The proton-hydrogen scattering problem has been treated numerically under the following approximations: (1) The protons describe straight-line classical trajectories; (2) the (spinless) electronic wave function is expanded in terms of a finite subset of traveling hydrogenic functions centered about either proton. The resulting set of coupled differential equations is solved without further approximation, except for numerical techniques. Most of the results reported include $1S$, $2S$, $2P_0$, and $2P_{\pm 1}$ states. A limited number of calculations include the $3S$, $3P_0$, and $3P_{\pm 1}$ states. The $2P$ direct excitation and transfer excitation cross sections follow the trend of the experimental data of Stebbings et al., but are low by a factor of roughly 2. The calculations also agree qualitatively with the experiments of Everhart et al. on 3° total transfer probability, but are somewhat out of phase in respect to the oscillation of this quantity with energy. Large polarizations of the final $2P$ states are predicted. Limitations of the model are discussed; possible modifications and improvements are suggested.

• Received 14 February 1966

DOI:https://doi.org/10.1103/PhysRev.147.13