We present relativistic many-body calculations of the fine-structure splittings of the
n2F Rydberg states of Rb
(n=4--16) using both order-by-order relativistic many-body perturbation theory (RMBPT), up to a subset of fourth-order corrections, and relativistic equation-of-motion coupled-cluster methods, including singles, doubles, and an approximate treatment of valence triples. Good overall agreement is found with the measurements of Brandenberger et al. [Phys. Rev. A 65, 042510 (2002); Phys. Rev. A 81, 032515 (2010)] to better than the 1% level, which is our expected level of theoretical uncertainty due to omitted higher-order correlation effects. It is shown that the RMBPT of the fine-structure splittings is complex and slowly convergent, and that relativistic effects are enhanced compared with the RMBPT of the ionization energy of the
2F states. We also analyze smaller field-theoretic contributions to the fine-structure splittings from retardation and the radiative self-energy and vacuum polarization, finding them to enter at the 0.1% level.
The three-body nonadditive interaction energy between helium atoms was calculated at 253 trimer configurations using the full-configuration-interaction (FCI) method. The analytic potential fitted to these energies is the best current representation of the three-body nonadditive interactions between helium atoms. At the equilateral triangle configuration with R=5.6 bohr, near the minimum of the total potential, the nonadditive three-body energy calculated at the FCI level amounts to -88.5 mK, compared to -98.5 mK at the coupled cluster with single, double, and noniterative triple excitations [CCSD(T)] level. The uncertainty of the former result resulting from basis set incompleteness is estimated to be 1.5 mK. The relative uncertainty of our present complete three-body fit, including the uncertainties resulting from the fitting procedure, is estimated at 2%, a fivefold improvement over the previous best potential. Overall, the FCI contribution beyond CCSD(T) is rather important, being of the same order of magnitude as the uncertainty of the sum of two-body interactions. The inclusion of this contribution makes uncertainties of the total trimer interaction energies dominated by the uncertainties of the two-body component.
New variational techniques are described which yield a factor of 1000 improvement in accuracy for the energies of the 1snd
1D and
3D states of helium up to n=8. Convergence to better than \ifmmode\pm\else\textpm\fi{}10 kHz is obtained, making possible high-precision comparisons with experiment for fine structure and singlet-triplet splittings. The comparisons are sensitive to QED, relativistic recoil, and second-order mass-polarization corrections.
The precise spectra of few-electron atoms plays a pivotal role in advancing fundamental physics, including the verification of quantum electrodynamics (QED) theory, the determination of the fine-structure constants, and the exploration of nuclear properties. With the rapid development of precision measurement techniques, the demand for atomic structure data has evolved from simply confirming existence to pursuing unprecedented accuracy. To meet the growing needs for precision spectroscopy experiments, we develop a series of high-precision theoretical methods based on B-spline basis sets, such as the non-relativistic configuration interaction (B-NRCI) method, the correlated B-spline basis functions (C-BSBFs) method, and the relativistic configuration interaction (B-RCI) method. These methods use the unique properties of B-spline functions, such as locality, completeness, and numerical stability, to accurately solve the Schrödinger and Dirac equations for few-electron atoms. Our methods yield significant results, particularly for helium and helium-like ions. Using these methods, we obtain accurate energies, polarizabilities, tune-out wavelengths, and magic wavelengths. Specifically, we achieve high-precision measurements of the energy spectra of helium, providing vital theoretical support for conducting related experimental researches. Additionally, we make high-precision theoretical predictions of tune-out wavelengths, paving the way for new tests of QED theory. Furthermore, we propose effective theoretical schemes to suppress Stark shifts, thereby facilitating high-precision spectroscopy experiments of helium The B-spline-basis methods reviewed in this paper prove exceptionally effective in high-precision calculations for few-electron atoms. These methods not only provide crucial theoretical support for precision spectroscopy experiments but also pave the new way for testing QED. Their ability to handle large-scale configuration interactions and incorporate relativistic and QED corrections makes them versatile tools for advancing atomic physics research. In the future, the high-precision theoretical methods based on B-spline basis sets are expected to be extended to cutting-edge fields, such as quantum state manipulation, determination of nuclear structure properties, formation of ultracold molecules, and exploration of new physics, thus continuously promoting the progress of precision measurement physics.
We theoretically investigate long-range interactions between an excited
L-state He atom and two identical
S-state He atoms for the cases of the three atoms all in spin-singlet states or all in spin-triplet states, denoted by He(${n}_{0}^{\ensuremath{\lambda}}S$)-He(${n}_{0}^{\ensuremath{\lambda}}S$)-He(${n}_{0}^{\ensuremath{'}\ensuremath{\lambda}}L$), with
n0 and ${n}_{0}^{\ensuremath{'}}$ principal quantum numbers, $\ensuremath{\lambda}=1$ or 3 the spin multiplicity, and
L the orbital angular momentum of a He atom. Using degenerate perturbation theory for the energies up to second-order, we evaluate the coefficients
C3 of the first-order dipolar interactions and the coefficients
C6 and
C8 of the second-order additive and nonadditive interactions. Both the dipolar and dispersion interaction coefficients, for these three-body degenerate systems, show dependences on the geometrical configurations of the three atoms. The nonadditive interactions start to appear in second-order. To demonstrate the results and for applications, the obtained coefficients
Cn are evaluated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates for $\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)$, $\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}P)$, $\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}P)$, and $\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}P)$. The calculations are given for three like nuclei for the cases of hypothetical infinite mass He nuclei, and of real finite mass
4He or
3He nuclei. The special cases of the three atoms in equilateral triangle configurations are explored in detail, and for the cases in which one of the atoms is in a
P state, we also present results for the atoms in an isosceles right triangle configuration or in an equally spaced collinear configuration. The results can be applied to construct potential energy surfaces for three helium atom systems.