Electron capture in a high-energy approximation

The process of electron capture by protons in atomic hydrogen is studied in the eikonal approximation formulated recently within the framework of the well known time-dependent semiclassical impact-parameter treatment. The cross sections for electron capture into the 1s, 2s, 2p 0 and 2p +or-1 states by protons from ground-state hydrogen are obtained in closed forms. The results are compared with the experimental data, and it is found that for high energy the present total capture cross section is in reasonable agreement with experiment. The high-energy asymptotic forms of the cross sections are also discussed.