Spin dephasing in the Gaussian local phase approximation

The Brownian motion of spins diffusing in an inhomogeneous magnetic field created by susceptibility effects is considered. Applying the correct form of the Gaussian approximation, the method allows calculating the local magnetization as well as the free induction decay for all diffusion regimes. The phase accumulated during the diffusional motion is treated by an averaging over all possible trajectories in terms of the Gaussian local phase approximation. Predictions of the Gaussian local phase approximation are compared with the Gaussian phase approximation for diffusion in a constant gradient in a slab, a cylinder, and a sphere. The Gaussian local phase approximation, thereby, shows several advantages compared to the Gaussian phase approximation: it is also valid in the static dephasing regime, predicts correctly both transverse components of the magnetization, and yields information about the local magnetization.