# QED and relativistic nuclear recoil corrections to the 413 nm tune-out wavelength for the $2\,^3S_1$ state of helium

## TL;DR

This paper presents high-precision relativistic and QED calculations of the helium 413 nm tune-out wavelength, revealing a small discrepancy with experimental data and providing insights for future tests of quantum electrodynamics.

## Contribution

The study introduces comprehensive relativistic-configuration-interaction calculations including nuclear recoil and QED effects for the helium 2^3S_1 state’s tune-out wavelength.

## Key findings

- Calculated tune-out wavelengths are 413.08426(4) nm and 413.09015(4) nm for different magnetic sublevels.
- Discovered a 1.8σ discrepancy between theoretical prediction and experimental measurement.
- Determined QED correction to the static dipole polarizability as 22.5 ppm.

## Abstract

Comparison of high accuracy calculations with precision measurement of the 413 nm tune-out wavelength of the He($2\,^3S_1$) 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 $2\,^3S_1(M_J=0)$ and $2\,^3S_1(M_J=\pm 1)$ 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 $2\,^3S_1(M_J=\pm 1)$ 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($2\,^3S_1$) state to be 22.5 ppm, which may enable a new test of QED in the future.