Relativistic effects in electron capture from a hydrogenlike atom by a fast-moving bare ion

Relativistic corrections are examined for electron capture from a hydrogenlike atom by a bare ion incident with a very high kinetic energy E. It is shown that the cross section for nonradiative capture via the double-scattering process suggested by Thomas behaves with E as E^-3 in the ultrarelativistic limit. In contrast, the first Born cross section for nonradiative capture behaves as E^-1. However, the radiative-capture cross section also behaves as E^-1, and has a much larger E-independent coefficient. Therefore in the ultrarelativistic limit nonradiative capture may be ignored in comparison with radiative capture.