标题： 非弹性电子散射引起的 Th 的核激发速率和动力学$^{229}$ 显示英文标题

标题： Inelastic electron scattering-induced nuclear excitation rates and dynamics in $^{229}$Th

摘要： 在本工作中，我们研究了由非弹性电子散射诱导的 $^{229}$钍核的激发率和种群动力学，重点探讨了电子能量、通量以及离子电荷状态对核激发过程的影响。 利用 Dirac Hartree-Fock-Slater 方法，我们在广泛的离子电荷态和电子能量范围内计算了 $^{229}$钍同质异能态（8.36 eV）和第二激发态（29.19 keV）的截面。 我们的结果表明，这些因素显著影响核激发效率。通过第二激发态间接激发对积累同质异能态核的影响不可忽略。 通过应用速率方程来模拟核种群的时间演化，我们显示，在最佳条件下，最多可达 10% 的 $^{229}$钍$^{4+}$离子可以积累在同质异能态中。 这些发现为优化电子-核相互作用提供了重要的见解，有助于推进基于 $^{229}$钍的核钟及相关精密测量应用的发展。 显示英文摘要

摘要： In the present work, we investigate the excitation rates and population dynamics of $^{229}$Th nuclei induced by inelastic electron scattering, focusing on how electron energy, flux, and ionic charge state influence the excitation process of the nuclei. Using the Dirac Hartree-Fock-Slater method, we calculate cross sections for both the isomeric state (8.36 eV) and the second-excited state (29.19 keV) of $^{229}$Th over a wide range of ionic charge states and electron energies. Our results demonstrate that these factors significantly impact the nuclear excitation efficiency. The effect of indirect excitation through the second-excited state on enhancing the accumulation of nuclei in the isomeric state cannot be ignored. By applying rate equations to model the temporal evolution of nuclear populations, we show that under optimal conditions, up to 10\% of $^{229}$Th$^{4+}$ ions can be accumulated in the isomeric state. These findings provide important insights for optimizing electron-nucleus interactions, contributing to the development of $^{229}$Th-based nuclear clocks and relevant precision measurement applications.