Helium fine structure theory for determination of \alpha

TL;DR

This paper advances the theoretical calculation of helium's fine-structure splitting using quantum electrodynamics, aiming to improve the determination of the fine-structure constant lpha through comparison with experimental data.

Contribution

It provides comprehensive QED-based calculations of helium fine-structure splitting, including higher-order corrections and comparison with experimental results, to refine lpha measurement methods.

Findings

Theoretical predictions are limited by an estimated 1.7 kHz unknown mlpha^8 term.

Comparison with recent experiments suggests the higher-order correction is smaller than estimated.

Further measurements in helium-like ions could significantly improve lpha determination.

Abstract

We present recent progress in the calculation of the helium fine-structure splitting of the 2^3P_J states, based on the quantum electrodynamic theory. Apart from the complete evaluation of m\alpha^7 and m^2/M\alpha^6 corrections, we have performed extensive tests by comparison with all experimental results for light helium-like ions and with the known large nuclear charge asymptotics of individual corrections. Our theoretical predictions are still limited by the unknown m\alpha^8 term, which is conservatively estimated to be 1.7 kHz. However, comparison with the latest experimental result for the 2^3P_0 - 2^3P_2 transition [M. Smiciklas and T. Shiner, Phys. Rev. Lett. 105, 123001 (2010)] suggests that the higher-order contribution is in fact much smaller than the theoretical estimate. This means that the spectroscopic determination of \alpha can be significantly improved if another measurement of the 2^3P_0 - 2^3P_2 transition in helium-like Li^+ or Be^{2+} ion is performed.