This paper proposes an effective diffusion equation method to analyze nuclear magnetic resonance (NMR) relaxation. NMR relaxation is a spin system recovery process, where the evolution of the spin system is affected by the random field due to Hamiltonians, such as dipolar couplings. The evolution of magnetization can be treated as a random walk in phase space described either by a normal or fractional phase diffusion equation. Based on these phase diffusion equations, the NMR relaxation rates and equations can be obtained, exemplified in the analysis of relaxations affected by an arbitrary random field, and by dipolar coupling for both like and unlike spins. The obtained theoretical results are consistent with the reported results in the literature. Additionally, the anomalous relaxation expression obtained from the Mittag-Leffler function based time correlation function can successfully fit the previously reported ¹³C T₁ NMR experimental data of polyisobutylene (PIB) in the blend of PIB and head-to-head poly(propylene) (hhPP). Furthermore, the proposed phase diffusion approach provides an intuitive way to interpret NMR relaxation, particularly for the fractional NMR relaxation, which is still a challenge to explain by the available theoretical methods. The paper provides additional insights into NMR and magnetic resonance imaging (MRI) relaxation experiments.

本文提出了一种有效的扩散方程方法来分析核磁共振（NMR）弛豫。NMR弛豫是自旋系统的恢复过程，其中自旋系统的演化受哈密顿量（例如偶极偶合）引起的随机场的影响。可以将磁化的演变视为相空间中的随机游动，该相空间由正态或分数相扩散方程式描述。基于这些相扩散方程式，可以获得NMR弛豫速率和方程式，以分析受任意随机场和偶极和自旋的偶极耦合影响的弛豫为例。所获得的理论结果与文献报道的结果相吻合。此外，PIB和头对头聚丙烯（hhPP）的共混物中的聚异丁烯（PIB）的¹³ C T ₁ NMR实验数据。此外，所提出的相扩散方法提供了一种解释NMR弛豫的直观方法，特别是对于分数NMR弛豫，这仍然是可用的理论方法来解释的挑战。本文提供了有关NMR和磁共振成像（MRI）弛豫实验的其他见解。