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arXiv · 2508.17538

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

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·Markus Ilchen·Niclas Wieland·Günter Huber·James H. Edgar·Jörg Evers·Olga Kocharovskaya·Ralf Röhlsberger·Yuri Shvyd'ko
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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.

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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, Markus Ilchen, Niclas Wieland, Günter Huber, James H. Edgar, Jörg Evers, Olga Kocharovskaya, Ralf Röhlsberger, Yuri Shvyd'ko. 2025-08-24. Probing the Linewidth of the 12.4-keV Solid-State $^{45}$Sc Isomeric Resonance. https://arxiv.org/abs/2508.17538

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