The nuclear recoil effect on the $^2 P_{3/2}$-state $g$ factor of B-like ions is calculated to first order in the electron-to-nucleus mass ratio $m/M$ in the range $Z=18$--$92$. The calculations are performed by means of the $1/Z$ perturbation theory. Within the independent-electron approximation, the one- and two-electron recoil contributions are evaluated to all orders in the parameter $\alpha Z$ by employing a fully relativistic approach. The interelectronic-interaction correction of first order in $1/Z$ is treated within the Breit approximation. Higher orders in $1/Z$ are partially taken into account by incorporating the screening potential into the zeroth-order Hamiltonian. The most accurate to date theoretical predictions for the nuclear recoil contribution to the bound-electron $g$ factor are obtained.
We study the process of vacuum birefringence in a strong electromagnetic field: a probe photon changes its polarization while traversing a counterpropagating laser beam. To describe this phenomenon, we calculate the polarization tensor in the field of a plane monochromatic wave to leading order with respect to its amplitude. The main goal of the study is to compare the results with the data obtained within the locally constant field approximation (LCFA). Here we identify the domain of the LCFA applicability in the case of a plane-wave external background. It is shown that the frequency of the probe photon and that of the external field are symmetrically involved in the relative uncertainty. The exact treatment of the spatiotemporal dependence beyond the LCFA becomes necessary at the energy scale 0.1-1 MeV.
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