One-loop binding corrections to the electron gg factor

We calculate the one-loop electron self-energy correction of order $\alpha\,(Z\,\alpha)^5$ to the bound electron $g$ factor. Our result is in agreement with the extrapolated numerical value and paves the way for the calculation of the analogous, but as yet unknown two-loop correction.Comment: 4 page

Quantum electrodynamics corrections to the 2P2P fine splitting in Li

We consider quantum electrodynamics (QED) corrections to the fine splitting $E(2P_{3/2}) - E(2P_{1/2})$ in the Li atom. We derive complete formulas for the $m\,\alpha^6$ and $m\,\alpha^7\,\ln\alpha$ contributions and calculate them numerically using highly optimized, explicitly correlated basis functions. The obtained results resolve disagreement between measurements and lay the foundations for investigation of QED effects in light, many-electron atoms.Comment: 11 page

Singular Hylleraas three-electron integrals

Calculations of the leading quantum electrodynamics effects in few electron systems involve singular matrix elements of the inter-electronic distances of the form $1/r_i^3$ and $1/r_{ij}^3$. Integrals that result when the nonrelativistic wave function is represented with a Hylleraas basis representation are studied. Recursion relations for various powers of the electron coordinates and the master integrals are derived in a form suited for high precision numerical evaluations.Comment: 20 pages, accepted for Phys. Rev.

Ground state hyperfine splitting in the Be+^+ ion

Relativistic and QED corrections are calculated for the hyperfine splitting (hfs) in the $2S_{1/2}$ ground state of $^{9}$Be$^+$ ions with an exact account for electronic correlations. The achieved accuracy is sufficient to determine the finite nuclear size effects from the comparison to the experimental hfs value. The obtained results establish the ground to determine the neutron halo in $^{11}$Be.Comment: 7 page

Refractive index and generalized polarizability

We investigate the role of retardation corrections to polarizability and to refractive index. We found that the classical electromagnetic theory of dielectrics requires corresponding modifications in terms of nonlocality of the dielectric constant. This nonlocality should be taken into account in the interpretation of accurate measurements of the optical refractivity.Comment: 4 page

Quantum electrodynamics mα6m \alpha^6 and mα7ln⁡αm \alpha^7 \ln \alpha corrections to the fine splitting in Li and Be+^+

We derive quantum electrodynamics corrections to the fine structure in three-electron atomic systems at $m \alpha^6$ and $m \alpha^7 \ln \alpha$ orders and present their numerical evaluations for the Li atom and Be$^+$ ion

Hyperfine structure in the HD molecule

We investigate interactions between the proton spin, the deuteron spin, and the orbital angular momentum in the electronic ground state of the HD molecule. These interactions lead to hyperfine splittings of molecular energy levels. Our numerical results for the first rotational level agree well with the currently most accurate measurement performed by Ramsey {\em et al.} in the 1950s. Knowledge of the hyperfine structure of other levels is necessary for the accurate determination of rovibrational transition energies in spectroscopic measurements. We present theoretical predictions and share the numerical code used to perform numerical calculations. This work sets the ground for high precision spectroscopic tests of hyperfine interactions in molecular systems. In particular we determine the value of the deuteron quadrupole moment $Q = 0.2856(2)$ fm$^2$ and give outlook for improving its accuracy by three orders of magnitude.Comment: 9 pages, three figures, corrected notatio

Explicitly correlated wave function for a boron atom

We present results of high-precision calculations for a boron atom's properties using wave functions expanded in the explicitly correlated Gaussian basis. We demonstrate that the well-optimized 8192 basis functions enable a determination of energy levels, ionization potential, and fine and hyperfine splittings in atomic transitions with nearly parts per million precision. The results open a window to a spectroscopic determination of nuclear properties of boron including the charge radius of the proton halo in the $^8$B nucleus

Deuteron and triton magnetic moments from NMR spectra of the hydrogen molecule

We present a theory and calculations of the nuclear magnetic shielding with finite nuclear mass effects and determine magnetic moments of deuteron and triton using the known NMR spectra of HD and HT molecules. The results $\mu_d = 0.857\,438\,234\,6(53)\;\mu_N$ and $\mu_t = 2.978\,962\,471(10)\;\mu_N$ are more accurate and in a good agreement with the currently accepted values.Comment: 5 pages, 1 figur

Electromagnetic moments of the bound system of charged particles

We consider a bound system of particles interacting via electromagnetic forces in an external electromagnetic field, including leading relativistic corrections. Each particle has a definite mass, charge, spin, and charge radius. We introduce suitable canonical transformations and a perturbation scheme to obtain a Hamiltonian which describes the global dynamics of the system. This enables the derivation of formulas for various electromagnetic moments, such as the magnetic dipole moment, the mean square charge radius, and the electric dipole polarizability.Comment: improved two-column version, 8 page