Relativistic corrections of m\alpha^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions

The major goal of the high-precision studies of ro-vibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set of relativistic and radiative corrections have been obtained for a wide range of ro-vibrational states of H_2^+ and HD^+ up to order R_\infty\alpha^4. In this work we complete calculations of various contributions to the R_\infty\alpha^4 order by computing the relativistic corrections to the binding energy of electron.Comment: 4 pages, 1 figur

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

Vacuum polarization calculations for hydrogenlike and alkalilike ions

Complete vacuum polarization calculations incorporating finite nuclear size are presented for hydrogenic ions with principal quantum numbers n=1-5. Lithiumlike, sodiumlike, and copperlike ions are also treated starting with Kohn-Sham potentials, and including first-order screening corrections. In both cases dominant Uehling terms are calculated with high accuracy, and smaller Wichmann- Kroll terms are obtained using numerical electron Green's functions.Comment: 23 pages, 1 figur

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

Radiative Corrections to One-Photon Decays of Hydrogenic Ions

Radiative corrections to the decay rate of n=2 states of hydrogenic ions are calculated. The transitions considered are the M1 decay of the 2s state to the ground state and the E1(M2) decays of the $2p_{1/2}$ and $2p_{3/2}$ states to the ground state. The radiative corrections start in order $\alpha (Z \alpha)^2$, but the method used sums all orders of $Z\alpha$. The leading $\alpha (Z\alpha)^2$ correction for the E1 decays is calculated and compared with the exact result. The extension of the calculational method to parity nonconserving transitions in neutral atoms is discussed.Comment: 22 pages, 2 figure

A New Tool for the Lamb Shift Calculation

We solve the Bethe-Salpeter equation for hydrogenic bound states by choosing an appropriate interaction kernel $K_c$. We want to use our solution to calculate up to a higher order the hydrogen Lamb-shift, and as a first application we present up to order \left(\aa / \pi\right)(\za)^7 the contribution of the lowest order self-energy graph, calculated {\it exactly}. The basic formalism is a natural extension to the hydrogenic bound states of the one previously presented by R. Barbieri and E. Remiddi and used in the case of positronium.Comment: 21 pages, Latex, Preprint DFUB-94-0

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

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

A cluster-separable Born approximation for the 3D reduction of the three-fermion Bethe-Salpeter equation

We perform a 3D reduction of the two-fermion Bethe-Salpeter equation based on Sazdjian's explicitly covariant propagator, combined with a covariant substitute of the projector on the positive-energy free states. We use this combination in the two fermions in an external potential and in the three-fermion problems. The covariance of the two-fermion propagators insures the covariance of the two-body equations obtained by switching off the external potential, or by switching off all interactions between any pair of two fermions and the third one, even if the series giving the 3D potential is limited to the Born term or more generally truncated. The covariant substitute of the positive energy projector preserves the equations against continuum dissolution without breaking the covariance.Comment: 21 pages, 1 figure This article has been deeply modified after refereeing. The presentation has been improved and examples have been added. Three subsections have been added (transition matrix elements, two-body limits, covariant Salpeter's equation). submitted to Journal of Physics

Relativistic, QED, and nuclear mass effects in the magnetic shielding of 3^3He

The magnetic shielding $\sigma$ of $^3$He is studied. The complete relativistic corrections of order $O(\alpha^2)$, leading QED corrections of order $O(\alpha^3 \ln\alpha)$, and finite nuclear mass effects of order $O(m/m_{\rm N})$ are calculated with high numerical precision. The resulting theoretical predictions for $\sigma = 59.967~43(10)\cdot 10^{-6}$ are the most accurate to date among all elements and support the use of $^3$He as a NMR standard.Comment: 10 pages, corrected minor errors in Eqs.(6,7