A tuning fork cut from a perfect metal rings at a single frequency. Its sound is as pure as a mathematical formula. But clamp it in a vise or dip it in a viscous liquid, and the tone smears, picks up noise, and loses its sharpness. The nucleus of scandium-45 behaves much the same way when placed in a crystal lattice. In a free state, the transition between the ground state and the isomer with an energy of 12.4 keV has a natural linewidth of just 1.4 femtoelectronvolts. This means the resonance is incredibly narrow: its quality factor (the ratio of the transition energy to the linewidth) reaches $10^{19}$. If a ruler had such precision, you could measure the distance from Earth to the Sun with an error of one atom.

But in a real crystal, the ideal tuning fork is muffled. Inhomogeneous broadening, the spread of resonance frequencies due to defects, impurities, and local fields, smears the line. Until now, no one knew how much. The experiment at the European XFEL provided the first quantitative answer. The X-ray laser excited scandium-45 nuclei in a metal foil and in crystals of Sc, ScN, Sc2O3, and ScAlMgO4 at a temperature of 20 K. Detectors tracked photons emitted with delays from microseconds to hundreds of milliseconds. A separate gated detector looked for coherent forward scattering, the synchronous re-emission of photons in the same direction that occurs when nuclei oscillate in concert, like the strings of an orchestra.

There was no signal. After a 2-millisecond delay, coherent forward scattering was absent at any setting. This means the decoherence time is less than 2 ms, and the inhomogeneous broadening exceeds 500 natural widths. In other words, the crystalline environment smears the resonance hundreds of times more than the fundamental limit. Simulations confirmed that with such broadening, the expected signal is at the limit of the setup's sensitivity.

But all is not lost. For the first time, elastic scattering at the transition energy of 12.4 keV was observed with a signal-to-noise ratio of about 4. From the ratio of the count rates in the elastic channel and fluorescence, the partial internal conversion coefficient for the K-shell was obtained: 390(60), which agrees with the theoretical value of 363. This indicates that the nuclear transition is indeed excited and decays, but coherence is quickly destroyed. Before this work, it was unknown whether coherent forward scattering from this isomer in a crystal could be observed at all. Now it is clear: in the materials studied, no, the broadening is too large.

The result outlines boundaries for future solid-state nuclear clocks. To make the tuning fork ring pure, crystals with cubic symmetry, a minimum of defects, and protection from radiation damage are needed. Perhaps methods of dynamic line narrowing using radio-frequency fields will help. If coherent forward scattering can be observed, it would open the way to femtoelectronvolt spectroscopy in the hard X-ray range and to the selection of optimal matrices for nuclear clocks. For now, scandium-45 in simple crystals resembles a tuning fork clamped in a vise: its tone is still audible, but the purity is lost.