The Impact Parameter Method for Electron Excitation of Optically Allowed Atomic Transitions

The semi-classical impact parameter method gives transition probabilities P ji ( R ) which, for impact parameters R large compared with the atomic radius, are proportional to the oscillator strengths f ji . When modified in such a way that reciprocity conditions are satisfied, the results obtained are in good agreement with quantal calculations even for near-threshold energies. Cross sections are calculated in two ways. When the coupling is weak Q ( i → j ) = ∫ ∞ R 0 P ji ( R )2π RdR where R 0 ≃ r < , the smaller of the mean radii r i , r j , and when the coupling is strong Q ( i → j ) = ½πR12 + ∫ ∞ R 1 P ji ( R )2π RdR where P ji ( R 1 ) = ½. We adopt the smaller of the two cross sections obtained. The method gives good agreement with experiment for H 1s rightarrow 2p, He 1s rightarrow 3p and Na 3s rightarrow 3p. It is superior to the Born approximation, which overestimates the low-energy contribution from small impact parameters. Cross sections are calculated for transitions between excited states of hydrogen.