Spectral Flux Enhancement of X Rays for Addressing Ultra Narrow Nuclear Transitions

Recently, the 1.4 feV ultranarrow nuclear transition at 12.4 keV energy in 45Sc was resonantly excited for the first time using radiation from the self-seeded EuXFEL laser [Y. Shvyd’ko et al., Resonant x-ray excitation of the nuclear clock isomer 45Sc, Nature (London) 622, 471 (2023)], establishing 45Sc as a promising candidate for a future Mössbauer nuclear clock. While this experiment demonstrated a high potential of x-ray free-electron laser sources for resonantly exciting nuclear isomers in the hard x-ray range, it also highlighted a severe limitation in the achievable excitation level caused by their extremely large spectral bandwidth ∼1  eV. In this Letter, we propose a method to enhance the spectral flux of x-ray free-electron laser radiation using a resonant absorber with a longitudinal gradient in the nuclear transition frequency. A portion of the incident pulse can be absorbed into a nuclear collective excitation, and converted back into x-ray radiation by reversing the sign of the frequency gradient. Spectral narrowing and flux enhancement of this re-emitted x-ray field is achieved by using a reversed frequency gradient with a smaller magnitude than the initial one. About a hundredfold of such spectral flux enhancement is feasible in 45Sc2⁢O3 single crystal, rendering a more efficient source for nuclear excitation and facilitating the experimental observation of resonant fluorescence and coherent forward scattering at the 12.4 keV transition, both of which are essential for realizing a nuclear clock.