Two-state atomic expansion methods for electron capture from multielectron atoms by fast protons

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The two-state, two-center atomic expansion method of Bates for charge transfer is generalized to calculate cross sections of electron capture from inner shells of multielectron atoms by fast protons. In the limit of small capture probabilities, the connections of the present approach with various first-order Born theories are investigated. It is shown that these Born methods for electron capture of multielectron atoms can be obtained from the present approach by further approximations. The method is applied to obtain cross sections of electron capture from C, N, O, Ne, and Ar atoms by fast protons in the energy region where the projectile velocity is nearly equal to the $K$-shell-electron orbital velocity of these atoms. Results of the calculations are compared with experimental measurements.