Thorium Breakthrough Paves Way for Ultra-Precise Atomic Clocks and Sensors

Researchers are tackling the longstanding challenge of efficiently producing thorium-229m, a nuclear isomer with immense potential for applications in nuclear clocks and precision metrology. Yumiao Wang, Yi Yang, Yixin Li, and colleagues from the Key Laboratory of Nuclear Physics and Ion-beam Application at Fudan University, alongside Ding Yue, Kai Zhao, and Youjing Wang, demonstrate a novel scheme utilising storage rings and electron beam ion traps to significantly enhance the yield of this elusive isotope. Their calculations reveal that employing cascade decay pathways via nuclear excitation by inelastic electron scattering and nuclear excitation by electron capture can boost production rates by up to four orders of magnitude, representing a crucial step towards realising the full potential of thorium-229m in emerging fields such as nuclear photonics and atomic nuclear clocks. Efficient and controllable generation of this isotope has long presented a major experimental hurdle, but new research details an optimised scheme utilising storage rings and electron beam ion traps to dramatically enhance production rates. Calculations demonstrate that indirect excitation pathways, leveraging nuclear excitation by inelastic electron scattering (NEIES) and nuclear excitation by electron capture (NEEC), can boost the yield of thorium-229m substantially. Specifically, NEIES offers a potential enhancement of up to four orders of magnitude through cascade de-excitation at high energies, while NEEC contributes an additional increase of several tens of times. This work proposes a cascade decay pathway where highly charged thorium ions are excited to higher nuclear states via NEIES and NEEC, followed by radiative or internal conversion cascades that ultimately populate the isomeric state. The research focuses on optimising these indirect excitation pathways under conditions typical of storage rings and electron beam ion traps, revealing significant improvements in thorium-229m production. By carefully selecting excitation schemes to higher energy levels, researchers have identified a method to optimise isomer yield, potentially surpassing the efficiency of direct excitation techniques. This approach leverages the relatively large nuclear transition probabilities of higher-lying states within thorium-229, enabling a more effective population of the desired isomeric state. The theoretical investigation calculates NEIES and NEEC cross sections, excitation rates, and their dependence on crucial parameters such as electron energy, ion charge state, and electronic configuration. These calculations provide quantitative guidance for optimising isomer production and informing the design of future experiments. The study details how the NEIES process occurs when electron energy exceeds the excitation threshold, while NEEC can be resonantly induced, offering precise control over the excitation process. Such a substantial increase in the thorium-229m yield rate promises to facilitate its application in diverse nuclear photonics fields, most notably in the development of highly accurate atomic nuclear clocks and advanced precision metrology tools. Theoretical modelling of thoriated isomer production via electron interactions requires detailed cross-section calculations A 72-qubit superconducting processor forms the foundation of this work, utilizing inelastic electron scattering (NEIES) and electron capture (NEEC) to enhance the production of the \textsuperscript{229m}Th nuclear isomer. Calculations were performed to demonstrate that optimized indirect excitation pathways significantly enhance the \textsuperscript{229m}Th production rate within storage rings (SRs) and electron beam ion traps (EBITs). Specifically, NEIES can provide an enhancement of up to four orders of magnitude through cascade de-excitation at high energies, while NEEC contributes an additional enhancement of up to several tens of times. The theoretical framework calculates NEIES and NEEC cross sections, excitation rates, and their dependence on electron energy, charge state, and electronic configuration. These calculations provide quantitative guidance for optimizing isomer production and informing the design of future nuclear-clock and NEEC experiments. Electronic wave functions were computed using the RADIAL package within the Dirac-Hartree-Fock-Slater framework, incorporating nuclear, direct electronic, and exchange contributions to define the underlying electron potential. The NEIES cross section is expressed as σNEIES(Ei) = 8π²c⁴Ei + c²p³iEf + c²pf × XT,λk²λ+2(2λ −1).2B(Tλ, Ji →Jf) × Xli,ji,lf,jf(2li + 1)(2lf + 1)(2ji + 1)(2jf + 1)(2λ + 1)² × lf li λ 0 0 0 2 li λ lf jf 1/2 ji 2 RT λ fi 2, where subscripts denote initial and final electronic states. Radial transition matrix elements, REλ fi for electric transitions and RMλ fi for magnetic transitions, were calculated using spherical Hankel functions and radial components of the Dirac wave functions. These elements measure the overlap between initial and final electronic Dirac wave functions, representing the electronic contribution to the interaction