Inner-Shell Electron Capture by a Swift Bare Ion: Second Born Effects

The second Born cross section for electron capture from a hydrogenlike atom of atomic number $Z_T$ by a bare ion of atomic number $Z_P$ and speed $v$ is evaluated for $(\frac{Z_P{e}^2}{\hslash v}\ll 1$ and $Z_T$ arbitrary. The ratio of the second to first Born cross sections increases rapidly as $Z_T$ increases; for $\left(\frac{Z_T{e}^2}{\hslash v}\right)\gtrsim 1$ this ratio is very large. These results indicate that second- and higher-order Born terms must be considered in calculating the cross section for inner-shell electron capture (or the time-reversed process).