Corrections to O( alpha 7(ln alpha )mc2) fine-structure splittings and O( alpha 6(ln alpha )mc2) energy levels in helium

Bound-State Relativistic Quantum Electrodynamics: A Perspective for Precision Physics with Atoms and Molecules

Precision physics aims to use atoms and molecules to test and develop the fundamental theory of matter, possibly beyond the Standard Model. Most of the atomic and molecular phenomena are described by the quantum electrodynamics (QED) sector of the Standard Model. Do we have the computational tools, algorithms, and practical equations for the most possible complete computation of atoms and molecules within the QED sector? What is the fundamental equation to start with? Is it still Schrödinger's wave equation for molecular matter, or is there anything beyond that? This paper provides a concise overview of the relativistic QED framework and recent numerical developments targeting precision physics and spectroscopy applications with common features of the robust and successful relativistic quantum chemistry methodology.

Precision Measurement of the n=2 Triplet P J=1 to J=0 Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields

Increasing accuracy of the theory and experiment of the n=2 ^{3}P fine structure of helium has allowed for increasingly precise tests of quantum electrodynamics (QED), determinations of the fine-structure constant α, and limitations on possible beyond the standard model physics. Here we present a 2 ppb measurement of the J=1 to J=0 interval. The measurement is performed using frequency-offset separated-oscillatory fields. Our result of 29 616 955 018(60) Hz represents a landmark for helium fine-structure measurements, and, for the first time, will allow for a 1-ppb determination of the fine-structure constant when QED theory for the interval is improved.

Atomic Structure Calculations of Helium with Correlated Exponential Functions

The technique of quantum electrodynamics (QED) calculations of energy levels in the helium atom is reviewed. The calculations start with the solution of the Schrödinger equation and account for relativistic and QED effects by perturbation expansion in the fine structure constant α. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, r1, r2 and r = |r→1−r→2|. The choice of the exponential basis functions of the form exp(−αr1−βr2−γr) allows us to construct an accurate and compact representation of the nonrelativistic wave function and to efficiently compute matrix elements of numerous singular operators representing relativistic and QED effects. Calculations of the leading QED effects of order α5m (where m is the electron mass) are complemented with the systematic treatment of higher-order α6m and α7m QED effects.

Ultrahigh-Precision Measurement of the n=2 Triplet P Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields

For decades, improved theory and experiment of the n=2 ^{3}P fine structure of helium have allowed for increasingly precise tests of quantum electrodynamics, determinations of the fine-structure constant α, and limitations on possible beyond-the-standard-model physics. Here we use the new frequency-offset separated-oscillatory-fields technique to measure the 2^{3}P_{2}→2^{3}P_{1} interval. Our result of 2 291 176 590(25) Hz represents a major step forward in precision for helium fine-structure measurements.

Helium Atom Excitations by the GW and Bethe-Salpeter Many-Body Formalism

The helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger equation is known for helium ground and excited states, and it represents a benchmark for any many-body methodology. Here, we check the ab initio many-body GW approximation and the Bethe-Salpeter equation (BSE) against the exact solution for helium. Starting from the Hartree-Fock method, we show that the GW and the BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving the time-dependent Hartree-Fock method. These findings suggest that the accuracy of the BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.

Fine structure of heliumlike ions and determination of the fine structure constant

We report a calculation of the fine-structure splitting in light heliumlike atoms, which accounts for all quantum electrodynamical effects up to order alpha{5} Ry. For the helium atom, we resolve the previously reported disagreement between theory and experiment and determine the fine-structure constant with an accuracy of 31 ppb. The calculational results are extensively checked by comparison with the experimental data for different nuclear charges and by evaluation of the hydrogenic limit of individual corrections.

Improved theory of helium fine structure

Improved theoretical predictions for the fine-structure splitting of 2(3)PJ levels in helium are obtained by the calculation of contributions of order alpha5 Ry. New results for transition frequencies nu(01) = 29616943.01(17) kHz and nu(12) = 2291161.13(30) kHz disagree significantly with the experimental values, indicating an outstanding problem in bound state QED.

Precise measurement of the J = 1 to J = 2 fine structure interval in the 2( 3)P state of helium

We measure the J = 1 to J = 2 fine structure interval in the ( 3)2P state of helium to be 2 291 175.9(1.0) kHz. We use laser excitation of an atomic beam along with an integrated electro-optic modulator technique to obtain this result. The result is consistent (2.9+/-3.2 kHz) with what could be considered an earlier version of this experiment but is not in good agreement ( 20+/-5 kHz and 22+/-8 kHz) with the two other precision determinations of this interval. The current theoretical prediction lies between and overlaps the experiments.