between the electron and the nucleus. The selected excitation scheme utilizes cascade decay to the \textsuperscript{229}Th isomeric state, leveraging relatively large nuclear transition probabilities of higher-lying states as determined by a projected shell model. This cascade approach optimizes isomer yield and achieves significantly higher efficiency compared to direct excitation methods. Enhanced thorium-229m production via inelastic and electron capture excitations represents a significant advancement in nuclear science Calculations demonstrate that nuclear excitation by inelastic electron scattering (NEIES) can enhance the production rate of thorium-229m by up to four orders of magnitude through cascade de-excitation at high energies. Furthermore, nuclear excitation by electron capture (NEEC) contributes an additional enhancement of up to several tens of times under typical storage ring and electron beam conditions. These significant increases in the yield rate of thorium-229m would facilitate its application in nuclear photonics, particularly in the development of atomic nuclear clocks. The detailed calculations of both NEIES and NEEC cross sections were performed utilising previously established frameworks, with the final expression for the NEIES cross section presented as σNEIES(Ei) = 8π²c⁴Ei + c²p³iEf + c²pf × a complex factor dependent on nuclear and electronic states. This equation incorporates the incident and outgoing electron energies, momenta, and the reduced nuclear transition probability, alongside sums accounting for angular momentum couplings and radial transition matrix elements. The formalism is also applicable to the NEEC process, allowing for comprehensive modelling of isomeric production. For electric transitions, the radial transition matrix element REλfi is calculated as Z∞0 h(1)λ(kr) [gi(r)gf(r) + fi(r)ff(r)] r²dr, while for magnetic transitions, RMλfi = κi + κf λ × Z∞0 h(1)λ(kr) [gi(r)ff(r) + gf(r)fi(r)] r²dr. These calculations employ Dirac wave functions computed using the RADIAL package, with the underlying electron potential determined within the Dirac-Hartree-Fock-Slater framework. The electron flux Φe(Ei) is modelled as a Gaussian distribution, Φe(Ei) = Ie eAeεe √π exp ” − Ei −Eir εe 2#, where Ie = eneve represents the electron beam current and εe is the electron beam energy spread. The NEEC cross section is expressed as σNEEC(Ei) = 8π³c²Ei + c²p³i × a factor dependent on nuclear transitions, and the resonance strength is calculated as SNEEC = Z dEiσNEEC (Ei). The excitation rate for a given channel is determined by λNEIES/NEEC = Z dEiσNEIES/NEEC(Ei)Φe(Ei), and in the case of NEEC, the rate can be expressed as λNEEC = SNEECΦe(Er) within the resonance approximation. The natural width of the resonant state, ΓNEEC, comprises the width of the final electronic state and the nuclear decay width, including both γ-decay and internal conversion contributions. Enhanced Thorium-229m Production via Indirect Excitation Pathways and Electron-Beam Techniques offers promising avenues for advanced research applications Researchers have developed an efficient scheme for producing thorium-229m, a low-energy nuclear isomer with potential applications in nuclear clocks and precision metrology. Current production methods present significant experimental challenges, but calculations indicate substantial enhancements are achievable using storage rings and electron beam ion traps. Specifically, indirect excitation pathways involving nuclear excitation by inelastic electron scattering and nuclear excitation by electron capture offer considerable improvements over direct excitation techniques. Calculations demonstrate that utilising cascade de-excitation at high energies via nuclear excitation by inelastic electron scattering can enhance thorium-229m production by up to four orders of magnitude. Furthermore, incorporating nuclear excitation by electron capture, particularly with a dual-electron-beam configuration, can provide an additional increase in yield of several tens of times. These enhancements stem from the optimised indirect excitation pathways, with the sixth excited state exhibiting the largest increase, reaching approximately a factor of 80. Simulations using a charge-breeding code, ebitsim, model the population dynamics of ionic charge states within the electron beam ion trap, accounting for processes like electron-impact ionization and radiative recombination. The authors acknowledge that the presented calculations rely on specific parameters for the storage ring and electron beam ion trap environments, and variations in these parameters could affect the predicted yield rates. Future research should focus on experimental validation of these theoretical predictions and optimisation of the excitation schemes. Successful implementation of these techniques would significantly increase the availability of thorium-229m, thereby facilitating advancements in nuclear photonics and the development of highly precise atomic nuclear clocks. 👉 More information 🗞 Enhanced Yield Rate of \textsuperscript{229m}Th via Cascade Decay in Storage Rings and Electron Beam Ion Traps 🧠 ArXiv: https://arxiv.org/abs/2601.22417 Tags: