Related papers: Quantum electrodynamics $m \alpha^6$ and $m \alpha…
A complete effective Hamiltonian for relativistic corrections at orders $m\alpha^6$ and $m\alpha^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels…
The effective Hamiltonian of $m\alpha^6$ and $m\alpha^6(m/M)$ order corrections for hydrogen molecular ions has been derived in [ Z.-X. Zhong, \emph{et al.}, Phys. Rev. A {\bf98}, 032502(2018).], in this work we express the energy…
Several new corrections of order $m\alpha^6$ to the energy levels of $S$ states in helium are obtained from radiative corrections to the Breit potential and from the polarization insertions in the two photon exchange graphs. While…
The hyperfine structures of the $2\,^3\!S_1$ and $2\,^3\!P_J$ states of the $^7$Be$^{2+}$ and $^9$Be$^{2+}$ ions are investigated within the framework of the nonrelativistic quantum electrodynamics (NRQED). The uncertainties of present…
We perform a calculation of quantum electrodynamics effects in excited states with $l>1$ of arbitrary two-body systems up to $\alpha^6\,\mu$ order. The obtained results are valid for hadronic atoms, as long as the strong interaction effects…
The relativistic second-order corrections at orders $m\alpha^6$ and $m\alpha^6(m/M)$ in hydrogen molecular ions are calculated. Convergence of numerical results is studied, which allows estimating the relative numerical uncertainty to be…
Quantum electrodynamics has been the first theory to emerge from the ideas of regularization and renormalization, and the coupling of the fermions to the virtual excitations of the electromagnetic field. Today, bound-state quantum…
Three-loop electronic vacuum-polarization corrections due to irreducible diagrams are evaluated for two-body muonic ions with nuclear charge numbers 1 <= Z <= 6. The corrections are of order alpha^3 (Zalpha)^2 m_r, where alpha is the…
The logarithmically enhanced alpha^7 ln(1/alpha) contribution to the hyperfine splitting of the positronium ground-state energy levels is calculated in the framework of dimensionally regularized nonrelativistic quantum electrodynamics. The…
We present a variational approach to evaluate relativistic corrections of order \alpha^2 to the Bethe logarithm for the ground electronic state of the Coulomb two center problem. That allows to estimate the radiative contribution at…
The rigorous QED evaluation of the one- and two-photon exchange corrections to the ground-state hyperfine splitting in Li-like ions is presented for the wide range of nuclear charge number $Z= 7 - 82$. The calculations are carried out in…
Theoretical predictions for the Lamb shift in helium are limited by unknown quantum electrodynamic effects of the order $\alpha^7m$, where $\alpha$ is the fine-structure constant and $m$ is the electron mass. We make an important step…
Relying on the redefined vacuum state approach, and based on one-particle three-loop Feynman diagrams, partial third-order interelectronic corrections to the valence electron energy shift are investigated in Li-like ions. The idea is to…
A systematic formalism for quantum electrodynamics in a classical uniform magnetic field is discussed. The first order radiative correction to the ground state energy of an electron is calculated. This then leads to the anomalous magnetic…
Quantum electrodynamical (QED) calculations of ionization energies of the $1snd\,D$ states are performed for the helium atom. We reproduce the previously known relativistic and QED effects up to order $m\alpha^5$ and extend the theory by…
The finite operators are derived for the recoil $m\alpha^6(m/M)$ order relativistic corrections (to spin-averaged energy levels) in hydrogen-like atoms and ions in the two- and three-body formalism beyond the adiabatic approximation.…
We study the semiclassical behaviour of a two--dimensional nonintegrable system. In particular we analyze the question of quantum corrections to the semiclassical quantization obtaining up to the second order of perturbation theory an…
Absolute transition frequencies of the $2s\; ^2{\rm S}_{1/2} \rightarrow 2p\;^2\mathrm{P}_{1/2,3/2}$ transitions in Be$^+$ were measured for the isotopes $^{7,9-12}$Be. The fine structure splitting of the $2p$ state and its isotope…
We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $m\alpha^7 \ln(\alpha)$-order radiative correction is derived in the NRQED framework.…
The simplest, algebraic quantum-electrodynamical corrections, due to the double-negative energy subspace and instantaneous interactions, are computed to the no-pair energy of two-spin-1/2-fermion systems. Numerical results are reported for…