Raman Scattering for Weakened Bonds in the Intermediate States of Impurity Centres

A theory of the Raman scattering in resonance with an electronic transition causing a strong softening of vibrations is proposed. In this case the potential surface of the excited state has a flat minimum or maximum in the configurational coordinate space. Two cases of the vibronic coupling are considered: (1) the coupling with a single coordinate and (2) the coupling with the phonon continuum. To describe the Raman scattering the Fourier-amplitude method is applied. In the first case the calculations are performed for the pseudo-JahnTeller effect in the excited state. In the second case, despite a strong mixing of phonons, the equations for the Raman Fourier amplitudes can be factorized and solved analytically. It is predicted that the second-order Raman scattering will be strongly enhanced. Moreover, the second-order Raman scattering is also enhanced as compared to the first-order scattering. The Raman excitation profiles show a structure caused by the Airy oscillations. The theory is applied to the triplet-triplet optical transition in Na-2 molecule confined at the surface of a He-4 droplet