Effect of phonon bottleneck on cross-relaxation

Zubarev's method ls used to study the effect of a phonon bottleneck in electron spin-lattice relaxation on cross-relaxation, A study is made of the case of strong spectral diffusion within the phonon spectrum, when the phonons that are resonant with respect to both groups of spins can be ascribed a single temperature. Equations are derived that describe the crossrelaxation when there is a bottleneck, and the stationary solutions of these equations are studied in various interesting limiting cases. It is shown that the presence of a phonon bottleneck in the electron spin-lattice relaxation facilitates cross-relaxation transfer of saturation from one group of spins to the other. The saturation is transferred only after a stationary state has been established, i.e. , after the time taken for the resonant phonons to relax with the thermal bath.