• Accepted Paper

Ionization energies for Rydberg 4He (1snp1,3P) states using the correlated B-spline basis function method

Jing Chi, Hao Fang, Yong-Hui Zhang, Li-Yan Tang, and Ting-Yun Shi

Phys. Rev. A - Accepted 3 September, 2026

DOI: https://doi.org/10.1103/2mj4-k8xt

Abstract

We extend the correlated B-spline basis function (C-BSBF) method to high-precision calculations of the ionization energies of helium Rydberg n1,3P states (n=2435). Using a unified basis set, we evaluate nonrelativistic energies, relativistic corrections of order mα4 (including finite-mass recoil), QED contributions of order mα5, and partial mα6 terms (singlet-triplet mixing, one- and two-loop radiative corrections). The remaining higher-order contributions are estimated via 1/n3 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 n=102. Combining our Rydberg ionization energies with high-precision experimental 2SnP transition frequencies yields the ionization energies for the metastable 21S and 23S states as stat(20)sys~MHz and stat(25)sys~MHz, respectively. The C-BSBF result for the 21S state is consistent with the experimental ionization energy obtained from Rydberg-series extrapolation, while for the 23S state the difference is 0.019(10) MHz.

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