Testing fundamental interactions on the helium atom

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 $\alpha$ 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 and determines the fine-structure constant $\alpha$ with an accuracy of 31~ppb. The isotope shift between ${}^3$He and ${}^4$He is treated theoretically with a sub-kHz 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, what remains unexplained. Apart from this, we find no significant discrepancies between theory and experiment for the helium atom. In the future, a calculation of the next-order ${\alpha }^{7}m$ effect for energy levels will enable determinations of the nuclear charge radii from atomic transition frequencies with an accuracy better than 1\%. Combined with the complementary determinations from muonic atoms, this will provide a sensitive test of universality in electromagnetic interactions of leptons and contribute to the solution of the proton charge radius puzzle.

9 pages, 1 figure

References in corpus (12)

• High-precision measurement of the atomic mass of the electron
• Nuclear Charge Radii of Be-7,9,10 and the one-neutron halo nucleus Be-11
• Complete two-loop correction to the bound-electron g factor
• ${\alpha }^4$ Ry corrections to singlet states of helium
• Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius
• Nonrelativistic QED approach to the bound-electron g factor
• Constraints on exotic spin-dependent interactions between electrons from helium fine-structure spectroscopy
• Improved theory of helium fine structure
• Helium energy levels including $m{\alpha }^6$ corrections
• Higher-order recoil corrections for triplet states of the helium atom
• Higher-order recoil corrections for singlet states of the helium atom
• High-precision spectroscopy of the forbidden 2 3S1 - 2 1P1 transition in quantum degenerate metastable helium

Cited by in corpus (40)

• Probing new spin-independent interactions through precision spectroscopy in atoms with few electrons
• Precision spectroscopy of helium in a magic wavelength optical dipole trap
• Generalized King linearity and new physics searches with isotope shifts
• QED calculation of the dipole polarizability of helium atom
• Complete ${\alpha }^{7}m$ Lamb shift of helium triplet states
• Comprehensive theory of the Lamb shift in light muonic atoms
• Direct measurement of the ${}^3$He${}^{+}$ magnetic moments
• Ultrahigh-precision measurement of the $n=2$ triplet P fine structure of atomic helium using frequency-offset separated oscillatory fields
• Nuclear Charge Radii of ${}^{10,11}$B
• QED calculations of energy levels of helium-like ions with $5\le Z\le 30$
• Non-linear isotope-shift effects in Be-like, B-like, and C-like argon
• Relativistic corrections to the Bethe logarithm for the $2^{3}S$ and $2^{3}P$ states of He
• Isotope shifts in ${}^{20,22}$Ne -- Precision measurements and global analysis in the framework of intermediate coupling
• QED effects on the nuclear magnetic shielding of ${}^3$He
• Atomic structure calculations of helium with correlated exponential functions
• Nonradiative ${\alpha }^{7}m$ QED effects in Lamb shift of helium triplet states
• A Custodial Symmetry for Muon g-2
• Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift
• Precise Frequency Measurement of the 2${}^1$S${}_0$-3${}^1$D${}_2$ Two-Photon Transition in atomic ${}^4$He
• Spectroscopic tests for short-range modifications of Newtonian and post-Newtonian potentials
• Variational versus perturbative relativistic energies for small and light atomic and molecular systems
• QED calculation of ionization energies of $1snd$ states in helium
• Calculation of Araki-Sucher correction for many-electron systems
• Quantum electrodynamic corrections to the $1s3d$ states of the helium atom
• Few-electron atomic ions in non-relativistic QED: the Ground state energy
• Fine and hyperfine splitting of the low-lying states of ${}^9$Be
• Revisiting the helium isotope-shift puzzle with improved uncertainties from nuclear structure corrections
• Application of the Hylleraas-$B$-spline basis set: Nonrelativistic Bethe logarithm of helium
• Relativistic corrections to the thermal interaction of bound particles
• Ab initio potential energy curves, scattering lengths, and rovibrational levels of the He${}_2^{+}$ molecular ion in excited electronic states
• On the spectral properties of the Bloch-Torrey equation in infinite periodically perforated domains
• Constraining exotic interactions
• Thermal corrections of lowest order for a helium atom
• Proposal for suppressing ac Stark shift in the He($2{}^3{S}_1\to 3{}^3{S}_1$) two-photon transition using magic wavelengths
• Helium-like and Lithium-like ions: Ground state energy
• Calculations of Bethe logarithms for Hydrogen and Helium atoms using B-splines in different gauges
• Preparation of individual magnetic sub-levels of ${}^4$He($2^3$S${}_1$) in a supersonic beam using laser optical pumping and magnetic hexapole focusing
• Thermal one-loop self-energy correction for hydrogen-like systems: Relativistic approach
• Nonrelativistic quantum electrodynamic approach to polarizabilities of light atoms
• Frequency measurements of transitions from the $2^3{P}_2$ state to the $5^1{D}_2$, $5^3{S}_1$, and $5^{3}D$ states in ultracold helium