change of spin is the dominant transition. The asymptotic form of the electron capture process for relativistic energies has been a subject of debate for some time. An overview of this question has been given by Mukherjee et al (1992) and Bransden and McDowell (1993), while a detailed discussion is given by Eichler and Meyerhof (1995). In the relativistic domain, the physical constraints of energy and momentum matching conspire to make capture a weakly-coupled process in comparison to ionization or excitation. Indeed it is interesting to remark that for rela-tivistic energies, and for small nuclear charges, vacuum coupling in the form 1