Angular distribution in proton-hydrogen charge-transfer collisions

Theoretical angular distributions for $p$-H charge transfer to the $1s$ state for energies of 1 keV and above have been examined and compared for three approximation schemes: The plane-wave Born approximation of Jackson and Schiff (JS), the Coulomb projected Born approximation of Geltman (G), and the distorted-wave eikonal approximation of one of the authors (D). The sharp dip in the forward distribution characteristic of JS is found to exist in G and D as well. As expected, G and D give identical results for all but the lowest energies. In the cases of G and D the dip, which is located close to that of JS, disappears and then reappears as the energy rises. Analytic high-energy limits for the angular dependence in both the JS and G cases have been found and are discussed.