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On the basis of quasipotential approach in quantum electrodynamics we calculate vacuum polarization and quadrupole corrections in first and second orders of perturbation theory in hyperfine structure of P-states in muonic deuterium. All corrections are presented in integral form and evaluated analytically and numerically. The obtained results can be used for the improvement of the transition frequencies between levels 2P and 2S., Comment: 7 pages

We consider a narrow magneto-dipole transition in the $^{169}$Tm atom at the wavelength of $1.14\,\mu$m as a candidate for a 2D optical lattice clock. Calculating dynamic polarizabilities of the two clock levels $[\text{Xe}]4f^{13}6s^2 (J=7/2)$ and $[\text{Xe}]4f^{13}6s^2 (J=5/2)$ in the spectral range from $250\,$nm to $1200\,$nm, we suggest the "magic" wavelength for the optical lattice at $807\,$nm. Frequency shifts due to black-body radiation (BBR), the van der Waals interaction, the magnetic dipole-dipole interaction and other effects which can perturb the transition frequency are calculated. The transition at $1.14\,\mu$m demonstrates low sensitivity to the BBR shift corresponding to $8\times10^{-17}$ in fractional units at room temperature which makes it an interesting candidate for high-performance optical clocks. The total estimated frequency uncertainty is less than $5 \times 10^{-18}$ in fractional units. By direct excitation of the $1.14\,\mu$m transition in Tm atoms loaded into an optical dipole trap, we set the lower limit for the lifetime of the upper clock level $[\text{Xe}]4f^{13}6s^2 (J=5/2)$ of $112\,$ms which corresponds to a natural spectral linewidth narrower than $1.4\,$Hz. The polarizability of the Tm ground state was measured by the excitation of parametric resonances in the optical dipole trap at $532\,$nm.

We present the results of a study of the diffusion of Rb atoms in paraffin - coated resonant vapor cells. We have modeled the Rb diffusion both in the cell and in the coating, assuming that the main loss of Rb atoms is due to the physical absorption of the atoms by the glass substrate. It is demonstrated that the equilibrium atomic density in the cell is a monotonic function of the thickness of the paraffin coating: the density increases with an increase in the thickness of the coating. The diffusion coefficient for rubidium in paraffin thin films has been determined to be equal to 4,7*10^-7 cm^2/s. The results of the experiment might be useful for a better understanding of the details involved in the processes of the interaction of alkali atoms with a paraffin coating.

We present the results of the study of an optical resonant cell filled by a vapor of the Rb atoms and coated with a non-stick polydimethylsiloxane (PDMS) polymer. We show that it is possible to define correctly the diffusion coefficient of the atoms in the coating, using geometric parameters of the cell and the vapor density in the cell volume only. The dependence of the diffusion coefficient on the cell curing time is presented. It is shown that the mysterious cell curing process can be explained in terms of the polymerization of the polymer coating by alkali atoms. Anomalous long dwell time of the Rb atoms on the PDMS coating is discussed as well.

On the basis of quasipotential approach to the bound state problem in quantum electrodynamics we calculate hyperfine structure intervals Delta E^{hfs}(2P_{1/2}) and Delta E^{hfs}(2P_{3/2}) for P-states in muonic deuterium. The tensor method of projection operators for the calculation of the hyperfine structure of P-states with definite quantum numbers of total atomic momentum F and total muon momentum j in muonic deuterium is formulated. We take into account vacuum polarization, relativistic, quadrupole and structure corrections of orders alpha^4, alpha^5 and alpha^6. The obtained numerical values of hyperfine splittings are useful for the analysis of new experimental data of the CREMA collaboration regarding to muonic deuterium., Comment: 21 pages, 2 figures

On the basis of quasipotential method in quantum electrodynamics we calculate corrections of order $\alpha^5$ and $\alpha^6$ to hyperfine structure of S-wave energy levels of muonic deuterium. Relativistic corrections, effects of vacuum polarization in first, second and third orders of perturbation theory, nuclear structure and recoil corrections are taken into account. The obtained numerical values of hyperfine splitting $\Delta E^{hfs}(1S)=50.2814$ meV (1S state) and $\Delta E^{hfs}(2S)=6.2804$ meV (2S state) represent reliable estimate for a comparison with forthcoming experimental data of CREMA collaboration. The hyperfine structure interval $\Delta_{12}=8\Delta E^{hfs}(2S)-\Delta E^{hfs}(1S)=-0.0379$ meV can be used for precision check of quantum electrodynamics predictions for muonic deterium., Comment: 18 pages, 7 figures

On the basis of quasipotential method in quantum electrodynamics we calculate nuclear finite size radiative corrections of order $\alpha(Z\alpha)^5$ to the hyperfine structure of S-wave energy levels in muonic hydrogen and muonic deuterium. For the construction of the particle interaction operator we employ the projection operators on the particle bound states with definite spins. The calculation is performed in the infrared safe Fried-Yennie gauge. Modern experimental data on the electromagnetic form factors of the proton and deuteron are used., Comment: 8 pages, 1 figure

We report on accurate measurements of the scalar and tensor polarizabilities of the 5D fine structure levels 5D3/2 and 5D5/2 in Rb. The measured values show reasonable correspondence to previously published theoretical predictions, but are more accurate. We implemented laser excitation of the 5D level in a laser cooled cloud of optically polarized Rb-87 atoms placed in a constant electric field., Comment: 8 pages, 9 figures

