Exact second Born electron capture forp+He

Formulation and exact numerical calculation of differential and total $1s-1s$ electron-capture cross sections with the use of the second Born approximation with the free-wave Green's function are presented. At energies above 15 MeV there appears in the differential cross section a peak characteristic of a second Born or two-step process. For total cross sections, our calculations show that below 7 MeV the second-order cross section is larger than the first-order cross section, indicating a breakdown of second-order Born approximation with the free-wave Green's function. Results using the peaking approximation of Drisko converge to our exact second Born results only at energies well above 30 MeV. According to our exact second-Born calculations, observation of the angular distribution above 15 MeV should reveal structure related to at least one two-step mechanism for electron capture.