Is semi-classical scattering theory accurate for transitions from low-lying vibrational states?

Various semi-classical approximations are compared with exact transition probabilities from the lowest vibrational state for the forced harmonic oscillator. The primitive semi-classical transition probability is shown to be seriously inaccurate except, paradoxically, for the most strongly forbidden classical transitions. Bessel and Airy uniformizations lead to substantial and equivalent improvements for the 0 →n transitions. For the 0 →0 transition, the Bessel uniformization is correct in near elastic situations but the Airy uniformization is required for cases of strong interaction.