X-ray pumping of the 229Th nuclear clock isomer

Structures and Properties of High-Concentration Doped Th:CaF2 Single Crystals for Solid-State Nuclear Clock Materials

Thorium-doped vacuum ultraviolet (VUV) transparent crystals is a promising candidate for establishing a solid-state nuclear clock. Here, we report the research results on high-concentration doping of 232Th:CaF2 single crystals. The structures, defects, and VUV transmittance performances of highly doped Th:CaF2 crystals are investigated by theoretical and experimental methods. The defect configurations formed by Th and the charge compensation mechanism (Ca vacancy or interstitial F atoms) located at its first nearest neighbor position are mainly considered and studied. The preferred defect configuration is identified according to the doping concentration dependence of structural changes caused by the defects and the formation energies of the defects at different Ca or F chemical potentials. The cultivated Th:CaF2 crystals maintain considerable high VUV transmittance levels while accommodating high doping concentrations, showcasing an exceptional comprehensive performance. The transmittances of 1-mm-thick samples with doping concentrations of 1.91 × 1020 and 2.76 × 1020 cm-3 can reach ∼62% and 53% at 150 nm, respectively. The VUV transmittance exhibits a weak negative doping concentration dependence. The system factors that may cause distortion and additional deterioration of the VUV transmittance are discussed. Balancing and controlling the impacts of various factors will be of great significance for fully exploiting the advantages of Th:CaF2 and other Th-doped crystals for a solid-state nuclear optical clock.

Resonant X-ray excitation of the nuclear clock isomer 45Sc

Resonant oscillators with stable frequencies and large quality factors help us to keep track of time with high precision. Examples range from quartz crystal oscillators in wristwatches to atomic oscillators in atomic clocks, which are, at present, our most precise time measurement devices1. The search for more stable and convenient reference oscillators is continuing2-6. Nuclear oscillators are better than atomic oscillators because of their naturally higher quality factors and higher resilience against external perturbations7-9. One of the most promising cases is an ultra-narrow nuclear resonance transition in 45Sc between the ground state and the 12.4-keV isomeric state with a long lifetime of 0.47 s (ref. 10). The scientific potential of 45Sc was realized long ago, but applications require 45Sc resonant excitation, which in turn requires accelerator-driven, high-brightness X-ray sources11 that have become available only recently. Here we report on resonant X-ray excitation of the 45Sc isomeric state by irradiation of Sc-metal foil with 12.4-keV photon pulses from a state-of-the-art X-ray free-electron laser and subsequent detection of nuclear decay products. Simultaneously, the transition energy was determined as [Formula: see text] with an uncertainty that is two orders of magnitude smaller than the previously known values. These advancements enable the application of this isomer in extreme metrology, nuclear clock technology, ultra-high-precision spectroscopy and similar applications.

Observation of the radiative decay of the 229Th nuclear clock isomer

The radionuclide thorium-229 features an isomer with an exceptionally low excitation energy that enables direct laser manipulation of nuclear states. It constitutes one of the leading candidates for use in next-generation optical clocks^1-3. This nuclear clock will be a unique tool for precise tests of fundamental physics^4-9. Whereas indirect experimental evidence for the existence of such an extraordinary nuclear state is substantially older¹⁰, the proof of existence has been delivered only recently by observing the isomer's electron conversion decay¹¹. The isomer's excitation energy, nuclear spin and electromagnetic moments, the electron conversion lifetime and a refined energy of the isomer have been measured^12-16. In spite of recent progress, the isomer's radiative decay, a key ingredient for the development of a nuclear clock, remained unobserved. Here, we report the detection of the radiative decay of this low-energy isomer in thorium-229 (^229mTh). By performing vacuum-ultraviolet spectroscopy of ^229mTh incorporated into large-bandgap CaF₂ and MgF₂ crystals at the ISOLDE facility at CERN, photons of 8.338(24) eV are measured, in agreement with recent measurements^14-16 and the uncertainty is decreased by a factor of seven. The half-life of ^229mTh embedded in MgF₂ is determined to be 670(102) s. The observation of the radiative decay in a large-bandgap crystal has important consequences for the design of a future nuclear clock and the improved uncertainty of the energy eases the search for direct laser excitation of the atomic nucleus.

