Internal Conversion in ThO2: The Key to Solid-State Nuclear Clocks ✛ ✎ ✦
Context
The low-energy nuclear spectroscopic transition in the thorium-229 isotope, with a unique excitation energy of about 8.35 eV comparable to electronic transitions in solids, attracts attention due to the prospect of creating nuclear clocks with unprecedented precision. Such clocks could become tools for testing the Standard Model and searching for dark matter. The phenomenon of internal conversion (IC), discovered by Lise Meitner, where nuclear energy is transferred to an electron, can compete with radiation in a solid-state environment, affecting clock performance. Understanding and controlling this process is critical for developing practical devices.
Methods
To calculate the IC rate, the authors applied a first-principles method using the full-potential linearized augmented plane-wave method with local orbitals (FP-LAPW+lo), implemented in the Elk code. This approach allows an accurate description of the electronic wave functions near the thorium nucleus, where the hyperfine interaction is localized, described by Maxwell's equations. The M1 transition matrix elements were computed directly from Bloch spinors including spin-orbit coupling, and the IC rate was determined using Fermi's golden rule by Fermi. To account for the finite nuclear size effect — the effect by Bohr–Weisskopf — a uniformly magnetized sphere model was used. The energy band gap was adjusted by a rigid shift to cover the range of experimental values.
Results
The calculated IC lifetimes range from 1 to 16 microseconds depending on the assumed band gap of ThO2 (5.2–7 eV). As the band gap increases, the lifetime sharply rises because the number of accessible interband transitions with an energy of 8.35 eV decreases. For gaps of 6–7 eV, the calculated lifetime is comparable to the experimentally measured value using Mössbauer spectroscopy of conversion electrons — 12.3(3) μs. The analysis showed that the dominant contribution to the rate comes from transitions involving thorium p-states, rather than f-states as might be expected.
Implications
The work demonstrates that internal conversion in solid-state systems is not a universal constant but is determined by the local electronic environment of the nucleus. This means that by choosing a material with a suitable band structure, the IC channel can be purposefully suppressed or enhanced. For nuclear clocks, this opens the way to creating systems with an isomer lifetime of hundreds of microseconds, which would allow readout via conversion electrons without significant line broadening.
Future development
Further development of the topic involves accounting for excitonic effects and a more accurate description of the electronic spectrum within many-body theory. It is also necessary to investigate other solid-state matrices, particularly thorium compounds with no nuclear spins on the ligands, to avoid magnetic dipole broadening. Preliminary calculations indicate the promise of materials such as sulfates, where the band gap can be just below 8.35 eV, providing an optimal balance between decay rate and lifetime.
Impact
The results will impact the development of quantum sensors and high-precision clocks, as well as experiments searching for dark matter and testing the constancy of fundamental constants.
Next steps
The immediate plans include calculations with excitonic correlations at the level of the Bethe-Salpeter equation and modeling of defect configurations typical of real experimental samples.
Key open problems
The research is directly connected to two big unsolved problems in physics: the nature of dark matter and the possible variation of fundamental constants, which can be tested using solid-state nuclear clocks.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
This work presents a first-principles calculation of the internal conversion rate for the Th-229 nuclear transition in a ThO2 crystal. It is shown that the isomer lifetime strongly depends on the band gap of the material and lies in the range of 1–16 μs, with the dominant contribution coming from thorium p-states.
Where its strength is
A quantitative link has been established between the band structure of the solid-state environment and the rate of nonradiative nuclear relaxation, turning internal conversion into a tunable parameter rather than a fixed constant.
Where it could go next
- Alternative host materials could be explored: our archive contains a study discussing nuclear state readout via conversion electrons, and extending the approach to other crystals might help optimize this process.based on: A Mousetrap in the Atomic Nucleus: Reading Thorium with Ejected Electrons arXiv:2506.03018v1
- It would be interesting to compare the obtained lifetimes with the requirements for detecting single conversion electrons in a realistic nuclear clock scheme—there is a related discussion on how faster readout could improve stability.based on: How to Speed Up Nuclear Clocks a Thousandfold arXiv:2606.00748
Worth trying
- Investigate whether the predicted lifetime dependence on the band gap holds when temperature effects and crystal lattice defects are taken into account.
- Assess whether an external electric field could be used to dynamically control the internal conversion rate by modulating the band structure near the nucleus.
Why this may matter
Controlling the internal conversion channel through matrix selection paves the way for solid-state nuclear clocks with isomer lifetimes optimized for specific readout schemes, potentially simplifying design and enhancing precision.
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The archive is crowded around this work: 5 reviews nearby, closest at 0.71. This ground is well walked — and there is plenty to compare against.
The thorium-229 isomer has the lowest known nuclear excitation energy — just 8.35 eV, slightly more than the energy of a visible light photon. Theoretically, it could be made to emit radiation by simply heating the sample to several thousand degrees or illuminating it with a powerful laser.
Key numbers
- nuclear transition energy of 229mTh: 8.35 eV
- experimental IC lifetime in ThO2: 12.3 μs
- calculated IC lifetime (range): 1–16 μs
- band gap of ThO2 (PBE): 4.31 eV
- thorium nucleus radius (model): 5.733 fm