  A large-scale full-configuration-interaction calculation based on
Dirac-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 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
$2\,^3S_1\rightarrow2\,^1S_0$ 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.
