written by David B. Pengra

Understanding the physics of pulsed nuclear magnetic resonance (NMR) is eased by a transformation to a rotating reference frame. Within such a frame, coincident with the applied RF H₁ field that rotates about the static H0 field, the net effective magnetic field is static, and the dynamics of spin precession yield to simple geometric analysis. In most treatments of NMR the resonant frame, defined by the Larmor frequency ω₀ = γH₀, is used. In this frame the effective field reduces to H1 only, and one can immediately derive the pulse widths needed to optimize the free induction decay (FID) signals--the so-called π/2 and 3π/2 pulses. But what happens in a frame that is off resonance? The same geometrical analysis shows that as the frequency of H₁ is detuned from resonance, (1) the pulse width needed to maximize the FID signal increases for "π/2" pulses and decreases for "3π/2" pulses, (2) at a critical value of detuning, the widths of both pulses converge to p2 times the width of the on-resonance π/2 pulse, (3) this critical detuning is equal to the Larmor frequency of H₁, and (4) the maximum amplitude the FID signal is unchanged as long as the detuning is less than the critical value. Detuning further causes the optimum pulse width to decrease and the magnitude of the FID signal to drop. This experiment helps students explore a wider range of predictions inherent in the classical model of NMR, and it can be performed on the popular TeachSpin PS1 apparatus with no extra equipment.

• Download BFY2015_Pengra.pdf - 1757kb Adobe PDF Document

Published November 17, 2015
Last Modified November 19, 2015

This file is included in the full-text index.
This file has previous versions.