Mechanisms of proton spin dephasing in a system of magnetic particles

For protons diffusing among a system of magnetic particles, the process by which initial phase coherence is lost depends substantially on particle size. In this article, evidence for three dephasing mechanisms is presented: an incremental process at small particle sizes (motional averaging regime), a discrete process at intermediate particle sizes (visit limited regime), and a continuous process at large particle sizes (static dephasing regime). While motional averaging regime and static dephasing regime are well known, the distinct dynamics in visit limited regime are often overlooked. Revisiting earlier analytic treatments for the dynamics in this regime, Monte Carlo simulations are performed to extract the details of dephasing and to test the concept of an inner zone of rapid dephasing herein named the full dephasing zone. It is shown that the emergence of a full dephasing zone marks the transition from motional averaging regime to visit limited regime since protons can be fully dephased in a single encounter. Moving from the visit limited regime to the static dephasing regime, a crossover between a purely discrete process and a purely continuous process occurs. Developing a simple model of the dephasing process, the average dephasing time is demonstrated to be relatively constant thus giving insight into the long lasting plateau in the relaxation rate.