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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., Comment: 10 pages, 8 tables

Accurate knowledge of interaction potentials among the alkali atoms and alkaline earth ions is very useful in the studies of cold atom physics. Here we carry out theoretical studies of the long-range interactions among the Li, Na, K, and Rb alkali atoms with the Ca$^+$, Ba$^+$, Sr$^+$, and Ra$^+$ alkaline earth ions systematically which are largely motivated by their importance in a number of applications. These interactions are expressed as a power series in the inverse of the internuclear separation $R$. Both the dispersion and induction components of these interactions are determined accurately from the algebraic coefficients corresponding to each power combination in the series. Ultimately, these coefficients are expressed in terms of the electric multipole polarizabilities of the above mentioned systems which are calculated using the matrix elements obtained from a relativistic coupled-cluster method and core contributions to these quantities from the random phase approximation. We also compare our estimated polarizabilities with the other available theoretical and experimental results to verify accuracies in our calculations. In addition, we also evaluate the lifetimes of the first two low-lying states of the ions using the above matrix elements. Graphical representation of the interaction potentials versus $R$ are given among all the considered atoms and ions., Comment: 6 tables, 3 figures

Quadrupole shifts for three prominent clock transitions, $[4f^{14} 6s] ^2S_{1/2} \rightarrow [4f^{14} 5d] ^2D_{3/2}$, $[4f^{14} 6s] ^2S_{1/2} \rightarrow [4f^{14} 5d] ^2D_{5/2}$ and $[4f^{14} 6s] ^2S_{1/2} \rightarrow [4f^{13} 6s^2] ^2F_{7/2}$, in the Yb$^+$ ion are investigated by calculating the quadrupole moments ($\Theta$s) of the $5d_{3/2,5/2}$ and $4f_{7/2}$ states using the relativistic coupled-cluster (RCC) methods. We find an order difference in the $\Theta$ value of the $4f_{7/2}$ state between our calculation and the experimental result, but our result concur with the other calculations that are carried out using different many-body methods than ours. However, our $\Theta$ value of the $5d_{3/2}$ state is in good agreement with the available experimental result and becomes more precise till date to estimate the the quadrupole shift of the $[4f^{14} 6s] ^2S_{1/2} \rightarrow [4f^{14} 5d] ^2D_{3/2}$ clock transition more accurately. To justify the accuracies in our calculations, we evaluate the hyperfine structure constants of the $6s_{1/2}$, $5d_{3/2,5/2}$ and $4f_{7/2,5/2}$ states of $^{171}$Yb$^+$ ion using the same RCC methods and compare the results with their experimental values. We also determine the lifetime of the $5d_{3/2}$ state to eradicate the scepticism on the earlier measured value as claimed by a recent experiment., Comment: 5 pages and 2 figures. Minor changes are incorporated

We report the implementation of equation-of-motion coupled-cluster (EOMCC) method in the four-component relativistic framework with the spherical atomic potential to generate the excited states from a closed-shell atomic configuration. This theoretical development will be very useful to carry out high precision calculations of varieties of atomic properties in many atomic systems. We employ this method to calculate excitation energies of many low-lying states in a few Ne-like highly charged ions, such as Cr XV, Fe XVII, Co XVIII and Ni XIX ions, and compare them against their corresponding experimental values to demonstrate the accomplishment of the EOMCC implementation. The considered ions are apt to substantiate accurate inclusion of the relativistic effects in the evaluation of the atomic properties and are also interesting for the astrophysical studies. Investigation of the temporal variation of the fine structure constant (\alpha) from the astrophysical observations is one of the modern research problems for which we also estimate the \alpha sensitivity coefficients in the above ions., Comment: 12 pages, 4 figures

We have developed one electron detachment theory from a closed-shell atomic configuration in the relativistic Fock-space coupled-cluster ansatz. Using this method, we determine sensitivity coefficients to the variation of the fine structure constant in the first three important low-lying transitions of the astrophysically interesting highly charged Mn IX, Fe X, Co XI and Ni XII ions. The potential of this method has been assessed by evaluating the detachment energies of the removed electrons and determining lifetimes of the atomic states in the above ions. To account the sensitivity of the higher order relativistic effects, we have used the four component wave functions of the Dirac-Coulomb-Breit Hamiltonian with the leading order quantum electrodynamics (QED) corrections. A systematic study has been carried out to highlight the importance of the Breit and QED interactions in the considered properties of the above ions.

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 $4P_{1/2} \rightarrow 4S$ and $4P_{3/2} \rightarrow 4S$ transitions due to the linearly polarized light which are useful to perform state-insensitive trapping of K atoms., Comment: 12 pages, 2 figures

Nuclear quadrupole moments ($Q$s) in three isotopes of potassium (K) with atomic mass numbers 39, 40 and 41 are evaluated more precisely in this work. The $Q$ value of $^{39}$K is determined to be 0.0614(6) $b$ by combining the available experimental result of the electric quadrupole hyperfine structure constant ($B$) with our calculated $B/Q$ result of its $4P_{3/2}$ state. Furthermore combining this $Q$ value with the measured ratios $Q$($ ^{40}$K)$/Q$($ ^{39}$K) and $Q$($ ^{41}$K)$/Q$($ ^{39}$K), we obtain $Q$($ ^{40}$K)$=-0.0764(10) \ b$ and $Q$($ ^{41}$K)$=0.0747(10) \ b$, respectively. These results disagree with the recently quoted standard values in the nuclear data table within the given uncertainties. The calculations are carried out by employing the relativistic coupled-cluster theory at the singles, doubles and involving important valence triples approximation. The accuracies of the calculated $B/Q$ results can be viewed on the basis of comparison between our calculated magnetic dipole hyperfine structure constants ($A$s) with their corresponding measurements for many low-lying states. Both $A$ and $B$ results in few more excited states are presented for the first time., Comment: 9 pages, 1 figure

Appraising the projected $10^{-18}$ fractional uncertainty in the optical frequency standards using singly ionized ions, we estimate the black-body radiation (BBR) shifts due to the magnetic dipole (M1) and electric quadrupole (E2) multipoles of the magnetic and electric fields, respectively. 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 clock proposal. The expected energy shifts for the respective clock transitions are estimated to be $4.38(3) \times 10^{-4}$ Hz for Ca$^+$ and $9.50(7) \times 10^{-5}$ Hz for Sr$^+$. These shifts are large enough and may be prerequisite for the frequency standards to achieve the foreseen $10^{-18}$ precision goal., Comment: 1 figure, 4 tables

Transition properties such as oscillator strengths, transition rates, branching ratios and lifetimes of many low-lying states in the doubly ionized scandium (Sc III) are reported. A relativistic method in the coupled-cluster framework has been employed to incorporate the electron correlation effects due to the Coulomb interaction to all orders by considering all possible singly and doubly excited electronic configurations conjointly with the leading order triply excited configurations in a perturbative approach. Present results are compared with the previously reported results for the transition lines of astrophysical interest. In addition, some of the transition properties and lifetimes of few low-lying states are given for the first time. Role of the correlation effects in the evaluation of the transition strengths are described concisely., Comment: 4 tables, 11 pages