AI 中文总结
该研究对$^{229}$ThO₂中特定同质异能跃迁带间内转换率进行从头算，通过特定方法计算，考虑相关效应并经剪刀移位处理，得出内转换寿命范围，发现其与带隙关系，为优化固态核时钟性能提供依据。
AI 中文摘要
我们对$^{229}$ThO₂中$\hbar\omega_{\rm nuc} \approx 8.35$ eV同质异能跃迁的带间内转换率进行了从头算计算。由于核跃迁能量超过ThO₂的电子带隙，同质异能素可通过将价电子共振激发到导带而进行非辐射衰变。我们将此过程表述为布里渊区垂直带间跃迁的求和，权重为以Th为中心的局部超精细矩阵元，其直接从全电子全势线性化增强平面波布洛赫旋量计算得出。包含有限核磁化模型以规范短程超精细相互作用并考虑玻尔 - 魏斯科普夫效应。应用剪刀移位以涵盖实验报道的ThO₂带隙后，我们发现计算出的内转换寿命在1 - 16 μs范围内。随着带隙接近$\omega_{\rm nuc}$，寿命强烈增加，因为核跃迁能量处的共振带间相空间减小。对于较大报道的ThO₂带隙，计算出的寿命与测量的转换电子穆斯堡尔寿命相当。我们的分析表明，选择带隙值略低于$\omega_{\rm nuc}$的固态宿主可以优化具有内转换电子读出的固态核时钟性能。
英文摘要
We present an ab initio calculation of the band-to-band internal-conversion rate of the $\hbarω_{\rm nuc} \approx 8.35$ eV isomeric transition in $^{229}$ThO$_2$. Because the nuclear transition energy exceeds the electronic band gap of ThO$_2$, the isomer can decay nonradiatively by resonantly promoting a valence electron into the conduction band. We formulate this process as a Brillouin-zone sum over vertical interband transitions weighted by local Th-centered hyperfine matrix elements, which are evaluated directly from all-electron full-potential linearized augmented-plane-wave Bloch spinors. A finite nuclear magnetization model is included to regularize the short-range hyperfine interaction and to account for the Bohr-Weisskopf effect. After applying scissor shifts to span the experimentally reported ThO$_2$ band gaps, we find calculated internal-conversion lifetimes in the range of $1-16~μ{\rm s}$. The lifetime increases strongly as the band gap approaches $ω_{\rm nuc}$ because the resonant interband phase space at the nuclear transition energy is reduced. For the larger reported ThO$_2$ gaps, the calculated lifetime is comparable to the measured conversion-electron Mössbauer lifetime [Nature 648, 300 (2025)]. Our analysis implies that choosing solid-state hosts with band-gap values slightly lower than $ω_{\rm nuc}$ can optimize solid-state nuclear clock performance with internal-conversion electron readout.
