Vibronic transitions between states with hard and soft phonon dynamics

The analytical theory of vibronic transitions between electronic states with hard and soft phonon dynamics is proposed. It is found that the low energy part of the spectrum is essentially enhanced due to appearance of the low-frequency pseudo-local mode in the final state. The Fourier transform of the corresponding spectrum, in proper units, has the universal shape (1 − it)−μ. The value of the exponent μ depends on the dimensionality of the system: in 3D, 2D and 1D lattices the values are 0.35, 0.23 and 0, respectively. The theory gives an analytical description of the lambda-shaped spectra observed experimentally.