Predicting the energies of Cf17+ for an optical clock

TL;DR

The paper addresses the challenge of predicting the clock-transition energy in the heavy, highly charged ion Cf$^{17+}$, where strong relativistic and electron-correlation effects are present. It treats Cf$^{17+}$ as a univalent system and uses a relativistic coupled-cluster scheme (CCSDT) with iterative nonlinear singles/doubles and valence/core triples, complemented by QED corrections and basis-set extrapolation, while accounting for the Breit interaction. The authors quantify how core–valence correlations and iterative triple excitations shape the low-lying spectrum, providing a quantitative prediction for the clock transition $5f_{5/2} \to 6p_{1/2}$ with an uncertainty of about $2.5\times 10^{2}$ cm$^{-1}$, and clarifying discrepancies with prior work by highlighting the importance of the Breit term. The results establish a robust theoretical pathway for identifying HCI clock transitions and can be extended to other heavy HCIs, thereby guiding experimental searches and precision spectroscopy at the frontier of optical clocks.

Abstract

Highly charged ions (HCIs) combine compact electronic structure with strong relativistic effects, offering both robustness against external perturbations and enhanced sensitivity to variations of the fine-structure constant. Recent advances in sympathetic cooling and trapping enable precision measurements of highly charged ions; however, fully exploiting their potential requires accurate theoretical predictions. In particular, reliable calculations of clock wavelengths are essential for experimentally locating HCI clock transitions. Here, we treat Cf17+ as a univalent ion and perform calculations within the relativistic coupled-cluster framework, iteratively including nonlinear single-double contributions and valence and core triple excitations. We also assess quantum-electrodynamic corrections and basis-set and partial-wave truncation effects. Our results establish the impact of different correlation contributions on the low-lying energy spectrum and provide a quantitatively reliable prediction of the 5f_5/2 - 6p_1/2 clock transition, highlighting the critical role of core-valence correlations and iterative triples for precision spectroscopy and optical clock development.