DOUBLE-ELECTRON CAPTURE BY POSITRONS PASSING THROUGH HELIUM

The total cross section for double-electron capture by positrons passing through helium atoms is calculated by the Born approximation for positron energies up to 250 eV. It is found that the maximum value of the cross section is 0.0058 πa02 and occurs at the positron energy of 100 eV. This value turns out to be of about 2 orders of magnitude smaller than the existing values of the cross section for single-electron capture by positrons in helium. In order to perform the calculation of the matrix element of the problem, the Feynman's parametrization method is used. The method is used for two parallel cases: (A) in its usual, straightforward form, which requires the introduction of three parameters, and (B) in a slightly modified form, to the authors' knowledge never used before, allowing the reduction of the number of the parameters to two. This double calculation is mainly intended to give, together with a more accurate result for the cross section, the possibility to investigate the convergence of the results obtained in a three-parameter calculation to the two-parameter ones. © 1969 The American Physical Society.