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 $\ddot{I}ƒ$, resonance strength $S$, and NEEC transition width $\hat{I}{“}_{\text{NEEC}}$) 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.

9 pages, 10 figures