Charge-state regulation of nuclear excitation by electron capture in $^{229}$Th ions

Abstract: Nuclear excitation by electron capture (NEEC) in $^{229}$Th holds significant potential for precise nuclear state manipulation. In this study, we thoroughly investigate NEEC in $^{229}\text{Th}^{q+}$ ions by integrating quantum numbers ($n, l, j$) effects and analyzing key parameters (e.g., resonance energy $E_r$, cross section $σ$, resonance strength $S$, and NEEC transition width $Γ_{\text{NEEC}}$) influences across charge state from $q=1^+$ to $90^+$. Especially, we focus on the charge-state regulation of the isomeric state (IS, 8.36 eV) and second-excited state (SE, 29.19 keV). Our calculations uncover critical charge-state-dependent behaviors of NEEC in $^{229}\text{Th}$ ions: (1) For the IS, valid NEEC channels exhibit threshold migration, where the dominant principal quantum number $n$ increases linearly with $q$ following the relation $n \approx 1.28q + 4.23$; meanwhile, single-$n$-channel $S$ stabilizes between $10^{-2}$ to $10^0$ barn eV via compensatory nucleus-electron coupling, ensuring the total resonance $S$ constant. (2) For the SE, its excitation energy far exceeds nearly all electron binding energies, leading to negligible channel screening and causing the total $S$ to increase monotonically with $q$. This research clarifies the intrinsic mechanisms of charge-state-driven nuclear-electronic interactions in $^{229}\text{Th}^{q+}$ NEEC and provides a critical reference for future experimental efforts to manipulate $^{229}\text{Th}$ nuclear states, particularly via indirect regulation of the SE.