Effect of concentration on light absorption and dispersion by impurity centres in the case of weak electron—phonon coupling

Abstract

The two-particle Green's function method is used to investigate the dependence of light absorption and dispersion due to substitutional impurity centres upon their concentration in the caae of weak electron-phonon coupling, taking into account the change of the quftsi-elastic constants due to the substitution. At low impurity concentrations the halfwidth of the zero-phonon line and the corresponding dispersion curve as well LIB their position in the spectrum are shown to vary linearly with concentration; at higher concentration the absorptios coefficient may deviate from linearity. Consider a cubic crystal with one atom per unit cell which can be substituted by another kind of atom, thus forming a disordered substitutional solid solution. It is evident that upon such a substitution both the mass of the crystal and its quasi-elastic constants change. I n the previous paper [I] the absorption and dispersion of light by such impurity centres in the case of weak electron-phonon coupling was investigated taking into account only the ratio of atomic masses of host and impurity centres. In the present work we assume that , u = --1, where M and rn are atomic masses of the host and the impurity centre, respectively, be negligibly small in comparison with the relative change of the quasielastic constants of the solid solution. We further assume that the impurity absorption region is far from that of the host crystal and the concentration of impurities is so small that the interaction between the centres can be neglected. Then the stationary states of strongly coupled electrons of such a system can be determined in the adiabatic approximation [2]. However, if the spacings between the energy levels of the optical electrons of the impurity atom are of the order of the phonon energy of the ideel host crystal the adiabatic approximation cannot be used to determine their stationary states. Let us assume that in the case under consideration we have to deal with weak electron-phonon coupling. Then writing the potential energy of the nuclear sub-system [3] in TaH EI YMeHbIIIeHHH.

Zero‐Phonon Transitions in the Optical Spectra of Impurity Molecular Crystals

“…I n our paper we are considering namely such systems. I n the case of degenerate or weakly split electronic levels the adiabatic approximation is invalid, which results in a considerable complication in the calculations of the electron-vibrational wave functions and transition probabilities (see, for example, [37], [38], [49], [52] V ( r , R ) is the potential energy of the interaction between electrons and nuclei.…”