Probing the Linewidth of the 12.4-keV ${}^{45}$Sc Isomeric Resonance in Solids by Nuclear Forward Scattering

Abstract

The ${}^{45}$Sc transition from the nuclear ground state to the 12.389-keV isomer (lifetime 0.46~s) has an ultranarrow natural linewidth $Γ_{\ind{0}}\simeq 1.4$~feV, corresponding to a quality factor $\simeq 10^{19}$. This makes ${}^{45}$Sc a compelling candidate for nuclear-clock metrology, provided that coherence in solids can be maintained close to the natural limit. Here we investigate the linewidth and coherence properties of the ${}^{45}$Sc resonance in solids following resonant x-ray pumping. Using the European XFEL, we confirm persistence of the long-lived isomer excitation in a solid-state environment via time-delayed incoherent $K_{\alpha ,\beta }$ emission and observe a weak delayed elastic channel at 12.4~keV, from which we extract a partial internal-conversion coefficient ${\alpha }_K=390(60)$. Time-domain nuclear forward scattering measurements in crystals of Sc, Sc${}_2$O${}_3$, ScN and ScAlMgO${}_4$ at 20~K show no statistically significant coherent forward-scattering signal beyond $2$~ms; within the adopted linewidth-broadening model, we infer an effective broadening $ΔΓ\gtrsim 500\,Γ_{\ind{0}}$. These results provide the quantitative constraints on linewidth broadening in solid-state ${}^{45}$Sc with an intrinsic natural linewidth in the femto-electronvolt range thereby laying the groundwork for precision metrology in the X-ray regime and future nuclear-clock frequency references using ${}^{45}$Sc nuclear isomer.

arXiv comment11 pages, 4 figures, 2 tables