Electron capture by positrons from atomic hydrogen using the second Born and Pade approximations

The cross sections for electron capture by positrons from atomic hydrogen are calculated using the second Born approximation and the method of Padé approximants for incident positron energy ranging from 12 to 500 eV. The results are compared with those obtained in the first Born approximation and other theoretical calculations. The contributions from the intermediate states higher than the first to the second-order rearrangement scattering amplitude are found to be significant. The nature of the variation of the second Born and the Padé differential cross sections with the angle of scattering is discussed.