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 $E^{-3\mathrm{}}$ in the ultrarelativistic limit. In contrast, the first Born cross section for nonradiative capture behaves as $E^{-1\mathrm{}}$. However, the radiative-capture cross section also behaves as $E^{-1\mathrm{}}$, and has a much larger $E$-independent coefficient. Therefore in the ultrarelativistic limit nonradiative capture may be ignored in comparison with radiative capture.