TARGET CONTINUUM DISTORTED-WAVE THEORY FOR COLLISIONS OF FAST PROTONS WITH ATOMIC-HYDROGEN

By considering the target continuum distorted-wave (TCDW) theory as the high-energy limit of the half-way house variational continuum distorted-wave theory, it is shown not only that there is no intermediate elastic divergence but also that the second-order amplitude based on a purely elastic intermediate state is of order v-6 and is thus negligible. The residual inelastic TCDW theory is developed to second-order at high velocities. It is used to describe charge exchange during collisions of fast protons with atomic hydrogen. Using an on-shell peaking approximation and considering 1s-1s capture it is shown that the residual purely second-order transition amplitude comprises two terms, one real term of order v-6 and one purely imaginary term of order v-7 ln v. At 5 MeV laboratory energy, it is shown that these are negligible.