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Dirac equation for an electron bound by a nucleus in the presence of externalaxially symmetric field can be solved numerically by using thedual-kinetic-balance conditions imposed on the finite basis set (A-DKB method[Rozenbaum et al, Phys. Rev. A 89, 012514 (2014)]). We present the applicationof this method to describe helium-like ions exposed to homogeneous externalmagnetic field. The second-order Zeeman shift and the nuclear magneticshielding constant are evaluated for the ground state, including the leadingcontribution of the interelectronic interaction. The A-DKB values are comparedwith the direct calculations by perturbation theory. The results for thenuclear magnetic shielding can serve for accurate determination of the nuclearmagnetic moments. The quadratic contribution to the Zeeman effect can berelevant for high-precision measurements of the transition energies inhelium-like ions.

Helium-like ions in magnetic field: application of the nonperturbative relativistic method for axially symmetric systems