Theoretical Treatment of Pulsed DNP Experiments: Effects of Spectral Exchange

In the present work, we provide a theoretical treatment of pulsed Overhauser-type dynamic nuclear polarization (DNP) in the presence of spectral exchange, namely, Heisenberg exchange. The expression for the DNP enhancement of a nuclear magnetic resonance (NMR) signal is generalized by redefining the "deviation factor", expressing the deviation of the electron spin polarization from its equilibrium value, averaged over the period of the pulse sequence. We can demonstrate that spectral exchange significantly increases the deviation factor and, thus, the NMR enhancement. The present treatment allows one to determine the optimal pumping frequency at different exchange rates.