QED and relativistic nuclear recoil corrections to the 413-nm tune-out wavelength for the 2 S1 3 state of helium Qed and relativistic nuclear recoil ... Yong-Hui Zhang et al.

Comparison of high-accuracy calculations with precision measurement of the 413-nm tune-out wavelength of the He(23S1) 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 23S1(MJ=0) and 23S1(MJ=±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 [Hyperfine Interact 240, 31 (2019)]10.1007/s10751-019-1574-y to compare results with the only current experimental value of 413.0938(9stat)(20syst) nm for the 23S1(MJ=±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(23S1) state to be 22.5 ppm, which may enable a new test of QED in the future.