Probing the Linewidth of the 12.4-keV Solid-State $^{45}$Sc Isomeric Resonance

TL;DR

This study investigates the spectral width of the $^{45}$Sc nuclear resonance in solid state, revealing environmental broadening effects that limit the resonance's natural linewidth and informing future nuclear clock development.

Contribution

The paper provides the first experimental bounds on solid-state broadening of the $^{45}$Sc resonance, approaching the natural linewidth and setting benchmarks for nuclear clock research.

Findings

Confirmed the isomer's lifetime via fluorescence measurements

Observed elastic fluorescence and estimated internal conversion coefficient

Set bounds on environmental broadening of the resonance

Abstract

The $^{45}$Sc nuclear transition from the ground to the isomeric state at 12.389~keV, with a lifetime of 0.46~s, exhibits an extraordinarily narrow natural width of 1.4~feV and a quality factor $\simeq 10^{19}$ -- surpassing those of the most precise atomic clocks -- making $^{45}$Sc a compelling platform for advanced metrology and nuclear clocks. Here we investigate how closely the spectral width and quality factor of the solid-state $^{45}$Sc resonance can approach these natural limits. Using the European X-ray Free-Electron Laser, we confirm the isomer's lifetime via time-delayed incoherent $K_{\alpha,\beta}$ fluorescence and observe previously unreported elastic fluorescence, yielding a partial internal conversion coefficient of 390(60). The absence of a clear nuclear forward scattering signal beyond a 2-ms delay implies environmental broadening of at least $500~\Gamma_{0}$ under experimental conditions, placing bounds on solid-state decoherence mechanisms. These findings set new experimental benchmarks for solid-state nuclear clock development.