Inverse Laplace transformation analysis of stretched exponential relaxation

We investigate the effectiveness of Inverse Laplace Transform (ILT) analysis method to extract distribution relaxation rates from nuclear magnetic resonance data with stretched exponential relaxation. Stretched-relaxation is a hallmark rates, and an analytical expression exists for this case spin-1/2 nucleus. compare theoretical those extracted via ILT several values stretching exponent at different levels experimental noise. The accurately captures distributions $\beta \lesssim 0.7$, signal noise ratios greater than $\sim 40$; however tend introduce artificial oscillatory components. further use approach analyze spin $I>1/2$ find that are captured by $I=1/2$. Our results provide solid foundation interpret general $I$ in terms fits.