We demonstrate the importance of electron correlation effects in the hyperfine structure constants of many low-lying states in 210 Fr and 212 Fr. This is achieved by calculating the magnetic dipole and electric quadrupole hyperfine structure constants using the Dirac-Fock approximation, second order many-body perturbation theory and the coupled-cluster method in the singles and doubles approximation in the relativistic framework. By combining our recommended theoretical results with the corresponding experimental values, improved nuclear magnetic dipole and electric quadrupole moments of the above isotopes are determined. In the present work, it is observed that there are large discrepancies between the hyperfine structure constants of the 7D 5/2 state obtained from the experimental and theoretical studies whereas good agreements are found for the other D 5/2 states. Our estimated hyperfine constants for the 8P , 6D, 10S and 11S states could be very useful as benchmarks for the measurement of these quantities.

Appraising the projected 10 −18 fractional uncertainty in the optical frequency standards using singly ionized ions, we estimate the blackbody radiation (BBR) shifts due to the magnetic dipole (M1) and electric quadrupole (E2) multipoles of the applied external electromagnetic field. Multipolar scalar polarizabilities are determined for the singly ionized calcium (Ca + ) and strontium (Sr + ) ions using the relativistic coupled-cluster method, though the theory can be exercised for any single-ion clocks. The expected energy shifts for the respective clock transitions are estimated to be 4.38(3) × 10 −4 Hz for Ca + and 9.50(7) × 10 −5 Hz for Sr + . These shifts are large enough and may be a prerequisite for the frequency standards to achieve the foreseen 10 −18 precision goal.

We report here oscillator strengths, transition rates, branching ratios and lifetimes due to allowed transitions in potassium (K) atom. We evaluate electric dipole (E1) amplitudes using an all order relativistic many-body perturbation method. The obtained results are compared with previously available experimental and theoretical studies. Using the E1 matrix elements mentioned above and estimated from the lifetimes of the 4P states, we determine precise values of static and dynamic polarizabilities for the first five low-lying states in the considered atom. The static polarizabilities of the ground and 4P states in the present work are more precise than the available measurements in these states. Only the present work employs relativistic theory to evaluate polarizabilities in the 3D states for which no experimental results are known to compare with. We also reexamine "magic wavelengths" for the 4P 1/2 → 4S and 4P 3/2 → 4S transitions due to the linearly polarized light which are useful to perform state-insensitive trapping of K atoms.

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