Differential cross sections are derived from a multistate impact-parameter treatment of heavy-particle collisions. Various approximations are suggested and their relationship with previous expressions are discussed. The equivalence between the differential cross sections in the impact-parameter and wave versions of the Born approximation is established for elastic and inelastic scattering and is illustrated explicitly for the $1s$, $2s$, $2p_0$, and $2p_{\pm 1}$ excitations of atomic hydrogen by proton and hydrogen-atom impact.

• Received 11 June 1973

DOI:https://doi.org/10.1103/PhysRevA.8.2915