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We report an investigation of the self-energy screening effects for the $g$ factor of the ground state of Li-like ions. The leading screening contribution of the relative order $1/Z$ is calculated to all orders in the binding nuclear strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). We also extend the known results for the $Z\alpha$ expansion of the QED screening correction by deriving the leading logarithmic contribution of order $\alpha^5\ln\alpha$ and obtaining approximate results for the $\alpha^5$ and $\alpha^6$ contributions. The comparison of the two approaches yields a stringent check of consistency of the two calculations and allows us to obtain improved estimations of the higher-order screening effects., Comment: Several misprints are corrected in ver.3; Sec. VI is updated in ver.2

The high spectral resolution R about 45,000 provided by IGRINS (Immersion Grating INfrared Spectrometer) at MacDonald Observatory and R 100,000 achieved by CRIRES (CRyogenic high-resolution InfraRed Echelle Spectrograph) at VLT (Very Large Telescope) challenges the present knowledge of infrared spectra. aims We aim to predict the full infrared spectrum of molecular hydrogen at a comparable accuracy. methods We take advantage of the recent theoretical ab initio studies on molecular hydrogen to compute both the electric quadrupole and magnetic dipole transitions taking place within the ground electronic molecular state of hydrogen. results We computed the full infrared spectrum of molecular hydrogen at an unprecedented accuracy and derive for the first time the emission probabilities including both electric quadrupole ($\Delta J = 0, \pm$2) and magnetic dipole transitions ($\Delta J = 0$) as well as the total radiative lifetime of each rovibrational state. Inclusion of magnetic dipole transitions increases the emission probabilities by factors of a few for highly excited rotational levels, which occur in the 3-20 $\mu$ range}, Comment: 6 pages, 1 figure, 2 tables. Full Table 2 is only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/630/A58. It can also be obtained on request to evelyne.roueff@obspm.fr

The quantum electrodynamic correction to the energy of the hydrogen molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching the level of 1 MHz for the dissociation energy, in a very good agreement with the parallel measurement [H\"olsch et al., Phys. Rev. Lett. 122, 103002 (2019)]. Molecular hydrogen has thus become a cornerstone of ultraprecise quantum chemistry, which opens perspectives for determination of fundamental physical constants from its spectra., Comment: 5 pages

We investigate electron-correlation effects in the $g$-factor of the ground state of Li-like ions. Our calculations are performed within the nonrelativistic quantum electrodynamics (NRQED) expansion up to two leading orders in the fine-structure constant $\alpha$, $\alpha^2$ and $\alpha^3$. The dependence of the NRQED results on the nuclear charge number $Z$ is studied and the individual $1/Z$-expansion contributions are identified. Combining the obtained data with the results of the all-order (in $Z\alpha$) calculations performed within the $1/Z$ expansion, we derive the unified theoretical predictions for the $g$-factor of light Li-like ions., Comment: 9 pages, 4 tables

We have investigated the ultracold interspecies scattering properties of metastable triplet He and Rb. We performed state-of-the-art ab initio calculations of the relevant interaction potential, and measured the interspecies elastic cross section for an ultracold mixture of metastable triplet $^4$He and $^{87}$Rb in a quadrupole magnetic trap at a temperature of 0.5 mK. Our combined theoretical and experimental study gives an interspecies scattering length $a_{4+87}=+17^{+1}_{-4}$ $a_0$, which prior to this work was unknown. More general, our work shows the possibility of obtaining accurate scattering lengths using ab initio calculations for a system containing a heavy, many-electron atom, such as Rb., Comment: 11 pages, 11 figures, accepted for publication in Phys. Rev. A

Metrology in atomic physics has been crucial for a number of advanced determinations of fundamental constants. In addition to very precise frequency measurements, the molar polarizability of an atomic gas has recently also been measured very accurately. Part of the motivation for the measurements is due to ongoing efforts to redefine the International System of Units (SI) for which an accurate value of the Boltzmann constant is needed. Here, we calculate the dominant shift of the molar polarizability in an atomic gas due to thermal effects. It is given by the relativistic correction to the dipole interaction, which emerges when the probing electric field is Lorenz transformed into the rest frame of the atoms that undergo thermal motion. While this effect is small when compared to currently available experimental accuracy, the relativistic correction to the dipole interaction is much larger than the thermal shift of the polarizability induced by blackbody radiation., Comment: 4 pages; RevTeX

