## Abstract

A multistate molecular approach to the proton-hydrogen collision is formulated in terms of an impact parameter perturbed stationary-states approximation. Spurious long range couplings are avoided and Galilean invariance is enforced by the inclusion of momentum translation factors which are determined variationally within an Euler-Lagrange formalism (Crothers & Hughes 1978). Well defined radial and rotational coupling matrix elements are employed in the 1-7 keV impact energy range in a six-state (1s<latex>$\sigma _{\text{g}}$</latex>, 2p<latex>$\sigma _{\text{u}}$</latex>, 2p<latex>$\pi _{\text{u}}$</latex>, 3p<latex>$\sigma _{\text{u}}$</latex>, 3p<latex>$\pi _{\text{u}}$</latex>, 4f<latex>$\sigma _{\text{u}}$</latex>) calculation of elastic and inelastic differential scattering cross sections, charge exchange probabilities and both direct and exchange H(2p) production total cross sections. They are also employed in the same energy range in a ten-state (1s<latex>$\sigma _{\text{g}}$</latex>, 2p<latex>$\sigma _{\text{u}}$</latex>, 3d<latex>$\pi _{\text{g}}$</latex>, 2p<latex>$\pi _{\text{u}}$</latex>, 2s<latex>$\sigma _{\text{g}}$</latex>, 3p<latex>$\sigma _{\text{u}}$</latex>, 3d<latex>$\sigma _{\text{g}}$</latex>, 4f<latex>$\sigma _{\text{u}}$</latex>, 4d<latex>$\pi _{\text{g}}$</latex>, 3p<latex>$\pi _{\text{u}}$</latex>) calculation of both direct and exchange H(2s) production total cross sections. The results are in excellent accord with experimental data and show considerable improvement on previous molecular calculations. This success is attributed to the inclusion of both momentum translation factors and radial coupling matrix elements.

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