Relativistic calculations for few-electron atomic systems with finite basis sets

Dmitry Glazov

Abstract:

Current state-of-the-art calculations for simple atomic systems routinely include the dominant bound-state QED contributions. To incorporate higher-order effects within relativistic atomic theory, a range of approaches based on the Dirac–Coulomb–Breit Hamiltonian has been developed. Although non-perturbative techniques are widely used, perturbation theory remains highly efficient, particularly in a recursive form that permits access to arbitrarily high orders. In Ref. [1], such a recursive perturbative framework was combined with a finite basis built from Slater determinants of one-electron orbitals generated using the dual kinetic balance approach [2]. This strategy enabled accurate evaluation of interelectronic-interaction effects on the energy levels of lithium-like and boron-like ions [1,3], and its extension to quasi-degenerate configurations allowed for analogous studies for helium-like systems [4,5]. Furthermore, this formalism was applied to compute the impact of interelectronic interactions on nuclear-recoil contributions in these ions [3,6].

Accurate predictions for magnetic-interaction observables such as the g-factor and hyperfine splitting require a consistent treatment of the negative-energy part of the Dirac spectrum. A dedicated method addressing this issue was introduced in Ref. [7], enabling the evaluation of third- and higher-order interelectronic-interaction corrections to the g-factor and hyperfine structure in lithium-like ions [7–9]. Extending the recursive construction to handle multiple perturbations makes it possible to quantify more delicate effects, including many-electron QED contributions [7,9] and nuclear-recoil terms [10-12]. Leading first- and second-order contributions have been obtained rigorously within bound-state QED, and together these results provide the most accurate theoretical values to date for the g-factor of lithium- and boron-like ions.

[1] D. A. Glazov et al., Nucl. Instr. Meth. Phys. Res. B 408, 46 (2017)
[2] V. M. Shabaev et al., Phys. Rev. Lett. 93, 130405 (2004)
[3] A. V. Malyshev et al., Phys. Rev. A 96, 022512 (2017)
[4] A. V. Malyshev et al., Phys. Rev. A 99, 010501(R) (2019)
[5] Y. S. Kozhedub et al., Phys. Rev. A 100, 062506 (2019)
[6] A. V. Malyshev et al., Phys. Rev. A 101, 052506 (2020)
[7] D. A. Glazov et al., Phys. Rev. Lett. 123, 173001 (2019)