Isomeric Excitation of ^{229}Th in Laser-Heated Clusters

We consider theoretically isomeric excitation of ^{229}Th in a laser-heated cluster. A ^{229}Th cluster is first radiated by an intense femtosecond laser pulse, causing ionization of the constituting atoms. The cluster will then survive for a time on the order of 1 ps, during which the electrons collide with the nuclei repeatedly and excite them to the isomeric state. Two mechanisms are responsible for the isomeric excitation: nuclear excitation by electron capture (NEEC) and nuclear excitation by inelastic electron scattering (NEIES). By changing the laser intensity, one can tune between NEEC and NEIES continuously. This laser-heated-cluster scheme not only provides a highly efficient means for isomeric excitation, but also provides an approach for the confirmation of the NEEC process, which has been predicted for over forty years without conclusive experimental verifications.

Growth and characterization of thorium-doped calcium fluoride single crystals

We have grown [Formula: see text]Th:CaF[Formula: see text] and [Formula: see text]Th:CaF[Formula: see text] single crystals for investigations on the VUV laser-accessible first nuclear excited state of [Formula: see text]Th, with the aim of building a solid-state nuclear clock. To reach high doping concentrations despite the extreme scarcity (and radioactivity) of [Formula: see text]Th, we have scaled down the crystal volume by a factor 100 compared to established commercial or scientific growth processes. We use the vertical gradient freeze method on 3.2 mm diameter seed single crystals with a 2 mm drilled pocket, filled with a co-precipitated CaF[Formula: see text]:ThF[Formula: see text]:PbF[Formula: see text] powder in order to grow single crystals. Concentrations of [Formula: see text] cm[Formula: see text] have been realized with [Formula: see text]Th with good (> 10%) VUV transmission. However, the intrinsic radioactivity of [Formula: see text]Th drives radio-induced dissociation during growth and radiation damage after solidification. Both lead to a degradation of VUV transmission, currently limiting the [Formula: see text]Th concentration to [Formula: see text] cm[Formula: see text].

A robust thorium-organic framework as a bifunctional platform for iodine adsorption and Cr(VI) sensitization

Simple synthetic modulation based on thorium nitrate and tris((4-carboxyl)phenylduryl)amine (H₃TCBPA) gives rise to a new thorium-based metal-organic framework, Th-TCBPA, which features excellent hydrolytic and thermal stabilities. Incorporating electron-rich TCBPA^3- linkers not only endows Th-TCBPA with high adsorption capacity toward radioiodine vapor, but also makes it a luminescence sensor for the highly sensitive and selective detection of Cr(VI) anions.

Recent advances in the applications of thorium-based metal-organic frameworks and molecular clusters

This perspective highlights the recent advances in the structural and practical aspects of thorium-based metal-organic frameworks (Th-MOFs) and molecular clusters. Thorium, as an underexplored actinide, features surprisingly rich coordination geometries and accessibility of the 5f orbital. These features lead to a myriad of topologies and electronic structures, many of which are undocumented for other tetravalent metal-containing MOFs or clusters. Moreover, Th-MOFs inherit the modularity, structural tunability, porosity, and versatile functionality of the state-of-the-art MOFs. Recognizing the radioactive nature of these thorium-bearing materials that may limit their practical uses, Th-MOFs and Th-clusters still have great potential for various applications, including radionuclide sequestration, hydrocarbon storage/separation, radiation detection, photoswitch, CO₂ conversion, photocatalysis, and electrocatalysis. The objective of this updated perspective is to propose pathways for the renaissance of interest in thorium-based materials.

Sensitivity of Neutron-Rich Nuclear Isomer Behavior to Uncertainties in Direct Transitions

Nuclear isomers are populated in the rapid neutron capture process (r process) of nucleosynthesis. The r process may cover a wide range of temperatures, potentially starting from several tens of GK (several MeV) and then cooling as material is ejected from the event. As the r-process environment cools, isomers can freeze out of thermal equilibrium or be directly populated as astrophysically metastable isomers (astromers). Astromers can undergo reactions and decays at rates very different from the ground state, so they may need to be treated independently in nucleosythesis simulations. Two key behaviors of astromers—ground state ↔ isomer transition rates and thermalization temperatures—are determined by direct transition rates between pairs of nuclear states. We perform a sensitivity study to constrain the effects of unknown transitions on astromer behavior. Detailed balance ensures that ground → isomer and isomer → ground transitions are symmetric, so unknown transitions are equally impactful in both directions. We also introduce a categorization of astromers that describes their potential effects in hot environments. We provide a table of neutron-rich isomers that includes the astromer type, thermalization temperature, and key unmeasured transition rates.

