High energy limit in rearrangement collisions

Abstract

The cross section for particle exchange from ground state to ground state in a three-particle collision is investigated. An asymptotic expansion for high incident energies can be given if the Fourier transforms of the interaction potentials allow an expansion in powers of 1/k for largek, which includes Coulomb interaction. It is shown that in general the first and second Born approximations provide the asymptotically leading terms. For special mass ratios, scattering into special (critical) angles becomes predominant. These angles, which are independent of energy, can also be determined employing classical arguments. Near the critical angles single terms of either the first or second Born approximation become dominant. If the exchanged mass is small, the interaction between the two heavy masses cancels near forward direction, implying the validity of the impact parameter theory. The results are discussed for Coulomb interaction as the simplest example (electron exchange). Here, the contributions by critical scattering are small unless the energies become exceedingly large.