A large-scale full-configuration-interaction calculation based on Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the 2 1 S0 and 2 3 S1 states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved n (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states. And a series of magic wavelengths with QED and hyperfine effects included for the 2 3 S1 → 2 1 S0 transition of helium are identified. In addition, the high-order Ac Stark shift determined by the dynamic hyperpolarizabilities at the magic wavelengths are also evaluated. Since the most promising magic wavelength for application in experiment is 319.8 nm, the high-accuracy magic wavelength of 319.815 3(6) nm of 4 He is in good agreement with recent measurement value of 319.815 92(15) nm [Nature Physics (2018)/arXiv:1804.06693], and present magic wavelength of 319.830 2(7) nm for 3 He would provide theoretical support for experimental designing an optical dipole trap to precisely determine the nuclear charge radius of helium in future.
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.
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