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 (9)

• ${\alpha }^4$ Ry corrections to singlet states of helium
• Improved theory of helium fine structure
• Complete ${\alpha }^{7}m$ Lamb shift of helium triplet states
• Helium energy levels including $m{\alpha }^6$ corrections
• 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
• Radiative ${\mathbf{\alpha }}^7\mathbf{m}$ QED contribution to the helium Lamb shift
• 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 (3)

• Relativistic treatment of diamagnetic susceptibility of helium
• Relativistic Bethe logarithm for triplet states of helium-like ions
• Nuclear magnetic shielding in heliumlike ions