Complex deuteron NMR signals

To determine the spin polarization of deuterons, nuclear magnetic resonance (NMR) is used. This is necessary for polarized targets, such as for the upcoming \(A_{zz}\) and \(b_{1}\) experiment at Jefferson Lab. NMR measures the impedance of a solenoid around a deuterated sample. Although the impedance is a complex value, conventionally only the real part of the impedance has been used for this purpose. However, often the tune is not precisely real, meaning the signal has at least some small imaginary portion. This conventionally has been dealt with by an offset parameter, such as Dulya’s false asymmetry method. For vector polarization, this suffices, as the tuning is factored into the overall error of the results, and for a small phase angle doesn’t make much of a difference. However, for tensor polarization, the exact lineshape of the signal is quite significant, and treating the impedance as complex during analysis removes the need for an offset parameter. It also provides more accurate results, as the conventional false asymmetry method over- or underestimates polarization, depending on the sign of the phase angle.