Spin Echos for Uncoupled Spins

The spin echo is one of the most fundamental building blocks for NMR pulse sequences. Its main purpose is to refocus chemical shifts. The simplest spin echo is that for uncoupled spins where only the offset, Ω (i.e. the frequency difference between the carrier and the resonance) need be considered. The pulse sequence is represented in the upper portion of the figure with the vector and product operator representations below. A 90_x pulse is first given to create magnetization along the -y axis of the rotating frame. During the first delay period, τ, the magnetization rotates in the x-y plane at a rate, Ω. The 180_x pulse rotates the magnetization 180 degrees about the x axis. During the second delay period, the magnetization again rotates in the x-y plane at a rate, Ω in the same direction as during the first delay. At the end of the second delay, the magnetization is on the y axis and the collection of the FID is started. It is important to note that the echo will always have its maximum at 2τ after the 90 degree pulse regardless of its offset, Ω or the duration of τ. The value of τ however is limited by the T₂.