Study of Inverse Laplace Transform Analysis of NMR Magnetization Data

We investigate the effectiveness of the Inverse Laplace Transform (ILT) analysis of NMR magnetization data in obtaining spin-lattice relaxation rate (W₁) distributions. The ILT analysis method provides an estimation of the probability distribution of W₁, which is significant in the study of condensed matter systems such as high-temperature superconductors. To observe the effectiveness of the method, we compare the probability distributions obtained for spin magnetization recovery curves of spin ½ nuclei with a stretched exponential form to analytic solutions of the distributions. For further study of the method, parameters such as the number of points and noise for the recovery curves are varied to observe their effect on the estimation of the probability distribution. We observe that these parameters contribute to unwanted oscillatory behavior in the estimated probability distribution solved using the ILT analysis method.