How to tell when a nucleus is in resonance

First, bring the molecules back to a detector

In 1938, Rabi, Zacharias, Millman and Kusch sent a molecular beam through two deflecting magnetic fields. Properly adjusted, the apparatus refocused selected molecules onto a detector. In the uniform field between the deflecting regions, they added a weak oscillating magnetic field. At resonance, some molecules changed their internal magnetic state. The second magnet then sent them along a different path, and fewer reached the detector.

Their letter used lithium chloride as an example. With the radio frequency fixed, they scanned the static field and plotted beam intensity against magnet current. Resonance appeared as a dip. The authors deferred final magnetic-moment values until the field was recalibrated: identifying a resonance was the start of the measurement.

Read the evidence: I. I. Rabi, J. R. Zacharias, S. Millman and P. Kusch (1938), A New Method of Measuring Nuclear Magnetic Moment, Phys. Rev. 53, 318 — original scan

A nucleus has a natural rhythm in a field

A nucleus with a magnetic moment precesses in a static field. A spinning top offers a first picture: its tilted axis circles around the vertical. Nuclear precession has a characteristic frequency. An oscillating field with the right rhythm can drive changes between the internal magnetic states.

In the simplest case, this frequency is proportional to the static field. In the equation, B is that field, and the gyromagnetic ratio describes the response of the nucleus. Ordinary frequency counts cycles per second; angular frequency counts radians per second. Chemical surroundings and nearby magnetic moments can shift or split the simple resonance and need attention in a real sample.

\omega_{\mathrm L}=|\gamma|B_0=2\pi\nu_{\mathrm L}

Read the evidence: I. I. Rabi, J. R. Zacharias, S. Millman and P. Kusch (1938), A New Method of Measuring Nuclear Magnetic Moment, Phys. Rev. 53, 318 — original scan E. M. Purcell, H. C. Torrey and R. V. Pound (1946), Resonance Absorption by Nuclear Magnetic Moments in a Solid, Phys. Rev. 69, 37–38 F. Bloch, W. W. Hansen and M. Packard (1946), Nuclear Induction, Phys. Rev. 69, 127

Replace the beam with a piece of paraffin

In 1946, Purcell, Torrey and Pound used a different sample and detector. They placed proton-containing paraffin in a radio-frequency resonator and monitored absorption with a balanced circuit. Scanning the static magnetic field through resonance caused a marked change in its output. The detectable effect had become energy lost from the radio-frequency circuit.

At room temperature, the populations of the two spin states differ only slightly. A small excess in the lower-energy state makes absorption outweigh stimulated emission. Strong driving tends to equalize the populations and saturate the signal. The surroundings restore the imbalance through relaxation. The observed absorption reflects both the driving and that recovery.

Read the evidence: E. M. Purcell, H. C. Torrey and R. V. Pound (1946), Resonance Absorption by Nuclear Magnetic Moments in a Solid, Phys. Rev. 69, 37–38

Protons in water produce an induced voltage

Also in 1946, Bloch, Hansen and Packard studied water at room temperature. A transverse oscillating field drove the nuclei. Their magnetic moments added up to a macroscopic magnetization, whose motion induced a voltage in a pickup coil. The team compared resonance fields at two driving frequencies and checked the result against earlier proton magnetic measurements.

This early observation used a continuous driving field. A later method applies a short radio-frequency pulse, then listens to the sample’s decaying induced signal, called free induction decay. It is useful to keep those operations and their dates distinct as the technique develops.

Read the evidence: F. Bloch, W. W. Hansen and M. Packard (1946), Nuclear Induction, Phys. Rev. 69, 127

One resonance, several ways to detect it

All three experiments connected resonance frequency with magnetic field. Their detectors reported different things: the number of molecules, radio-frequency absorption and an induced voltage. Rabi received the 1944 prize; Bloch and Purcell shared the 1952 prize. The methods made a tiny nuclear magnetic response accessible through repeatable scans.

Turning a signal into a magnetic moment also required the field actually experienced by the sample, together with treatment of line width, local surroundings and drive strength. Medical magnetic-resonance imaging builds on nuclear signals and adds spatial gradients and reconstruction to locate their source. That spatial encoding was a further development beyond these early resonance measurements.