Use of the local harmonic approximation in the theory of radiationless transitions

Abstract

The possibility of applying the «local harmonic approximation» to the calculation of the generating functions used in the theory of radiationless transitions has been investigated. The approximation attempts to «adapt» point by point the generating function to the curvature of the potential, varying the oscillator frequency in a suitable manner. In the simple case of two identical Morse oscillators separated by a constant energy gap ΔE, the radiationless transition probability has been computed for a wide range of ΔE values. The results are compared with those obtained by summing over the exact bound states of a Morse oscillator. It is found that the line shape is qualitatively correct although some spurious negative contribution is introduced by the approximation.