Use of limit theorems in the theory of many-phonon processes

A study is made of the problem of electron transitions at a local center in a crystal (for example, an $F$ center) with allowance for the electron-phones interaction in the adiabatic approximation. A probability formulation of the problem is given. It ts shown that the characteristic function whose Fourier transform describes the line profile is infinitely divisible. If the phonon dispersion is neglected, the characteristic function is stable and has parameters that depend on the temperature. A law of mirror symmetry is formulated in terms of stable distributions. Some new results on the temperature dependence of the line width are obtained.