Electron Capture by Protons Passing through Hydrogen

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Abstract
A formal treatment of the capture problem is presented and a suitable approximation scheme valid for fast collisions is developed. The approximation consists of: (1) using a suitable perturbed initial wave function instead of the unperturbed initial wave function used in the Born approximation, (2) neglecting the contribution of what we call two-step capture processes, and (3) in an impulse approximation fashion, neglecting the effect of the binding of the electron in the atom in the initial state "during" the collision. All the above three approximations result from an attempt to express the transition matrix for capture in terms of two-body operators. The improved wave function is orthogonal to the final wave function in the limit of infinitely heavy incident ion, unlike the Born approximation wave function. Consequently the (incident ion)-(nucleus) interaction has zero matrix element for transition from the initial state to the final state. Only the (incident ion)-(electron) interaction contributes to the capture cross section in this approximation. Good agreement with experiment is obtained in the particular case of protons picking up electrons from hydrogen gas for proton energies above 25 kev.