Convergence of the perturbation series for high-energy electron capture

The convergence problem of the Born perturbation series is investigated for proton-hydrogen electron capture at a projectile energy of 5 MeV through calculating each order iteratively until convergence is achieved. The intermediate states are expanded by a large set of pseudostates constructed from the Gauss-type orbitals. It is demonstrated that the series converges up to the second order when single-centre wavefunctions are used for the expansion while a three-step process via target and projectile continua is contributing significantly to the Thomas mechanism when two-centre wavefunctions are used. (author)