Abstract
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 a and the electron-to-nucleus mass ratio m/M.
For energies, theoretical results are complete through orders alpha(6)m and alpha(6)m(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(3) P state is predicted with a much better accuracy, 1.7 kHz, as a consequence of a calculation of the next-order alpha(7)m 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 He-3 and He-4 is treated with a subkilohertz accuracy, which allows for a high-precision determination of the differences of the nuclear charge radii delta r(2).
Several such determinations, however, yield results that are in a 4 sigma 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 alpha(7)m 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.