Using Python to Curve Fit Tensor Polarized Deuteron Signals

Dynamic nuclear polarization (DNP) is a necessary tool for certain experiments, such as the measurement of Azz and b1, and the polarization of such targets can be measured via nuclear magnetic resonance (NMR). The NMR signal of a proton is a simple Lorentzian, but a deuteron signal is more complex, having two overlapping peaked functions, due to the deuteron being a spin-1 particle. In materials, such as ND3, where the peaks are not fully superimposed, it is not just the vector polarization (Pz) that can be measured, being a pure scaling of the signal from an unenhanced thermal equilibrium (TE) signal, but also the tensor polarization (Pzz), which is a measure of the difference between the two component signals. This is even further complicated in materials, such as d-propanediol, with different types of deuteron bonds, creating multiple pairs of peaks in the signal. Ideally, this total signal would be compared to a TE signal to calculate Pzz in a similar manner to Pz, but deuteron TE signals are very small and difficult to distinguish from noise. I have thus developed a Python macro to fit a raw polarized deuteron signal to the functional form laid out by Dulya et al. The resultant fitted functions match the data with a standard deviation of less than 1%, and Pzz is able to be derived from them, but so far they do not match Pzz as calculated via TE methods. In future, I will also need to amend Dulya et al.'s function to account for hole-burning techniques to increase tensor polarization.