Abstract
The semi-classical impact parameter method gives transition probabilities Pji(R) which, for impact parameters R large compared with the atomic radius, are proportional to the oscillator strengths fji. 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) = ∫∞R0 Pji(R)2πRdR where R0 r<, the smaller of the mean radii ri, rj, and when the coupling is strong Q(i→j) = ½πR12 + ∫∞R1 Pji(R)2πRdR where Pji(R1) = 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.
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