Reevaluating NMR coupling. Magnetic resonance imaging, spectroscopy, and other applications of nuclear magnetic resonance rely on the sensitivity of nuclear spins to their magnetic environment. The spins couple not only to externally applied magnetic fields but also to the dipolar fields produced by other spins. The continuous motion of atoms and molecules in liquids and gases provides a constantly varying environment that averages out the dipolar fields of neighboring spins (top) and greatly simplifies experimental and theoretical analysis. The long-range couplings don’t average out so neatly (bottom), so the distant dipolar field is usually approximated as an additional applied field whose strength is proportional to the local magnetization. Though that approximation has been remarkably successful for decades, some straightforward experiments can produce results dramatically different from expectations. For example, a uniformly magnetized spherical sample has no dipole field, but tipping a trivially small fraction of the...

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