High-precision measurements of the fine-structure splittings in helium high Rydberg states have been reported, yet corresponding ab initio benchmarks for direct comparison remain unavailable. In this work, we extend the correlated B-spline basis function (C-BSBF) method to calculate the fine-structure splittings of high Rydberg states in ${}^4\mathrm{He}$. The calculations include the $m{\alpha }^4$- and $m{\alpha }^5$-order contributions, the singlet–triplet mixing effect, and the estimated spin-dependent $m{\alpha }^6$-order corrections obtained using a $1/n^3$ scaling approximation. High-precision ab initio results are obtained for principal quantum numbers $n=24–37$ with kilohertz-level accuracy and further extended to $n=45–51$ by extrapolation and fitting. The theoretical results show excellent agreement with quantum-defect theory (QDT) predictions and allow direct comparison with experimental measurements. Additionally, the discrepancy observed at $n=34$ is expected to be clarified with improved experimental precision.

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• Atomic spectra
• Electron correlation calculations for atoms & ions
• Electronic structure of atoms & molecules
• Fine & hyperfine structure
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions