Radiative electron capture in heavy-ion collisions

The cross section for radiative capture of bound electrons (REC) by fast heavy ions is calculated in (i) the impulse approximation, (ii) the impact parameter apprximation and (iii) the first Born approximation. The last two methods yield the same result. It agrees with the result given by the impulse approximation in the case of small perturbation of the initial electronic state during the collision. The question how REC may be utilized to measure electronic momentum densities is investigated. For this purpose higher order effects are calculated.