Testing fundamental interactions on the helium atom

We critically examine the current status of theoretical calculations of the energies, the fine structure, and the isotope shift of the lowest-lying states of helium, searching for unresolved discrepancies with experiments. Calculations are performed within the quantum electrodynamics expansion in powers of the fine structure constant α and the electron-to-nucleus mass ratio m /M . For energies, theoretical results are complete through orders α⁶m and α⁶m²/M , with the resulting accuracy ranging from 0.5 to 2 MHz for the n =2 states. The fine-structure splitting of the 2 ³P state is predicted with a much better accuracy, 1.7 kHz, as a consequence of a calculation of the next-order α⁷m effect. An excellent agreement of the theoretical predictions with the recent measurements of the fine structure provides one of the best tests of the bound-state QED in few-electron systems. The isotope shift between ³He and ⁴He is treated with a subkilohertz accuracy, which allows for a high-precision determination of the differences of the nuclear charge radii δ r² . Several such determinations, however, yield results that are in a 4 σ disagreement with each other, which remains unexplained. Apart from this, we find no significant discrepancies between theory and experiment for the helium atom. A further calculation of the yet unknown α⁷m correction to energy levels will provide a sensitive test of universality in electromagnetic interactions of leptons by comparison of nuclear charge radii obtained by the helium and muonic helium spectroscopy.