Electron capture from inner shells by fully stripped ions

Cross sections for electron capture from inner atomic shells by fully stripped ions, of velocities high compared to the electron velocities in the inner-shell orbits, are calculated in the second Born approximation. The theory of Drisko for electron capture by protons from hydrogen is generalized to projectiles and targets of arbitrary atomic numbers $Z_1$ and $Z_2$, respectively. For ions of low velocity, the effects of binding and Coulomb deflection are accounted for in a manner similar to that of Brandt and his co-workers in the theory for direct ionization to the continuum of the target atom. The results are in good agreement with experimental capture cross sections, whereas the Oppenheimer-Brinkman-Kramers approximation overestimates such cross sections. The contribution of electron capture to inner-shell ionization cross sections increases with increasing $\frac{Z_1}{Z_2}$ and brings them into agreement with experiment.