Kinetic equations for a paramagnetic center in a dielectric medium with non-Born terms and the theory of spin-lattice relaxation

Usually in the theory of spin-phonon kinetic equations one proceeds from the spin Hamiltonian as the dynamic part of a closed system. This approach does not enable us to include in the kinetic equation relaxation processes associated with electronic transitions involving states not included in the spin Hamiltonian. In this paper the electron-phonon kinetic equations are obtained with relaxation coefficients which also depend on transitions via the excited electronic states. In order to describe these transitions, we must also take into account non-Born terms of the collision integral. The collision integral derived here is represented as a function of the various Fourier transforms of lattice correlation functions and the transition frequencies of the electronic and the phonon subsystems. This forms a convenient basis for description of the relaxation transition probabilities and of the EPR linewidth caused by the various one- and two-phonon processes. Besides the well-known relaxation processes, the existence is shown of others, overlooked in the theory of spin-lattice relaxation based on perturbation theory. A general form of the spin-phonon kinetic equations is introduced, including the effects of excited states.