Electron capture to the continuum

The second-order Oppenheimer-Brinkman-Kramers approximation is used to derive simple analytical formulae, evaluated to the lowest order in the fine-structure constant alpha in the numerator, for the differential cross section for electron capture to the continuum (ECC) by incident bare ions having velocity nu from target hydrogenic atomic systems. Relativistic as well as non-relativistic forms are derived. Comparison of the theory with the experimental data of Dahl (1985) and Andersen et al. (1986) for H + , He 2+ +He collisions is fairly satisfactory for energies >50 keV amu -1 . However, although the velocity dependence obtained by Andersen et al. is nu -11.3+or-0.2 in the range of impact energies 1-2.6 MeV amu -1 , this does not imply that the asymptotic nu -11 velocity dependence given by the non-relativistic second-order OBK cross section is almost attained. It is shown that this cannot happen until an energy >500 MeV amu -1 is reached where allowance for relativity produces a considerable change in the energy fall off.