Zeeman effect of the hyperfine structure levels in hydrogenlike ions

The fully relativistic theory of the Zeeman splitting of the $1s$ hyperfine structure levels in hydrogenlike ions is considered for the magnetic field magnitude in the range from 1 to 10 T. The second-order corrections to the Breit -- Rabi formula are calculated and discussed. The results can be used for a precise determination of nuclear magnetic moments from $g$ factor experiments.Comment: 13 page

Lamb shift in muonic deuterium atom

We present new investigation of the Lamb shift (2P_{1/2}-2S_{1/2}) in muonic deuterium (mu d) atom using the three-dimensional quasipotential method in quantum electrodynamics. The vacuum polarization, nuclear structure and recoil effects are calculated with the account of contributions of orders alpha^3, alpha^4, alpha^5 and alpha^6. The results are compared with earlier performed calculations. The obtained numerical value of the Lamb shift 202.4139 meV can be considered as a reliable estimate for the comparison with forthcoming experimental data.Comment: 24 pages, 11 figures. arXiv admin note: text overlap with arXiv:hep-ph/061229

Computational investigation of static multipole polarizabilities and sum rules for ground-state hydrogen-like ions

High precision multipole polarizabilities, $\alpha_{\ell}$ for $\ell \le 4$ of the $1s$ ground state of the hydrogen isoelectronic series are obtained from the Dirac equation using the B-spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of $Z$ with a relative accuracy of 10$^{-6}$ up to $Z = 100$ are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules $\sum_i f^{(\ell)}_{0i} = 0$ for all multipoles from $\ell = 1$ to $\ell = 4$. The dispersion coefficients for the long-range H-H and H-He$^+$ interactions are given.Comment: 8 figures, 8 table

Electron shielding of the nuclear magnetic moment in hydrogen-like atom

The correction to the wave function of the ground state in a hydrogen-like atom due to an external homogenous magnetic field is found exactly in the parameter $Z\alpha$. The $j=1/2$ projection of the correction to the wave function of the $ns_{1/2}$ state due to the external homogeneous magnetic field is found for arbitrary $n$. The $j=3/2$ projection of the correction to the wave function of the $ns_{1/2}$ state due to the nuclear magnetic moment is also found for arbitrary $n$. Using these results, we have calculated the shielding of the nuclear magnetic moment by the $ns_{1/2}$ electron.Comment: 15 page

Lamb shift in muonic helium ion

The Lamb shift (2P_{1/2}-2S_{1/2}) in the muonic helium ion (mu ^4_2He)^+ is calculated with the account of contributions of orders alpha^3, alpha^4, alpha^5 and alpha^6. Special attention is given to corrections of the electron vacuum polarization, the nuclear structure and recoil effects. The obtained numerical value of the Lamb shift 1379.028 meV can be considered as a reliable estimate for the comparison with experimental data.Comment: 18 pages, 11 figure

Relativistic dynamical polarizability of hydrogen-like atoms

Using the operator representation of the Dirac Coulomb Green function the analytical method in perturbation theory is employed in obtaining solutions of the Dirac equation for a hydrogen-like atom in a time-dependent electric field. The relativistic dynamical polarizability of hydrogen-like atoms is calculated and analysed.Comment: 15 pages, 3 figures (not included, but hard copies are available upon request

Hyperfine Structure of S-States in Muonic Helium Ion

Corrections of orders alpha^5 and alpha^6 are calculated in the hyperfine splittings of 1S and 2S - energy levels in the ion of muonic helium. The electron vacuum polarization effects, the nuclear structure corrections and recoil corrections are taken into account. The obtained numerical values of the hyperfine splittings -1334.56 meV (1S state), -166.62 meV (2S state) can be considered as a reliable estimate for the comparison with the future experimental data. The hyperfine splitting interval Delta_{12}=(8 Delta E^{hfs}(2S)- Delta E^{hfs}(1S)) = 1.64 meV can be used for the check of quantum electrodynamics.Comment: 14 pages, 5 figure

Muonic hydrogen ground state hyperfine splitting

Corrections of orders alpha^5, alpha^6 are calculated in the hyperfine splitting of the muonic hydrogen ground state. The nuclear structure effects are taken into account in the one- and two-loop Feynman amplitudes by means of the proton electromagnetic form factors. The modification of the hyperfine splitting part of the Breit potential due to the electron vacuum polarization is considered. Total numerical value of the 1S state hyperfine splitting 182.638 meV in the (mu p) can play the role of proper estimation for the corresponding experiment with the accuracy 30 ppm.Comment: 18 pages, Talk presented at the 11th Lomonosov Conference on Elementary Particle Physics, Moscow State University, August 200

Theory of muonic hydrogen - muonic deuterium isotope shift

We calculate the corrections of orders alpha^3, alpha^4 and alpha^5 to the Lamb shift of the 1S and 2S energy levels of muonic hydrogen (mu p) and muonic deuterium (mu d). The nuclear structure effects are taken into account in terms of the proton r_p and deuteron r_d charge radii for the one-photon interaction and by means of the proton and deuteron electromagnetic form factors in the case of one-loop amplitudes. The obtained numerical value of the isotope shift (mu d) - (mu p) for the splitting (1S-2S) 101003.3495 meV can be considered as a reliable estimation for corresponding experiment with the accuracy 10^{-6}. The fine structure interval E(1S)-8E(2S) in muonic hydrogen and muonic deuterium are calculated.Comment: 22 pages, 7 figure