Impact parameter treatments of certain hydrogen-proton and hydrogen-hydrogen excitation collisions

Consideration is given to the impact parameter form of the Born approximation and of the pRA approximation (i.e. the first-order approximation to which the perturbed stationary state, or PSS, approximation tends). Calculations are carried out on the excitation of normal hydrogen atoms to the 2s or 2p states in encounters with protons and other normal hydrogen atoms. The results obtained provide some information on the range of validity of the Born approximation. The impact-parameter treatment corresponding to a simplified version of the second Born approximation is given and discussed. Attention is drawn to the fact that for certain transitions the pRA approximation fails seriously when the encounter is very close.