- Accepted Paper
Ionization energies for Rydberg He () states using the correlated B-spline basis function method
Phys. Rev. A - Accepted 3 September, 2026
DOI: https://doi.org/10.1103/2mj4-k8xt
Phys. Rev. A - Accepted 3 September, 2026
DOI: https://doi.org/10.1103/2mj4-k8xt
We extend the correlated B-spline basis function (C-BSBF) method to high-precision calculations of the ionization energies of helium Rydberg states (–). Using a unified basis set, we evaluate nonrelativistic energies, relativistic corrections of order (including finite-mass recoil), QED contributions of order , and partial terms (singlet-triplet mixing, one- and two-loop radiative corrections). The remaining higher-order contributions are estimated via scaling. The resulting ionization energies achieve kHz-level accuracy and are in excellent agreement with independent Hylleraas calculations, thereby providing cross-validation between two distinct theoretical approaches. From these data, the quantum-defect parameters are determined and used to extrapolate the ionization energies up to . Combining our Rydberg ionization energies with high-precision experimental transition frequencies yields the ionization energies for the metastable and states as ~MHz and ~MHz, respectively. The C-BSBF result for the state is consistent with the experimental ionization energy obtained from Rydberg-series extrapolation, while for the state the difference is 0.019(10) MHz.
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