The first Born approximation for collisions between heavy particles

Cross sections for collisions involving heavy particles are considered in the first Born approximation. The impact parameter and semi-classical treatments are compared with the wave treatment. It is proved that the cross sections given by the three treatments are effectively equal even at moderate and low impact energies. The very slight differences that exist are decreased if the cross section is summed over final-state and averaged over initial-state spatial degeneracies. To illustrate the position some specific transitions are examined in detail.