Precise ab initio calculations of $^4$He($1snp \, ^3P_J$) fine structure of high Rydberg states

TL;DR

This paper presents high-precision ab initio calculations of the fine-structure splittings in high Rydberg states of helium, achieving kilohertz accuracy and enabling direct comparison with experimental data.

Contribution

The work extends the C-BSBF method to include higher-order effects and provides the first ab initio benchmarks for high Rydberg states of helium with unprecedented accuracy.

Findings

Results agree well with quantum-defect theory predictions.

Calculated splittings for n=24-37 with kilohertz precision.

Extended calculations to n=45-51 through extrapolation.

Abstract

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 $^4$He. The calculations include the $m\alpha^4$- and $m\alpha^5$-order contributions, the singlet-triplet mixing effect, and 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.