A unified description of the spin-spin and spin-lattice relaxation rates applied to nitroxide spin labels in viscous liquids

For nitroxide spin labels the application of electron and nuclear spin rela xation theory has caused a seeming paradox to develop, even in the fast mot ion limit. Two well-resolved EPR lines are seen when using N-15 nitroxide s pin labels (or three lines with N-14 nitroxide spin labels) due to the inte raction of the electron with the nitrogen nucleus. The observed line widths are related to the spin-spin relaxation rates. The different widths indica te that the spin-spin relaxation rates for the two (or three) lines depend on the nuclear manifold, or nuclear spin state z quantum number. The theory (developed by Kivelson and Freed) treated each line independently and gave a quantitative accounting of the differences seen in the relaxation rates of the lines. When the same treatment is applied to the spin-lattice relaxa tion rates, a strong dependence of the spin-lattice relaxation rate on the particular line (nuclear manifold) chosen is predicted. However, the experi mental spin-lattice relaxation rates show no dependence on the nuclear mani fold (nuclear quantum number). The treatment presented here shows that by f ollowing the operator method of Abragam one can develop a consistent pictur e for both spin-lattice relaxation and spin-spin relaxation that leads to t heoretical predictions that agree with the experimental results.