Hyperfine structure of S states in Li and Be^+

A large-scale configuration-interaction (CI) calculation is reported for the hyperfine splitting of the 2^2S and 3^2S states of ^7Li and ^9Be^+. The CI calculation based on the Dirac-Coulomb-Breit Hamiltonian is supplemented with a separate treatment of the QED, nuclear-size, nuclear-magnetization distribution, and recoil corrections. The nonrelativistic limit of the CI results is in excellent agreement with variational calculations. The theoretical values obtained for the hyperfine splitting are complete to the relative order of \alpha^2 and improve upon results of previous studies.Comment: 4 pages, 2 table

Two-Loop Bethe Logarithms for non-S Levels

Two-loop Bethe logarithms are calculated for excited P and D states in hydrogenlike systems, and estimates are presented for all states with higher angular momenta. These results complete our knowledge of the P and D energy levels in hydrogen at the order of alpha^8 m_e c^2, where m_e is the electron mass and c is the speed of light, and scale as Z^6, where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms of order (alpha/pi)^2 (Z alpha)^6 ln[(Z alpha)^(-2)] m_e c^2 for D states and all states with higher angular momenta. For higher excited P and D states, a number of poles from lower-lying levels have to subtracted in the numerical evaluation. We find that, surprisingly, the corrections of the "squared decay-rate type" are the numerically dominant contributions in the order (alpha/pi)^2 (Z alpha)^6 m_e c^2 for states with large angular momenta, and provide an estimate of the entire B_60-coefficient for Rydberg states with high angular momentum quantum numbers. Our results reach the predictive limits of the quantum electrodynamic theory of the Lamb shift.Comment: 14 pages, RevTe

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

Hadronic Vacuum Polarization and the Lamb Shift

Recent improvements in the determination of the running of the fine-structure constant also allow an update of the hadronic vacuum-polarization contribution to the Lamb shift. We find a shift of -3.40(7) kHz to the 1S level of hydrogen. We also comment on the contribution of this effect to the determination by elastic electron scattering of the r.m.s. radii of nuclei.Comment: 7 pages, latex, 1 figure -- Submitted to Phys. Rev. A -- epsfig.sty require

Stark shift and parity non-conservation for near-degenerate states of xenon

We identify a pair of near-degenerate states of opposite parity in atomic Xe, the 5p^5 10s \,\, ^2[3/2]_2^o at $\rm{E}=94759.927$ cm$^{-1}$ and 5p^5 6f \,\, ^2[5/2]_2 at $\rm{E}= 94759.935$ cm$^{-1}$, for which parity- and time-odd effects are expected to be enhanced by the small energy separation. We present theoretical calculations which indicate narrow widths for both states and we report a calculated value for the weak matrix element, arising from configuration mixing, of $|W|=2.1$ Hz for $^{132}$Xe. In addition, we measured the Stark effect of the $5p^5\,6f$ $^2[5/2]_{2}$ and $5p^5 \,6f \ ^2[3/2]_2$ ($\rm{E} =94737.121\,\rm{cm}^{-1}$) states. The Stark-shift of the $6f$ states is observed to be negative, revealing the presence of nearby $6g$ states at higher energies, which have not been observed before. The Stark-shift measurements imply an upper limit on the weak matrix element of $|W|\!<\!5$ Hz for the near-degenerate states (10s \,\, ^2[3/2]_2^o and 6f \,\, ^2[5/2]_2), which is in agreement with the presented calculations.Comment: 11 pages, 6 figure

Two-Loop Bethe Logarithms for Higher Excited S Levels

Processes mediated by two virtual low-energy photons contribute quite significantly to the energy of hydrogenic S states. The corresponding level shift is of the order of (alpha/pi)^2 (Zalpha)^6 m_e c^2 and may be ascribed to a two-loop generalization of the Bethe logarithm. For 1S and 2S states, the correction has recently been evaluated by Pachucki and Jentschura [Phys. Rev. Lett. vol. 91, 113005 (2003)]. Here, we generalize the approach to higher excited S states, which in contrast to the 1S and 2S states can decay to P states via the electric-dipole (E1) channel. The more complex structure of the excited-state wave functions and the necessity to subtract P-state poles lead to additional calculational problems. In addition to the calculation of the excited-state two-loop energy shift, we investigate the ambiguity in the energy level definition due to squared decay rates.Comment: 14 pages, RevTeX, to appear in Phys. Rev.

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 corrections of order m\alpha^6 to the two-center problem

Effective potentials of the relativistic m\alpha^6 order correction for the ground state of the Coulomb two-center problem are calculated. They can be used to evaluate the relativistic contribution of that order to the energies of hydrogen molecular ions or metastable states of the antiprotonic helium atom, where precision spectroscopic data are available. In our studies we use the variational expansion based on randomly chosen exponents that permits to achieve high numerical accuracy.Comment: 12 pages, 3 tables 2 figures; submitted to the Journal of Physics

Ground State Hyperfine Structure of Muonic Helium Atom

On the basis of the perturbation theory in the fine structure constant $\alpha$ and the ratio of the electron to muon masses we calculate one-loop vacuum polarization and electron vertex corrections and the nuclear structure corrections to the hyperfine splitting of the ground state of muonic helium atom $(\mu e ^4_2He)$. We obtain total result for the ground state hyperfine splitting $\Delta \nu^{hfs}=4465.526$ MHz which improves the previous calculation of Lakdawala and Mohr due to the account of new corrections. The remaining difference between the theoretical result and experimental value of the hyperfine splitting equal to 0.522 MHz lies in the range of theoretical error and requires the subsequent investigation of higher order corrections.Comment: Talk presented at the scientific session-conference of Nuclear Physics Department RAS "Physics of fundamental interactions", 25-30 November 2007, ITEP, Moscow, 18 pages, 5 figure

Relativistic calculations of pionic and kaonic atoms hyperfine structure

We present the relativistic calculation of the hyperfine structure in pionic and kaonic atoms. A perturbation method has been applied to the Klein-Gordon equation to take into account the relativistic corrections. The perturbation operator has been obtained \textit{via} a multipole expansion of the nuclear electromagnetic potential. The hyperfine structure of pionic and kaonic atoms provide an additional term in the quantum electrodynamics calculation of the energy transition of these systems. Such a correction is required for a recent measurement of the pion mass