Optical transition in an impurity centre of a crystal: Mixing of phonons

The new method of calculation of the Fourier transform of the optical spectrum of an impurity centre in a crystal in the case of quadratic vibronic coupling with phonons is proposed. In the method, by applying the Stratonovich identity, the quadratic coupling is replaced by the fluctuating linear coupling; the latter is treated by means of the Bloch–DeDominicis theorem. As a result, the problem is reduced to the calculation of the determinant of the symmetric complex matrix and of the corresponding reciprocal matrix. The matrix elements are given by the pair correlation functions of the contributing configurational coordinates.