High-precision spectroscopy as a test of quantum electrodynamics in light atomic systems

Abstract

This paper presents a review of recent progress in high-precision calculations for the ground state and low-lying excited states of helium, including the nonrelativistic energy, relativistic corrections of α2 Ry, and quantum electrodynamic (QED) corrections of lowest order α3 Ry and next-to-leading-order α4 Ry, where α is the fine-structure constant. The calculations include the terms of order α4 Ry recently obtained by Pachucki (Phys. Rev. A, 74, 062510 (2006)). Estimates of the terms of order α5 Ry, including two-loop binding corrections, are included. Comparisons with experimental ionization energies indicate reasonably good agreement for the 1s2 1S0, 1s2s 1S0, 1s2s 3S1, and 1s2p 3Pcm states, but there is a significant discrepancy for the 1s2p 1P1 state of 5.6± 3.2 MHz. An asymptotic formula for the calculation of the Bethe logarithm for Rydberg states with large angular momentum L is presented in an Appendix. PACS Nos.: 31.30.Gs, 31.30.Jv