Theory of scattering of electromagnetic waves of the microwave range in a turbid medium

The coefficient of extinction of electromagnetic waves of the microwave range due to their scattering from clusters suspended in an amorphous medium and responsible for turbidity is calculated. Turbidity resembles the case when butter clusters transform water into milk. In the case under investigation, the clusters are conductors (metallic or semiconducting). The extinction coefficient is connected in a familiar way with the cross section of light scattering from an individual cluster. A new formula is derived for the light scattering cross section in the case when damping of oscillations of an electron is due only to spontaneous emission of light quanta. In this case, the resonant scattering cross section for light can be very large. It is shown that this can be observed only in a whisker nanocluster. In addition, the phonon energy on a whisker segment must be higher than the photon energy, which is close to the spacing between the electron energy levels in the cluster.