Knowledge Bank

The absorption cross section for diatomic molecules is calculated for these transitions under the following assumptions: 1. The vibrational eigenfunctions of the upper state are assumed to be a continuum and are represented by a delta function at the turning point of the upper state repulsive potential which is weighted by the inverse of the slope of the potential curve at the turning point. 2. The lower state vibrational eigenfunctions are constant between the turning points and zero beyond. Assumption one is valid for charge exchange or Rydberg transitions where the upper state has a shallow potential energy curve and the equilibrium internuclear distance is large compared to the ground state. Assumption two is valid if the temperature is high enough such that several vibrational states of the ground electronic state are contributing to the absorption. It the repulsive part of the upper state potential is assumed to be that of a harmonic oscillator, the absorption cross section can be expressed as a simple function of the photon frequency.