QED and relativistic nuclear recoil corrections to the 413 nm tune-out wavelength for the $2{}^3{S}_1$ 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 electro-dynamic (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 $2{}^3{S}_1(M_J=\pm 1)$ states are 413.084 26(4) nm and 413.090 15(4) nm, respectively. Compared with the only current experimental value of 413.0938(9stat)(20syst) nm for the $2{}^3{S}_1(M_J=\pm 1)$ state, there is 1.8$\sigma$ discrepancy between present theoretical work 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.

6 pages; 2 figures

References in corpus (4)

• High-precision measurement of the atomic mass of the electron
• Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius
• Frequency-dependent polarizability of helium including relativistic effects with nuclear recoil terms
• Higher-order recoil corrections for singlet states of the helium atom

Cited by in corpus (1)

• Proposal for suppressing ac Stark shift in the He($2{}^3{S}_1\to 3{}^3{S}_1$) two-photon transition using magic wavelengths