Theoretical calculations of isotope shifts in highly charged Ni$^{12+}$ ion

TL;DR

Ni$^{12+}$ is analyzed as a clock candidate in highly charged ions, with MBPT+CI calculations (including emu CI) used to determine the energies of the four lowest excited states and their isotope-shift constants. The study employs a Dirac-Coulomb-Breit framework in a $V^{N-6}$ potential, constructs a large basis with B-splines, and derives uncertainties by combining CBS, reference-set, and emu-CI corrections via $\sigma = \sqrt{\sigma_{\mathrm{CBS}}^2 + \sigma_{\mathrm{ref}}^2 + \sigma_{\mathrm{emu}}^2}$. The results show an average energy deviation of about $0.08\%$ from experiment and sub-$1\%$ valence-correlation-induced uncertainties for isotope shifts, with mass shifts dominating the IS and field shifts strongly suppressed; QED effects are treated with a radiative potential, and the work provides benchmarks for QED treatments in multi-valence HCIs. These findings support Ni$^{12+}$ as a high-precision platform for clock applications and fifth-force searches via King plots, while highlighting areas for future refinement, such as QED recoil and hyperfine contributions for $^{61}$Ni.

Abstract

We present relativistic many-body perturbation theory plus configuration interaction (MBPT+CI) calculations of the lowest four excited states of Ni$^{12+}$, a promising candidate for highly charged ion (HCI) optical clocks. By combining the convergence behavior from multiple calculation models, we perform a detailed analysis of the electron-correlation effects and both the excitation energies and their uncertainties are obtained. Our computed energies for the first two excited states deviate from experimental values by less than $10~\mathrm{cm^{-1}}$, with relative uncertainties estimated below $0.2\%$. Building on the same computational procedure, we calculate the mass shift and field shift constants for the lowest four excited states of Ni$^{12+}$, and the resulting isotope shifts exhibit valence-correlation-induced relative uncertainties below the $1\%$ level. These results provide essential atomic-structure input for high-precision isotope shift spectroscopy in Ni$^{12+}$.

Figures (7)

• Figure 1: Schematic diagram of the CI matrix in the emu CI method. $N_\mathrm{small}$ denotes the size of the small CI subspace containing the more important configurations, while $N_\mathrm{large}$ represents the dimension of the original CI space.
• Figure 2: Convergence of the calculated energies of the lowest four excited states in different computational models as a function of the principal quantum number cutoff $n_{\max}$, with the partial-wave cutoff fixed at $\ell_{\max} = 4$.
• Figure 3: Convergence of the calculated energies of the lowest four excited states in single-reference CI results as a function of the principal quantum number cutoff $n_{\max}$ and partial-wave cutoff $\ell_{\max}$.
• Figure 4: Convergence of the calculated $k_{\mathrm{SMS}}$ and $k_{\mathrm{NMS}}$ of the lowest four excited states in different computational models as a function of the principal quantum number cutoff $n_{\max}$, with the partial-wave cutoff fixed at $\ell_{\max} = 4$.
• Figure 5: Convergence of the calculated $k_{\mathrm{SMS}}$ and $k_{\mathrm{NMS}}$ of the lowest four excited states in single-reference CI results as a function of the principal quantum number cutoff $n_{\max}$ and partial-wave cutoff $\ell_{\max}$.