Exciting the Isomeric ^{229}Th Nuclear State via Laser-Driven Electron Recollision

We propose a new approach to excite the isomeric ^{229}Th nuclear state, which has attracted much attention recently as a potential "nuclear clock." Our approach is based on a laser-driven electron recollision process, the core process of strong-field atomic physics. Bringing together knowledge of recollision physics and of the related nuclear physics, we calculate the isomeric excitation probability. This new approach does not require precise knowledge of the energy of the isomeric state. The excitation is well timed which may be exploited to control the coherence of the isomeric state. Experimental realization is within reach using tabletop laser systems.

Absolute X-ray energy measurement using a high-accuracy angle encoder

This paper presents an absolute X-ray photon energy measurement method that uses a Bond diffractometer. The proposed system enables the prompt and rapid in situ measurement of photon energies over a wide energy range. The diffractometer uses a reference silicon single-crystal plate and a highly accurate angle encoder called SelfA. The performance of the system is evaluated by repeatedly measuring the energy of the first excited state of the potassium-40 nuclide. The excitation energy is determined as 29829.39 (6) eV, and this is one order of magnitude more accurate than the previous measurement. The estimated uncertainty of the photon energy measurement was 0.7 p.p.m. as a standard deviation and the maximum observed deviation was 2 p.p.m.

Measurement of the ^{229}Th Isomer Energy with a Magnetic Microcalorimeter

We present a measurement of the low-energy (0-60 keV) γ-ray spectrum produced in the α decay of ^{233}U using a dedicated cryogenic magnetic microcalorimeter. The energy resolution of ∼10  eV, together with exceptional gain linearity, allows us to determine the energy of the low-lying isomeric state in ^{229}Th using four complementary evaluation schemes. The most precise scheme determines the ^{229}Th isomer energy to be 8.10(17) eV, corresponding to 153.1(32) nm, superseding in precision previous values based on γ spectroscopy, and agreeing with a recent measurement based on internal conversion electrons. We also measure branching ratios of the relevant excited states to be b_{29}=9.3(6)% and b_{42}<0.7%.

DFT calculation of 229thorium-doped magnesium fluoride for nuclear laser spectroscopy

The ²²⁹thorium nucleus has an extremely low-energy isomeric state that could be manipulated with light in the vacuum ultraviolet (VUV) range. Recent measurements based on internal conversion electrons place the isomer energy at 8.28(17) eV (Seiferle B et al 2019), within the transmission window of large-band-gap materials, such as fluoride single crystals. Doping ²²⁹Th into VUV-transparent materials realizes a spectroscopy target with a high nuclei density and might form the basis of a solid-state nuclear clock. This paper presents a theoretical study of the optical properties of a thorium-doped MgF₂ crystal. Using the Vienna Ab-initio Simulation Package, we perform density functional theory calculations of the electronic and optical properties of Th:MgF₂. We determine whether thorium will be accepted as a dopant and identify the charge compensation mechanism and geometry. The simulations indicate, that the band gap of Th-doped MgF₂ will be significantly reduced compared to undoped MgF₂, below the expected ²²⁹Th isomer energy. This result is in striking contrast to a similar study performed for Th-doped CaF₂ (Dessovic P et al 2014 J. Phys. Condens. Matter 26 105402).

Electronic Bridge Excitation in Highly Charged ^{229}Th Ions

The excitation of the 8 eV ^{229m}Th isomer through the electronic bridge mechanism in highly charged ions is investigated theoretically. By exploiting the rich level scheme of open 4f orbitals and the robustness of highly charged ions against photoionization, a pulsed high-intensity optical laser can be used to efficiently drive the nuclear transition by coupling it to the electronic shell. We show how to implement a promising electronic bridge scheme in an electron beam ion trap starting from a metastable electronic state. This setup would avoid the need for a tunable vacuum ultraviolet laser. Based on our theoretical predictions, determining the isomer energy with an uncertainty of 10^{-5}  eV could be achieved in one day of measurement time using realistic laser parameters.

Energy of the ^{229}Th Nuclear Clock Isomer Determined by Absolute γ-ray Energy Difference

The low-lying isomeric state of ^{229}Th provides unique opportunities for high-resolution laser spectroscopy of the atomic nucleus. We determine the energy of this isomeric state by taking the absolute energy difference between the excitation energy required to populate the 29.2-keV state from the ground state and the energy emitted in its decay to the isomeric excited state. A transition-edge sensor microcalorimeter was used to measure the absolute energy of the 29.2-keV γ ray. Together with the cross-band transition energy (29.2  keV→ground) and the branching ratio of the 29.2-keV state measured in a recent study, the isomer energy was determined to be 8.30±0.92  eV. Our result is in agreement with the latest measurements based on different experimental techniques, which further confirms that the isomeric state of ^{229}Th is in the laser-accessible vacuum ultraviolet range.