Accurate theoretical predictions including leading QED corrections for $2^2P_{1/2} - 2^2S_{1/2}$ (D1) and $2^2P_{3/2} - 2^2S_{1/2}$ (D2) transition energies have been obtained for $^{6,7}$Li isotopes. Our results for the Bethe logarithms $\ln k_0(2^2S) = 5.178\,169(4)$, and for mass polarization corrections $\Delta \ln k_0(2^2S) = 0.113\,81(3)$ are in disagreement with ones obtained recently in the literature. In contrast, results $\ln k_0(2^2P) = 5.179\,81(7)$ and $\Delta \ln k_0(2^2P) = 0.111\,3(5)$ are in good agreement with them. From our theoretical predictions and recent measurements of $^{6,7}$Li D-lines at NIST, we determine the mean square charge radius difference between $^7$Li and $^6$Li nuclei, in agreement with determinations based on the $3^2S_{1/2}-2^2S_{1/2}$ transition, what demonstrates consistency of atomic spectroscopy determination of fundamental properties of nuclei., Comment: 7 pages, 5 tables

The Lande g factor describes the response of an atomic energy level to an external perturbation by a uniform and constant magnetic field. In the case of many-electron systems, the leading term is given by the interaction mu_B*(L+2S.B), where L and S are the orbital and spin angular momentum operators, respectively, summed over all electrons. For helium, a long-standing experimental-theoretical discrepancy for P states motivates a reevaluation of the higher-order terms which follow from relativistic quantum theory and quantum electrodynamics (QED). The tensor structure of relativistic corrections involves scalar, vector, and symmetric and anti-symmetric tensor components. We perform a tensorial reduction of these operators in a Cartesian basis, using an approach which allows us to separate the internal atomic from the external degrees of freedom (magnetic field) right from the start of the calculation. The evaluation proceeds in a Cartesian basis of helium eigenstates, using a weighted sum over the magnetic projections. For the relativistic corrections, this leads to a verification of previous results obtained using the Wigner-Eckhart theorem. The same method, applied to the radiative correction (Bethe logarithm term) leads to a spin-dependent correction which is different for singlet versus triplet P states. Theoretical predictions are given for singlet and triplet 2P and triplet 3P states and compared to experimental results where available., Comment: 11 pages; RevTeX

The correction to the polarizability of helium due to black-body radiation is calculated near room temperature. A precise theoretical determination of the black-body radiation correction to the polarizability of helium is essential for dielectric gas thermometry and for the determination of the Boltzmann constant. We find that the correction, for not too high temperature, is roughly proportional to a modified hyperpolarizability (two-color hyperpolarizability), which is different from the ordinary hyperpolarizability of helium. Our explicit calculations provide a definite numerical result for the effect and indicate that the effect of black-body radiation can be excluded as a limiting factor for dielectric gas thermometry using helium or argon., Comment: 8 pages; RevTeX

Changes in the mean-square nuclear charge radii along the lithium isotopic chain were determined using a combination of precise isotope shift measurements and theoretical atomic structure calculations. Nuclear charge radii of light elements are of high interest due to the appearance of the nuclear halo phenomenon in this region of the nuclear chart. During the past years we have developed a new laser spectroscopic approach to determine the charge radii of lithium isotopes which combines high sensitivity, speed, and accuracy to measure the extremely small field shift of an 8 ms lifetime isotope with production rates on the order of only 10,000 atoms/s. The method was applied to all bound isotopes of lithium including the two-neutron halo isotope Li-11 at the on-line isotope separators at GSI, Darmstadt, Germany and at TRIUMF, Vancouver, Canada. We describe the laser spectroscopic method in detail, present updated and improved values from theory and experiment, and discuss the results., Comment: 34 pages, 24 figures, 14 tables

A closed form expression for the three-electron Hylleraas integral involving the inverse quadratic power of one inter-particle coordinate is obtained, and recursion relations are derived for positive powers of other coordinates. This result is suited for high precision calculations of relativistic effects in lithium and light lithium-like ions., Comment: Submited to Phys. Rev. A