Ab initio calculations of the electronic structure of Ac+

Accurate spectroscopic investigations of the heaviest elements are inherently challenging, due to their short lifetimes and low production yields. Success of such measurements requires both dedicated experimental techniques and strong theoretical support. Laser resonance chromatography (LRC) is a promising approach for heavy ion spectroscopy, in particularly for metals with low vapour pressure, such as actinium. We have employed the state-of-the-art relativistic Fock space coupled cluster approach as well as the configuration interaction with many-body perturbation theory method to calculate the energy levels, the transition amplitudes, the branching ratios, and the hyperfine structure parameters of the lowest excited states in Ac+. Knowledge of these properties is required for the design of experiments. Our calculations are in close agreement with experimental transition energies, leading us to expect a similar level of accuracy for the calculated hyperfine structure parameters. Based on these predictions, two possible experimental schemes are proposed for the planned LRC measurements.

💡 Research Summary

The authors present a comprehensive ab initio study of the singly‑charged actinium ion (Ac⁺), targeting the electronic‑structure data required for forthcoming laser resonance chromatography (LRC) experiments. Two state‑of‑the‑art relativistic many‑body methods are employed: Fock‑space coupled‑cluster (FSCC) and configuration‑interaction combined with many‑body perturbation theory augmented by Brueckner orbitals (CI + MBPT + Br). Both approaches are built on the Dirac‑Coulomb Hamiltonian and incorporate Breit and QED corrections, ensuring that relativistic effects, which are pronounced for Z = 89, are fully accounted for.

FSCC calculations start from a closed‑shell Ac³⁺ (6p⁶) reference and add two electrons in the two‑particle sector to generate the Ac⁺ states of interest. The model space is partitioned into a main part (7s, 6d) and an intermediate part (7p, 5f, 8p, 6f, 8s, 7d) using the extrapolated intermediate Hamiltonian (XIH) technique to avoid convergence problems. Correlation energies are extrapolated to the complete‑basis‑set (CBS) limit with the Martin scheme, while diffuse functions are added to capture excitation energies accurately. CI + MBPT + Br treats valence‑valence correlation through a full CI, core‑valence correlation through second‑order MBPT, and improves the one‑body orbitals by solving the Brueckner equation, thereby embedding core‑polarisation effects directly into the wavefunctions. Random‑phase approximation (RPA) corrections are applied when evaluating transition matrix elements and hyperfine operators.

Energies of six low‑lying excited configurations—7s 7p ³P₀, 6d 7p ¹P₁, 6d 7s ³D₁, ³D₂, ¹D₂, and 6d² ³F₂—are computed with both methods and compared to the NIST database. The theoretical values differ from experiment by roughly 5 % on average, indicating that the calculated transition wavelengths are reliable for experimental planning. Transition rates and lifetimes are derived from the CI + MBPT + Br matrix elements combined with experimental transition energies. The resulting partial rates agree well with the semi‑empirical values compiled by Kramida, except for the 6d 7s ³D₁ → 7s² ¹S₀ transition, where the calculated rate is anomalously large; the authors attribute this to possible multipole mixing or residual methodological uncertainties.

Hyperfine structure (HFS) constants A₀ (magnetic dipole) and qzz (electric quadrupole gradient) are obtained via the finite‑field method, adding the HFS operators to the Hamiltonian and extracting linear response derivatives. By pairing the calculated A₀ and qzz with experimentally measured hyperfine splittings (A, B), nuclear magnetic dipole moments and quadrupole moments can be extracted for various Ac isotopes. The authors estimate uncertainties by comparing FSCC and CI + MBPT + Br results, achieving an anticipated relative error of 1–2 % for the HFS constants.

Based on the calculated spectroscopic data, two LRC schemes are proposed. Scheme 1 exploits the strong 7s 7p ³P₀ → 6d 7p ¹P₁ electric‑dipole transition to shelve electrons into a metastable state, producing a measurable change in drift time through a helium buffer gas. Scheme 2 uses the 6d 7s ³D₁ → 7s² ¹S₀ transition, which, despite a longer lifetime, offers a clear drift‑time signature due to differing collisional cross‑sections. Both schemes benefit from the high transition strengths and relatively long lifetimes predicted by the calculations, ensuring that the laser scanning range can be narrowed and experimental run times minimized.

In conclusion, the paper delivers the most accurate theoretical description to date of Ac⁺ electronic structure, validates the methodology by cross‑checking two independent high‑level relativistic approaches, and translates these results into concrete experimental designs for LRC. The work not only paves the way for precise nuclear‑property measurements of actinium isotopes but also establishes a robust computational‑experimental workflow that can be extended to even heavier elements such as lawrencium (Lr, Z = 103).