Testing fundamental interactions on the helium atom

Understand

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 $\alpha$ and the electron-to-nucleus mass ratio $m/M$.
• For energies, theoretical results are complete through orders $\alpha^6m$ and $\alpha^6m^2/M$, 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 $\alpha^7m$ effect.