Electron Capture by Protons Passing through Hydrogen

A theoretical calculation is made of the capture of an electron by a particle of charge $Z^{\prime }e$ passing a hydrogen-like atom of charge $\mathrm{Ze}$. Numerical results are presented for protons passing through hydrogen gas. In contrast to earlier treatments of this problem, the complete interaction Hamiltonian is retained as the perturbation causing the electron transfer. Previous workers assumed that the interaction between the incident particle and the electron was the only perturbation causing the transition and ignored the interaction between the incident particle and the nucleus of the atom. Such a neglect is unjustified. The results of this paper show that when the complete interaction is used the agreement between theory and experiment is good for all energies greater than 25 kev ($\frac{\mathrm{hv}}{e^2}>~1$) in the case of protons in hydrogen, even though the Born approximation is employed. This is a marked improvement over previous calculations which were approximately four to five times larger than experiment.