Bayesian Approach to T1 Analysis in NMR Spectroscopy with Applications to Solid State Physics

Abstract

We applied the Bayesian framework to the analysis of nuclear spin–lattice relaxation curves. In the simplest case, nuclear spin–lattice relaxation is described by a single exponential function. However, relaxations to which the exponential function does not fit well are often observed in real NMR experiments. One of the reasons for those relaxations is the sample inhomogeneity. For such cases, it is common practice to analyze the curve by fitting a stretched exponential function exp(−(t/T1)β) to the data, where T1 is the nuclear spin–lattice relaxation time. Another possibility is the coexistence of different relaxation mechanisms. In this situation, the relaxation curves should be fitted by the summation of several relaxation functions. For scientists to interpret relaxation curves, a data-driven method is required to determine which of the two possibilities is more plausible. In this paper, we propose a Bayesian method to select the appropriate relaxation function and even the number of relaxation components. We demonstrate that our method effectively determines the relaxation model on the basis of numerical experiments and the experimental data of nuclear spin–lattice relaxation of the nonmagnetic semiconductor SmS.