Comparison between the continuum distorted-wave and the second Brinkman-Kramers approximations at high energies electron capture

The authors study electron capture from the K-shell of a hydrogenic target to the K-shell of a bare ion at the asymptotic high-energy limit. The agreement between the continuum distorted-wave (CDW) and the second-order Brinkman-Kramers (B2) approximations is theoretically proved not only for total cross sections but also for angular distributions. The shape of both approximations near the double scattering critical angle is carefully analysed in terms of the transverse impulse transfer. Numerical results for the CDW, exact and peaking B2 approximations are compared for proton-hydrogen resonant capture.