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For a two-level system corresponding to a particle of spin ½ in a random field in the Z direction, the relaxation function[image omitted]has been estimated, the magnitude Ω(t) being the sum of the isotropic interactions of the particle in question with particles j executing diffusional motion. Specifically Ω(t)=ω0 + Σ ω(Mj, rj), where ω0 = constant, Mj is a random time-independent parameter, ω(M, r) decreases with r faster than r-3 and rj = rj(t) is a diffusional, random function. From the expression for <σ+(t)>, we establish general features of the relaxation phenomenon for diffusional processes, and calculate the relaxation rate 1/T2 and relaxation shift Δω to be 1/T2-iΔω = 4π[image omitted]CAvMλM, where C is the concentration of particles and λM is the scattering length for an equation of the Schrödinger type with an imaginary potential -iω(M, r) instead of U/ℏ, and diffusion coefficient [image omitted] instead of ℏ/2m. We also found that for the case of 'external' relaxation, the Redfield approach proved valid only under the simultaneous restrictions of low concentration and weak interaction.

Non-adiabatic transitions in two-level systems are investigated theoretically for a random time dependence of ħω, the energy difference, between the levels. We assumed that ω = ω(x) and the coordinate x = x(t) is a random function of time. Diffusion and Poisson processes (both homogeneous and with a source) for x(t) were assumed. The cases of linear crossing terms (ω = γx) and non-linear terms (ω = ωe exp (- αx) + ω0) were considered. Values of the non-adiabatic transition probability per unit time were obtained by perturbation theory for ω1τc << 1 where τc is the correlation time and ω1 is the off-diagonal matrix element.

The E.S.R. line shape of the iminoxyl radical in viscous liquids was investigated at several temperatures. The results are interpreted by theoretical calculation of the line shape at an arbitrary value by using a diffusion model for the motion of the molecules.