Atomic structure calculations of helium with correlated exponential functions

Abstract

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 $\alpha$. The nonrelativistic wave function is represented as a linear combination of basis functions depending on all three interparticle radial distances, $r_1$, $r_2$ and $r=|{\vec{r}}_1-{\vec{r}}_2|$. The choice of the exponential basis functions of the form $\exp (-\alpha r_1-\beta r_2-\gamma r)$ 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 ${\alpha }^{5}m$ (where $m$ is the electron mass) are complemented with the systematic treatment of higher-order ${\alpha }^{6}m$ and ${\alpha }^{7}m$ QED effects.

References in corpus (27)

• Theoretical energies of low-lying states of light helium-like ions
• Experiment and Theory in Computations of the He Atom Ground State
• Fine structure of helium-like ions and determination of the fine structure constant
• Nonrelativistic ionization energy for the helium ground state
• ${\alpha }^4$ Ry corrections to singlet states of helium
• Testing fundamental interactions on the helium atom
• Theory of the Lamb shift in hydrogen and light hydrogen-like ions
• A Determination of the Fine Structure Constant using Precision Measurements of Helium Fine Structure
• Precision spectroscopy of helium in a magic wavelength optical dipole trap
• Improved theory of helium fine structure
• Reexamination of helium fine structure
• Complete ${\alpha }^{7}m$ Lamb shift of helium triplet states
• Helium energy levels including $m{\alpha }^6$ corrections
• Nonrelativistic energy levels of helium atom
• Higher-order recoil corrections for triplet states of the helium atom
• Ultrahigh-precision measurement of the $n=2$ triplet P fine structure of atomic helium using frequency-offset separated oscillatory fields
• Higher-order recoil corrections for singlet states of the helium atom
• XUV frequency comb metrology on the ground state of helium
• High-precision spectroscopy of the forbidden 2 3S1 - 2 1P1 transition in quantum degenerate metastable helium
• Bethe logarithm for the helium atom
• Relativistic corrections to the Bethe logarithm for the $2^{3}S$ and $2^{3}P$ states of He
• Nonradiative ${\alpha }^{7}m$ QED effects in Lamb shift of helium triplet states
• Helium fine structure theory for determination of α
• 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
• QED calculation of ionization energies of $1snd$ states in helium
• Quantum electrodynamic corrections to the $1s3d$ states of the helium atom

Cited by in corpus (8)

• Bound-state relativistic quantum electrodynamics: a perspective for precision physics with atoms and molecules
• Higher-order QED corrections to the hyperfine splitting in ${}^3$He
• Relativistic two-electron atomic and molecular energies using $LS$ coupling and double groups: role of the triplet contributions to singlet states
• Relativistic treatment of diamagnetic susceptibility of helium
• QED corrections to the correlated relativistic energy: one-photon processes
• Relativistic Bethe logarithm for triplet states of helium-like ions
• Nuclear magnetic shielding in heliumlike ions
• Retardation Effects in Atom-Wall Interactions