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.

The blackbody radiation (BBR) shift of the 5s − 4d 5/2 clock transition in 88 Sr + 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 wave function 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 88 Sr + trapped ion. The scalar polarizabilities of the 5s and 4d 5/2 levels, as well as the tensor polarizability of the 4d 5/2 level, are presented together with the evaluation of their uncertainties. The lifetimes of the 4d 3/2 , 4d 5/2 , 5p 1/2 , and 5p 3/2 states are calculated and compared with experimental values.

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 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 S = −1.240(4) × 10 −10 Hz/(V/m) 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)].

We have calculated parity nonconserving 7s − 6d 3/2 amplitude EPNC in 2 23Ra + using highprecision 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.

Electric quadrupole moments of the metastable nd 3/2 and nd 5/2 states of Ca + , Sr + , and Ba + are calculated using the relativistic all-order method including all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function to provide recommended values for the cases where no experimental data are available. The contributions of all non-linear single and double terms are also calculated for the case of Ca + for comparison of our approach with the CCSD(T) results. The third-order many body perturbation theory is used to evaluate contributions of high partial waves and the Breit interaction. The remaining omitted correlation corrections are estimated as well. Extensive study of the uncertainty of our calculations is carried out to establish accuracy of our recommended values to be 0.5% -1% depending on the particular ion.