Modeling of Spin Echo Signals from the Gaussian Pulse Train Using Phase Cycling

The Carr–Purcell–Meiboom–Gill pulse sequence is widely used in magnetic resonance methods to measure the spin–spin relaxation time T2. The time T2 is a characteristic decay time of the refocused spin echo signals. Ideally, the refocusing pulses of this sequence should invert all the spins of the spectrum, i.e., have a rotation angle of 180°. This condition is met in NMR experiments, since the pulse amplitude in them is much larger than the spectrum width in magnetic field units. In the case of pulsed EPR, it is usually impossible to effectively invert all the spins of the spectrum by the refocusing pulse. In this situation, when the echo is observed, other signals appear that depend not only on the time T2, but also on the spin–lattice relaxation time T1. In this paper, numerical calculations of the echo signal amplitudes in the Carr–Purcell–Meiboom–Gill sequence with a Gaussian pulse shape are performed. Phase cycling of the sequence is proposed to isolate the refocused echo signals.