QED and relativistic nuclear recoil corrections to the 413-nm tune-out wavelength for the 2  S13 state of helium

Abstract

Comparison of high-accuracy calculations with precision measurement of the 413-nm tune-out wavelength of the He(2 3 S 1 ) state provides a unique test of quantum electrodynamics (QED). We perform large-scale relativistic-configuration-interaction (RCI) calculations of the tune-out wavelength that include the mass-shift operator and fully account for leading relativistic nuclear recoil terms in the Dirac-Coulomb-Breit (DCB) Hamiltonian. We obtain the QED correction to the tune-out wavelength using perturbation theory, and the effect of finite nuclear size is also evaluated. The resulting tune-out wavelengths for the 2 3 S 1 (M J = 0) and 2 3 S 1 (M J = ±1) states are 413.084 26(4) nm and 413.090 15(4) nm, respectively. When we incorporate the retardation correction of 0.000 560 0236 nm obtained by Drake et al. [Hyperfine Interact 240, 31 (2019)] to compare results with the only current experimental value of 413.0938(9 stat )(20 syst ) nm for the 2 3 S 1 (M J = ±1) state, there is 1.4σ discrepancy between theory and experiment, which stimulates further theoretical and higher precision experimental investigations on the 413-nm tune-out wavelength. In addition, we also determine the QED correction for the static dipole polarizability of the He(2 3 S 1 ) state to be 22.5 ppm, which may enable a new test of QED in the future.

Measurement of a helium tune-out frequency: an independent test of quantum electrodynamics

“…Separately, we improved on the state-of-the-art calculation ( 28 ) of the tune-out frequency by accounting for finite nuclear mass, relativistic, QED, finite nuclear size, and finite wavelength retardation effects ( 27 , 29 ). We achieved a 10-fold improvement in precision and found a theoretical value of 725,736,252(9) MHz for f TO (−1,0).…”

Testing QED by measuring a He* tune-out wavelength

“…Recent calculations formulate the tune-out as a zero in the Rayleigh scattering cross-section for an atom interacting with an electromagnetic plane wave [3]. Accounting for perturbative QED corrections, the effect of finite nuclear size, and finite wavelength retardation corrections yields a predicted value of 725.744841(7) THz [4], compared to our first experimental value of 725.7393(16stat)(35syst) THz [2].…”

Measurement of the 671-nm tune-out wavelength of Li7 by atom interferometry

“…There are also many calculations of tune-out wavelengths and, frequently, several tune-out wavelengths are calculated in the same paper. The calculation of the 413nm tune-out wavelength for He * has been made by several research groups [31,32] and in some works with very sophisticated methods [33][34][35]. Many works have been devoted to the alkali atoms: lithium [17,36], including a calculation with Hylleraas wave functions [37], sodium [17], potassium [17,38], rubidium [17,26,27,29], cesium [17], and francium [39,40].…”