Charge transfer in proton-hydrogen collisions

A nonperturbative approach to the problem of charge transfer in proton-hydrogen collisions is developed in which the wave function corresponding to the outgoing scattered wave in the incident channel is evaluated by solving the Schrödinger equation it satisfies. The present formulation has the advantage of bringing into the theory not only the effects that are due to the Coulomb distortions but also those due to the polarization of the target atom. Our calculation of the capture cross section ($1s\to 1s$), which has been done with neglect of the polarization effect, agrees well with experiment in the low-energy region between 8 and 100 keV. A new interesting feature of our theory is that the cross section for capture shows a maximum at an energy of 9 keV. For proton energies below this value the cross section starts decreasing, finally approaching zero. For higher energies it starts falling with increasing energy in the usual way.