On a first order theory for charge exchange with Coulomb boundary conditions

Closed-form formulae are derived for impact-parameter dependent K-K shell electron capture probability amplitudes, as well as for total and differential cross sections by using the first order theory with Coulomb boundary conditions (CBI). The singular behaviour found for the electron capture probability in the limit of small impact parameters is best understood by relating the CBI approximation to the weak-coupling solution of a two-state atomic-orbital close-coupling problem. Cross section calculations are performed for K-K shell capture by protons from He + , Li 2+ , Be 3+ , B 4+ and C 5+ ions.