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A large-scale full-configuration-interaction calculation based onDirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2\,^1S_0$ and$2\,^3S_1$ states of helium. The operators of the normal and specific massshifts are directly included in the DCB framework to take the finite nuclearmass correction into account. High-accuracy energies and matrix elementsinvolved n (the main quantum number) up to 13 are obtained from onediagonalization of Hamiltonian. The dynamic dipole polarizabilities arecalculated by using the sum rule of intermediate states. And a series of magicwavelengths with QED and hyperfine effects included for the$2\,^3S_1\rightarrow2\,^1S_0$ transition of helium are identified. In addition,the high-order Ac Stark shift determined by the dynamic hyperpolarizabilitiesat the magic wavelengths are also evaluated. Since the most promising magicwavelength for application in experiment is 319.8 nm, the high-accuracy magicwavelength of 319.815 3(6) nm of $^4$He is in good agreement with recentmeasurement 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 opticaldipole trap to precisely determine the nuclear charge radius of helium infuture.

Relativistic full-configuration-interaction calculations of magic wavelengths for the $2\,^3S_1\rightarrow2\,^1S_0$ transition of helium isotopes