Rearrangement Collisions For High Energies (Linear Model)

The high energy behaviour of the cross section for particle exchange in a three particle collision is investigated for arbitrary masses and a rather general class of potentials. For convenience we use a linear model. It is shown that in general the first and second Born approximation provide the leading terms for high energies. If the exchanged mass is “small” the interaction between the two heavy masses cancels. The wave treatment and the impact parameter version give identical results. For particular mass ratios either the first or the second Born approximation provides the leading term. Then even backscattering can be dominant. The high energy results agree with the asymptotic expansion for two exactly solvable cases.