Precise ab initio calculations of ${}^4$He($1snp{}^3{P}_J$) fine structure of high Rydberg states

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.