The nuclear recoil effect on the g factor of Li-like ions is evaluated. The one-electron recoil contribution is treated within the framework of the rigorous QED approach to the first order in the electron-to-nucleus mass ratio m/M and to all orders in the parameter αZ. These calculations are performed in a range Z=3-92. The two-electron recoil term is calculated for low- and middle-Z ions within the Breit approximation using a four-component approach. The results for the two-electron recoil part obtained in the Letter strongly disagree with the previous calculations performed using an effective two-component Hamiltonian. The obtained value for the recoil effect is used to calculate the isotope shift of the g factor of Li-like ^{A}Ca^{17+} with A=40 and A=48 which was recently measured. It is found that the new theoretical value for the isotope shift is closer to the experimental one than the previously obtained value.

Fully relativistic approach to evaluate the correlation effects in highly charged ions is presented. The interelectronic-interaction contributions of first and second orders in 1/Z are treated rigorously within the framework of bound-state quantum electrodynamics, whereas the calculations of the third-and higherorder contributions are based on the Dirac-Coulomb-Breit Hamiltonian. The developed approach allows one to deal with single as well as degenerate or quasi-degenerate states. We apply this approach to the calculations of the correlation contributions to the n = 1 and n = 2 energy levels in heliumlike ions.The obtained contributions are combined with the one-electron and screened QED corrections, nuclear recoil and nuclear polarization corrections to get the total theoretical predictions for the ionization and transition energies in high-Z heliumlike ions. * Corresponding author: a.v.malyshev@spbu.ru 1

Ab initio QED calculations of the ground-state binding energies of berylliumlike ions are performed for the wide range of the nuclear charge number: Z=18-96. The calculations are carried out in the framework of the extended Furry picture starting with three different types of the screening potential. The rigorous QED calculations up to the second order of the perturbation theory are combined with the third- and higher-order electron-correlation contributions obtained within the Breit approximation by the use of the large-scale configuration-interaction Dirac-Fock-Sturm method. The effects of nuclear recoil and nuclear polarization are taken into account. The ionization potentials are obtained by subtracting the binding energies of the corresponding lithiumlike ions. In comparison with the previous calculations the accuracy of the binding energies and the ionization potentials is significantly improved.Comment: 2 figures, 5 table

Using the field theory renormalization group, we study the critical behavior of two systems subjected to turbulent mixing. The first system, described by the equilibrium model A, corresponds to the relaxational dynamics of a nonconserved order parameter. The second system is the strongly nonequilibrium reactiondiffusion system, known as the Gribov process or directed percolation process. The turbulent mixing is modeled by the stochastic Navier-Stokes equation with a random stirring force with the correlator ∝ δ(t − t )p 4−d−y , where p is the wave number, d is the space dimension, and y is an arbitrary exponent. We show that the systems exhibit various types of critical behavior depending on the relation between y and d. In addition to known regimes (original systems without mixing and a passively advected scalar field), we establish the existence of new strongly nonequilibrium universality classes and calculate the corresponding critical dimensions to the first order of the double expansion in y and ε = 4 − d (one-loop approximation).

Infrared asymptotic behaviour of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with correlation function of the form ∝ δ(the component of the wave vector, perpendicular to the distinguished direction ('direction of the flow') -the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990)]. The structure functions of the scalar field in the infrared range exhibit scaling behaviour with exactly known critical dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular to the flow are essentially different. In contrast to the isotropic Kraichnan's rapid-change model, the structure functions show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity. On the contrary, the dependence of the internal scale (or diffusivity coefficient) persists in the infrared range. Generalization to the velocity field with a finite correlation time is also obtained. Depending on the relation between the exponents in the energy spectrum E ∝ k 1−ε ⊥ and in the dispersion law ω ∝ k 2−η ⊥ , the infrared behaviour of the model is given by the limits of vanishing or infinite correlation time, with the crossover at the ray η = 0, ε > 0 in the ε-η plane. The physical (Kolmogorov) point ε = 8/3, η = 4/3 lies inside the domain of stability of the rapid-change regime; there is no crossover line going through this point.