Symmetric eikonal approximation for electron capture at relativistic energies

A symmetric eikonal approximation is used to obtain a symmetric approximate formula in closed form for the cross section for 1s-1s electron capture from a target hydrogenic ion with nucleus ALPHA (atomic number ZETAsubALPHA) by an incident bare positive ion BETA (atomic number ZETAsubBETA) moving with relativistic velocity it is assumed that αZETAsub(ALPHA) and αZETAsub(BETA) << 1 where α is the fine structure constant. The formula for the capture cross section yields satisfactory accordance with numerical calculations carried out by previous workers using a similar approximation, but produces cross sections which are significantly less than those given by the non-symmetric eikonal approximation formula, except at extremely high energies. (author)