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

arXiv:2508.17538v3 Announce Type: replace 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 $\Gamma_{\ind{0}}\simeq 1.4$~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 $\Delta\Gamma \gtrsim 500\,\Gamma_{\ind{0}}$. 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.

Authors:Peifan Liu, Miriam Gerharz, Berit Marx-Glowna, Willi Hippler, Jan-Etienne Pudell, Alexey Zozulya, Brandon Stone, Deming Shu, Robert Loetzsch, Sakshath Sadashivaiah, Lars Bocklage, Christina Boemer, Shan Liu, Vitaly Kocharyan, Dietrich Krebs, Tianyun Long, Weilun Qin, Matthias Scholz, Kai Schlage, Ilya Sergeev, Hans-Christian Wille, Ulrike Boesenberg, Gianluca Aldo Geloni, Jörg Hallmann, Wonhyuk Jo, Naresh Kujala, Anders Madsen, Angel Rodriguez-Fernandez, Rustam Rysov, Kelin Tasca, Tomasz Kolodziej, Xiwen Zhang, Niclas Wieland, Günter Huber, James H. Edgar, Jörg Evers, Olga Kocharovskaya, Ralf Röhlsberger, Yuri Shvyd'ko

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 $\Gamma_{\ind{0}}\simeq 1.4$~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 $\Delta\Gamma \gtrsim 500\,\Gamma_{\ind{0}}$. 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.

Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other); Nuclear Experiment (nucl-ex); Optics (physics.optics)

arXiv:2508.17538 [quant-ph]

(or arXiv:2508.17538v3 [quant-ph] for this version)

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

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