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The phase time coupling effect on NMR relaxation is investigated based oncoupled and uncoupled phase diffusion. The results indicate that phase and timecoupling could significantly impact the NMR relaxation time. The spectraldensity term in the relaxation time expression is modified with an apparentangular frequency, which could be twice the conventional angular frequency whenthe phase-time coupling is strong. A phase-time coupling constant is proposedto modify the conventional angular frequency to the apparent angular frequency.The modified NMR relaxation time can successfully fit the experimental datataken from Ref. [6]. The results could improve our understanding and analysisof NMR relaxation.

Effect of phase and time coupling on NMR relaxation rate by random walk in phase space