Dansha Jiang

Blackbody-radiation shift in a 88Sr+ ion optical frequency standard

The blackbody-radiation (BBR) shift of the 5s–4d5/2 clock transition in 88Sr+ is calculated to be 0.250(9) Hz at room temperature, T = 300 K, using the relativistic all-order method where all single and double excitations of the Dirac–Fock wavefunction are included to all orders of perturbation theory. The BBR shift is a major component in the uncertainty budget of the optical frequency standard based on the 88Sr+ trapped ion. The scalar polarizabilities of the 5s and 4d5/2 levels, as well as the tensor polarizability of the 4d5/2 level, are presented together with the evaluation of their uncertainties. The lifetimes of the 4d3/2, 4d5/2, 5p1/2 and 5p3/2 states are calculated and compared with experimental values.

Development of a configuration-interaction plus all-order method for atomic calculations

We develop a theoretical method within the framework of relativistic many-body theory to accurately treat correlation corrections in atoms with few valence electrons. This method combines the all-order approach currently used in precision calculations of properties of monovalent atoms with the configuration-interaction approach that is applicable for many-electron systems. The method is applied to Mg, Ca, Sr, Zn, Cd, Ba, and Hg to evaluate ionization energies and low-lying energy levels.

Calculation of parity-nonconserving amplitude and other properties of Ra+

We have calculated parity nonconserving 7s - 6d_{3/2} amplitude E_PNC in 223Ra+ using high-precision relativistic all-order method where all single and double excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Detailed study of the uncertainty of the parity nonconserving (PNC) amplitude is carried out; additional calculations are performed to estimate some of the missing correlation corrections. A systematic study of the parity conserving atomic properties, including the calculation of the energies, transition matrix elements, lifetimes, hyperfine constants, quadrupole moments of the 6d states, as well as dipole and quadrupole ground state polarizabilities, is carried out. The results are compared with other theoretical calculations and available experimental values.

Black-body radiation shifts and theoretical contributions to atomic clock research

A review of theoretical calculations of black-body radiation (BBR) shifts in various systems of interest to atomic clock research is presented. Calculations for monovalent systems, such as Ca+, Sr+, and Rb are carried out using a relativistic all-order single-double method, where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. A recently developed method for accurate calculations of BBR shifts in divalent atoms such as Sr is discussed. This approach combines the relativistic all-order method and the configuration interaction method. The evaluation of uncertainties in theoretical values of BBR shifts is discussed in detail.

Electric quadrupole moments of metastable states of Ca+, Sr+, and Ba+

The electric quadrupole moments of the metastable nd3/2 and nd5/2 states of Ca +, Sr+, and Ba+ are calculated using the relativistic all-order method including all single, double, and partial triple excitations of the DiracHartree-Fock wave function to provide recommended values for the cases where no experimental data are available. The contributions of all nonlinear single and double terms are also calculated for the case of Ca+ for comparison of our approach with results of the coupled-cluster method with singles, doubles, and perturbative triples. Third-order many-body perturbation theory is used to evaluate the contributions of high partial waves and the Breit interaction. The remaining omitted correlation corrections are estimated as well. An extensive study of the uncertainty of our calculations is carried out to establish the accuracy of our recommended values as 0.5–1 % depending on the particular ion. A comprehensive comparison of our results with other theoretical values and experimental results is carried out. Our result for the quadrupole moment of the 3d5/2 state of the Ca+ ion, 1.849 17 ea0 , is in agreement with the most precise recent measurement 1.83 1 ea0 2 by Roos et al. Nature London 443, 316 2006 .

Blackbody radiation shift in

The operation of atomic clocks is generally carried out at room temperature, whereas the definition of the second refers to the clock transition in an atom at absolute zero. This implies that the clock transition frequency should be corrected in practice for the effect of finite temperature, of which the leading contributor is the blackbody radiation (BBR) shift. Experimental measurements of the BBR shifts are difficult. In this work, we have calculated the blackbody radiation shift of the ground-state hyperfine microwave transition in {sup 87}Rb using the relativistic all-order method and carried out a detailed evaluation of the accuracy of our final value. Particular care is taken to accurately account for the contributions from highly excited states. Our predicted value for the Stark coefficient, k{sub S}=-1.240(4)x10{sup -10} Hz/(V/m){sup 2}, is three times more accurate than the previous calculation [E. J. Angstman, V. A. Dzuba, and V. V. Flambaum, Phys. Rev. A 74, 023405 (2006)].

^{87}

We developed a theoretical method within the framework of relativistic many-body theory to accurately treat correlation corrections in atoms with few valence electrons. Preliminary results for systems of interest to atomic clock development are reported. We also calculated the blackbody radiation shift of the ground-state hyperfine microwave transition in 87Rb using the relativistic all-order method and evaluated the accuracy of our final value. The uncertainty estimate is discussed in detail.

Rb frequency standard

A review of the theoretical calculations of the blackbody radiation (BBR) shifts in various systems of interest to the atomic clock research in presented. The calculations for monovalent systems, such as Ca+, Sr+, and Rb are carried out using the relativistic all-order single-double method where all single and double excitations of the Dirac-Fock wave function are included to all orders of perturbation theory. New method for accurate calculations of BBR shifts for divalent systems such as Sr is discussed. The new approach combines the relativistic all-order method and the configuration interaction method. The evaluation of the uncertainty of the BBR shift values is discussed in detail.