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The precise spectroscopy of few-electron atoms plays a pivotal role in advancing fundamental physics, encompassing the verification of quantum electrodynamics (QED) theory, the determination of finestructure constants, and the exploration of nuclear properties. With the rapid development of precision measurement techniques, the demand for atomic structure data has evolved from mere confirmation of existence to the pursuit of unprecedented accuracy. To meet the growing needs for precision spectroscopy experiments, we have developed a series of high-precision theoretical methods based on B-spline basis sets, including 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 leverage 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 have yielded significant results, particularly for helium and helium-like ions. Using these methods, we have obtained accurate energies, polarizabilities, tune-out wavelengths, and magic wavelengths. Specifically, we have achieved high-precision determinations of the energy spectra of helium, providing vital theoretical support for related experimental research. Additionally, we have made highprecision theoretical predictions of tune-out wavelengths, paving the way for new tests of QED theory. Furthermore, we have proposed effective theoretical schemes to suppress Stark shifts, thereby facilitating high-precision spectroscopy experiments of helium.
The B-spline-basis methods reviewed in this paper have proven exceptionally effective in highprecision calculations for few-electron atoms. These methods have not only provided crucial theoretical support for precision spectroscopy experiments but have also paved new avenues 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 grounded in B-spline basis sets are poised to expand into frontier areas, including quantum state manipulation, nuclear structure property determination, ultracold molecule formation, and new physics exploration, thereby continuously driving the progress of precision measurement physics.-
Keywords:
- B-spline basis sets /
- few-electron atoms /
- polarizabilities /
- tune-out and magic wavelengths
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