Nuclear pair electron spin echo envelope modulation

The interaction of electron spins with homonuclear spin pairs in their vicinity is one the dominating mechanisms echo decay at low temperature and concentration. Here, we study this mechanism using established concepts envelope modulation (ESEEM). We obtain analytical expressions for Hahn echo, refocused stimulated Carr–Purcell pulse trains small numbers π pulses. well approximated by product nuclear pair ESEEM functions. same approximation can explain dependence on first interpulse delay provides reasonable time scale estimates echos after an odd number echoes even pulses are rather sensitive to correlations within larger clusters. Approximations improve both factorising bath into disjoint clusters, provided that due belonging different clusters considered addition cluster modulation. two have mathematical form as filter functions these sequences noise spectroscopy. This coincidence a computationally very efficient way predicting induced pairs. predicts previously observed (Bahrenberg et al., 2021) increase amplitude when refocusing incremented other fixed but longer. In contrast, spin-noise concept fails predict effect.