Stimulated Emission

When a group of spins is driven into higher energy levels by the action of an RF field, why don't these spins immediately release the absorbed energy and drop back to their original lower energy states?  

  

Long before the discovery of NMR, Albert Einstein developed a quantum mechanical description of the emission of energy from atomic systems.  Since NMR relaxation ultimately involves a release of energy from the spin system, the Einstein formulation applies equally well to NMR.  According to Einstein's analysis, emission of energy from an atomic system may be either spontaneous or induced (stimulated).  
Spontaneous emission of energy is a radiative process involving the release of a photon and typified by phenomena such as fluorescence and phosphorescence.  Einstein showed that the probability of spontaneous emission is strongly frequency-dependent (proportional to f³).  In the visible region of the spectrum, f ≈ 10¹² Hz, and spontaneous emission is a dominant process.  In the radiofrequency range where NMR energies are found, however, f ≈ 100 MHz, and so spontaneous emission becomes extremely improbable.

Here is another way to think about this concept: The energy gap between the spin-up and spin-down states in NMR is really quite small by atomic emission standards — at 1.5T it is only about 2 x 10⁻⁷ eV (electron-volts). By comparison, visible light photons have energies of about 2 eV, or 10 million times higher. There is thus a considerable "advantage" for a high-energy light photon to be emitted by phosphorescence, but relatively little "motivation" for an already low energy nuclear spin to switch states spontaneously.

(Based on drawing by glitterweazl at drawception.com)

Most energy emission in NMR must be induced through a direct interaction of a nucleus with its external environment.  This interaction may be through the electrical or magnetic fields generated by other nuclei, electrons, or molecules, or result from interaction with the with the RF coil and field.

Advanced Discussion (show/hide)»

From Einstein's theory, the probability (P) of spontaneous energy emission of an ensemble of N spin-1/2 magnetic moments in free space is given by

where μ_o is the permeability of free space, ω is the angular frequency, γ is the gyromagnetic ratio, h is Planck's constant, and c is the speed of light. For 1 ml of water at 1 T this translates into spontaneous emission of only 0.024 photons per second, an extremely low number.

As described by Bloembergen, Pound, Dicke, and Tropp in their papers below, the probability of spontaneous emission can be increased many thousand-fold resulting in a coherently “super-radiant” state. This occurs under two conditions: 1) when phase coherence exists between individual proton spins (such as after RF-stimulation when the net magnetization has transverse components), and 2) when the spins interact with a tuned RF-coil serving as a cavity resonator in a process called radiation damping.

There remains some controversy about the nature of this spontaneous emission, however, and as yet no complete quantum mechanical formulation has been established, as outlined in the paper by David Hoult below.

A more complete and final answer will await a fully worked out quantum theory of near field radiation effects, likely arising from the discipline of cavity quantum electrodynamics (CQED) - far beyond my current or future brain capacity to comprehend!

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References
     Bloembergen N, Pound RV. Radiation damping in magnetic resonance experiments. Phys Rev 1954; 95:8-12. (description of spontaneous emission and thermal relaxation mechanisms)   
     Dicke RH. Coherence in spontaneous radiation processes. Phys Rev 1954; 93:99-110.
     Hoult DI. The origins and present status of the radio wave controversy in NMR. Concepts Magn Reson Part A 2009; 34A:193-216. (controversial paper that disputes Dicke's calculations and idea of radio wave emission in NMR)
     Tropp JS. A fully quantum mechanical theory of radiation damping and the free-induction decay in magnetic resonance. eMagRes 2016, 5:1077-1086.(excellent recent review getting closer to the final answer but not yet there.)

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Related Questions
     If a system seeks to minimize its total energy level, why don't all the protons simply fall into the lower energy state?  

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