We have experimentally studied sub-Doppler laser cooling in a magneto-optical trap for thulium atoms working at the wavelength of 410.6\,nm. Without any dedicated molasses period of sub-Doppler cooling, the cloud of $3\times 10^6$ atoms at the temperature of 25(5)\,$\mu$K was observed. The measured temperature is significantly lower than the Doppler limit of 240$\mu$K for the cooling transition at 410.6\,nm. High efficiency of the sub-Doppler cooling process is due to a near-degeneracy of the Land\'e-$g$ factors of the lower $4f^{13}6s^{2}\, (J\,=\,{7}/{2})$ and the upper $4f^{12}5d_{3/2}6s^{2}\, (J\,=\,{9}/{2})$ cooling levels.}, Comment: 4 pages, 4 figures

Thulium atoms are trapped in a magneto-optical trap using a strong transition at 410 nm with a small branching ratio. We trap up to $7\times10^{4}$ atoms at a temperature of 0.8(2) mK after deceleration in a 40 cm long Zeeman slower. Optical leaks from the cooling cycle influence the lifetime of atoms in the MOT which varies between 0.3 -1.5 s in our experiments. The lower limit for the leaking rate from the upper cooling level is measured to be 22(6) s$^{-1}$. The repumping laser transferring the atomic population out of the F=3 hyperfine ground-state sublevel gives a 30% increase for the lifetime and the number of atoms in the trap., Comment: 4 pages, 6 figures

We demonstrate laser slowing of a hot thulium atomic beam using the nearly closed cycling transition $4\textrm{f}^{13}6\textrm{s}^2(^2\textrm{F}^\circ)(J=7/2)\leftrightarrow4\textrm{f}^{12}(^3\textrm{H}_5)5\textrm{d}_{3/2}6\textrm{s}^2(J=9/2)$ at 410.6 nm. Atoms are decelerated to velocities around 25 m/s by a 40 cm Zeeman slower. The flux of slowed atoms is evaluated as $10^7 \textrm{s}^{-1}\textrm{cm}^{-2}$. The experiment explicitly indicates the possibility of trapping Tm atoms in a magneto-optical trap., Comment: 3 pages, 4 figures

By the theory based on the equilibrium binding model, phase diagrams have been calculated for the poly rA poly rU system in the presence of Mg2+, Ni2+, Cd2+, with Na+ 0.1 M. Binding constants (KA, KU, KAU, KA2U) have been determined, the best agreement with the early experimental results being observed. Calculations of diagrams with Mg2+ are shown to permit obtaining satisfactory results if steady mean constants of ion binding to polynucleotides of all the mentioned structures are used. But in the cases with Ni2+ and Cd2+, constants dependences on ion concentrations must be taken into account, especially with high ion contents in the presence of which compaction of molecules of single-stranded poly A emerges. It has been revealed that the main factor being responsible for differences in diagrams for Ni2+ and Cd2+ is a significant variation of their constants of binding to poly A. Temperature dependences of conformational transitions obtained by UV spectroscopy for low polymer concentrations are compared with those obtained by IR and VCD spectroscopy at high contents of these molecules and, accordingly, metal ions in solution. Differences and peculiarities conditioning irreversibility of the earlier observed disproportional 2->3 transition are clarified., Comment: 10 pages, 6 figures

We study the logarithmic and ratio asymptotic of linear forms constructed from a Nikishin system which satisfy orthogonality conditions with respect to a system of measures generated from another Nikishin system. This construction combines type I and type II multiple orthogonal polynomials. The logarithmic asymptotic of the linear forms is expressed in terms of the extremal solution of an associated vector valued equilibrium problem for the logarithmic potential. The ratio asymptotic is described by means of a conformal representation of an appropriate Riemann surface of genus zero onto the extended complex plane., Comment: 46 pages

We have studied possible candidates for laser cooling transitions in $^{169}$Tm in the spectral region 410 -- 420 nm. By means of saturation absorption spectroscopy we have measured the hyperfine structure and rates of two nearly closed cycling transitions from the ground state $4\textrm{f}^{13}6\textrm{s}^2(^2\textrm{F}_0)(J_g=7/2)$ to upper states $4\textrm{f}^{12}(^3\textrm{H}_5)5\textrm{d}_{3/2}6\textrm{s}^2(J_e=9/2)$ at 410.6 nm and $4\textrm{f}^{12}(^3\textrm{F}_4)5\textrm{d}_{5/2}6\textrm{s}^2(J_e=9/2)$ at 420.4 nm and evaluated the life times of the excited levels as 15.9(8) ns and 48(6) ns respectively. Decay rates from these levels to neighboring opposite-parity levels are evaluated by means of Hartree-Fock calculations. We conclude, that the strong transition at 410.6 nm has an optical leak rate of less then $2\cdot10^{-5}$ and can be used for efficient laser cooling of $^{169}$Tm from a thermal atomic beam. The hyperfine structure of two other even-parity levels which can be excited from the ground state at 409.5 nm and 418.9 nm is also measured by the same technique. In addition we give a calculated value of $7(2)$ s$^{-1}$ for the rate of magnetic-dipole transition at 1.14 $\mu$m between the fine structure levels $(J_g=7/2)\leftrightarrow(J'_g=5/2)$ of the ground state which can be considered as a candidate for applications in atomic clocks., Comment: 8 pages, 5 figures