We study an optical transition in a center with strongly reduced local elastic springs in the excited electronic state. In this
case the transition takes place to the vicinity of a flat minimum of the potential energy in the configurational coordinate
space. The existence of such a minimum results in the resonant increase of the local density of states of low-frequency
phonons, i.e., in the appearance of the resonant (pseudo-local) mode of a low frequency in the excited state. Existence of
such a mode in this state means that the strong mode mixing takes place at the transition. To take this effect into account,
we apply an operator transform method (V. Hizhnyakov, J. Phys. C, 20,6073, 1987). We find that if a parameter of the
quadratic vibronic coupling is close to its critical value, corresponding to the dynamical instability of the excited state,
then the zero-phonon line is practically absent in the spectrum and the long-wave part of the phonon sideband is strongly
enhanced, resulting in formation of so-called lambda-shaped absorption spectrum. The measurements of the optical
spectra of this type have been reported in the literature.
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