Theory of Proton-Hydrogen Collisions

Abstract

The theory of excitation and charge exchange in proton-hydrogen collisions is discussed within the framework of the impact-parameter method. Consideration is given to the importance of proper boundary conditions. The time-dependent equations linking the amplitudes of the target with those of the rearranged system are written in matrix form. By eliminating the rearrangement amplitudes from these equations, a second-order matrix equation is derived which may be used as a basis for successive approximations which are automatically second order. The theory is generalized with the aid of a two-center expansion of the electronic wave function. The method is illustrated by computing first-and second-order distortion approximations for the reactions ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ and ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{H}\mathrm{}\left(1s\right)+{\mathrm{H}}^{+}$, and the results are compared with previous calculations.