NMR in the Rotating Frame of Reference

In the absence of B, the vector M keeps its equilibrium value and position M0 in the z direction. M is thus time-invariant in the rotating frame of reference, so that 

If the frame rotates at the Larmor frequency u0 = 2 7t v0, the rotational field term of eq. (1.28) reaches co0jy. Since the effective field is zero, the Larmor equation (1.8 a) is obtained  

This means further that the rotational field cojy opposes B0 k in the rotating frame of reference (Fig. 1.6(a)), finally cancelling B0k when the coordinate system rotates at Larmor frequency co0. 

If an rf field Bl with cuj = 2 7t Vj is applied perpendicularly to B0 along the x axis, the effective field Beff in the frame of reference rotating at oj, is obtained from Fig. 1.6(a)  

If the frame of reference rotates at the radio frequency vx matching the 

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The third method involves a three pulse sequence, 90 — r — 180° — x — 90°, with a repetition time of tr s. This pulse sequence refocuses the magnetization vector M0 into its equilibrium position within the repetition time, thus representing a pulse driven relaxation acceleration. This technique, known as DEFT NMR [23, 24] (driven equilibrium Fourier transform NMR) can be understood by following the behavior of the magnetization vector Mq under the influence of the pulse sequence in the rotating frame of reference (Fig. 2.17(a-e)). 

Note that we use A v to refer to the rotating-frame frequency (sometimes called the resonance offset). This is the difference between the Larmor frequency and the reference frequency v0 - vr. The above equation shows that the same physical law expressed in the equation on the left-hand side (precession rate is proportional to y and to B0) is operating in the equation on the right-hand side (resonance offset is proportional to y and to fires) in the rotating frame of reference, as long as we introduce the pseudofield. In the NMR spectrum, A v is the distance from the center of the spectral window to the NMR peak (Fig. 6.2), also represented as 2 in units of radians per second. If the peak is in the downfield half (left half) of the spectrum, the Larmor frequency is greater than the reference frequency ( v0 > vr) and we have a positive resonance offset (A v > 0). This corresponds to the motion of the net magnetization... 

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