A polarization analysis of the fine-structure intervals for the $n = 17$ Rydberg states of Mg and the $n = 29$ states of Si$^{2+}$ is performed. The coefficients of all terms in the polarization expansion up to $r^{-8}$ were computed using a semi-empirical single electron analysis combined with the relativistic all-order single-double method (MBPT-SD) which includes all single-double excitations from the Dirac-Fock wave functions to all orders of perturbation theory. The revised analysis yields dipole polarizabilities of $α_1 = 35.04(3)$ a.u. for Mg$^+$ and $α_1 = 7.433(25)$ a.u. for Si$^{3+}$, values only marginally larger than those obtained in a previous analysis (E. L. Snow and S. R. Lundeen (2007) Phys. Rev. A {\bf 75} 062512, {\em ibid} (2008) {\bf 77} 052501). The polarizabilities are used to make estimates of the multiplet strength for the resonant transition for both ions. The revised analysis did see significant changes in the slopes of the polarization plots. The dipole polarizabilities from the MBPT-SD calculation, namely 35.05(12) a.u. and 7.419(16) a.u., are within 0.3% of the revised experimental values.
We investigate the role of the electron correlation effects in the calculations of the electric dipole polarizabilities (α) of elements belonging to three different groups of periodic table. To understand the propagation of the electron correlation effects at different levels of approximations, we employ the relativistic many-body methods developed, based on the first principles, at mean-field Dirac-Fock (DF), third order many-body perturbation theory (MBPT(3)), random-phase approximation (RPA) and the singly and doubly approximated coupled-cluster methods at the linearized (LCCSD) and non-lin…
High precision multipole polarizabilities, $α_{\ell}$ for $\ell \le 4$ of the $1s$ ground state of the hydrogen isoelectronic series are obtained from the Dirac equation using the B-spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of $Z$ with a relative accuracy of 10$^{-6}$ up to $Z = 100$ are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules $\sum_i f^{(\ell)}_{0i} = 0$ for all multipoles from $\ell = 1$ to $\ell = 4$. The dispersion coefficients for the long-range H-H…
We present a general approach within the relativistic coupled-cluster theory framework to calculate exactly the first order wave functions due to any rank perturbation operators. Using this method, we calculate the static dipole and quadrupole polarizabilities in some alkali atoms and alkaline earth-metal ions. This may be a good test of the present theory for different rank and parity interaction operators. This shows a wide range of applications including precise calculations of both parity and CP violating amplitudes due to rank zero and rank one weak interaction Hamiltonians. We also give …
Derivations for the higher tensor components of the quadrupole polarizabilities are given and their values for the metastable states of the Ca$^+$, Sr$^+$ and Ba$^+$ alkaline earth-metal ions are estimated. We also give the scalar quadrupole polarizabilities of the ground and metastable states of these ions to compare our results with the previously available theoretical and experimental results. Reasonably good agreement between our calculations with the previous values of scalar quadrupole polarizabilities demonstrate their correctness. The reported scalar and tensor quadrupole polarizabilit…
In this work, analytical formulas for the static multipole polarizabilities of hydrogen-like ions are derived by using the analytical wave functions and the reduced Green function and by applying a numerical fitting procedure. Our results are then applied to the studies of blackbody radiation shifts to atomic energy levels at different temperatures. Our analytical results can be served as a benchmark for other theoretical methods.
We use the perturbed relativistic coupled-cluster theory to compute the static electric dipole polarizabilities of the singly ionized alkali atoms, namely, Na$^+$, $^+$, Rb$^+$, Cs$^+$ and Fr$^+$. The computations use the Dirac-Coulomb-Breit Hamiltonian with the no-virual-pair approximation and we also estimate the correction to the static electric dipole polarizability arising from the Breit interaction.
We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowing this transition polarizability is required in a number of high-precision experiments, such as microwave atomic clocks and searches for CP-violating permanent electric dipole moments. While the traditional polarizability arises in the second-order of interaction with the externally-applied electric field, the differential polarizability involves additional contribution from the hyperfine interaction of atomic el…
Relativistic many-body perturbation theory is applied to study properties of ions of the francium isoelectronic sequence. Specifically, energies of the 7s, 7p, 6d, and 5f states of Fr-like ions with nuclear charges Z = 87 - 100 are calculated through third order; reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for 7s - 7p, 7p - 6d, and 6d - 5f electric-dipole transitions; and 7s - 6d, 7s - 5f, and 5f_5/2 - 5f_7/2 multipole matrix elements are evaluated to obtain the lifetimes of low-lying excited states. Moreover, for the ions Z = 87 - 92 calculati…
Effective oscillator strength distributions are systematically generated and tabulated for the alkali atoms, the alkaline-earth atoms, the alkaline-earth ions, the rare gases and some miscellaneous atoms. These effective distributions are used to compute the dipole, quadrupole and octupole static polarizabilities, and are then applied to the calculation of the dynamic polarizabilities at imaginary frequencies. These polarizabilities can be used to determine the long-range $C_6$, $C_8$ and $C_{10}$ atom-atom interactions for the dimers formed from any of these atoms and ions, and we present tab…
We use the multiconfiguration Dirac-Hartree-Fock (MCDHF) method combined with the relativistic configuration interaction (RCI) approach (GRASP2K) to provide a consistent set of transition energies and radiative transition data for the lower $n =3$ states in all Cl-like ions of astrophysical importance, from \ion{Cr}{8} to \ion{Zn}{14}. We also provide excitation energies calculated for \mbox{Fe X} using the many-body perturbation theory (MBPT, implemented within FAC). The comparison of the present MCDHF results with MBPT and with the available experimental energies indicates that the theoretic…
The static and dynamic electric multipolar polarizabilities and second hyperpolarizabilities of the H$_2^+$, D$_2^+$, and HD$^+$ molecular ions in the ground and first excited states are calculated nonrelativistically using explicitly correlated Hylleraas basis sets. The calculations are fully nonadiabatic; the Born-Oppenheimer approximation is not used. Comparisons are made with published theoretical and experimental results, where available. In our approach, no derivatives of energy functions nor derivatives of response functions are needed. In particular, we make contact with earlier calcul…
We discuss possible search for optical transitions in Sm13+ and Sm14+ using ab initio calculations of differential dynamic polarizability. We calculate dynamic polarizability for M1 transition between first and second excited states of Sm14+ . Transition amplitudes and energies within optical range for states that contribute to the polarizability of the mentioned transition are presented. Employing simple analytical formula for polarizability data in the vicinity of a resonance and assuming that several values of the polarizability for different laser frequencies will be measured one can find …
Using perturbed relativistic coupled-cluster (PRCC) theory we compute the ground state electric dipole polarizability, $α$, of doubly ionized alkaline earth metal ions $\rm{Mg}^{2+}$, $\rm{Ca}^{2+}$, $\rm{Sr}^{2+}$, $\rm{Ba}^{2+}$ and $\rm{Ra}^{2+}$. In the present work we use the Dirac-Coulomb-Breit atomic Hamiltonian and we also include the Uehling potential, which is the leading order term in the vacuum polarization corrections. We examine the correction to the orbital energies arising from the Uehling potential in the self-consistent field calculations as well as perturbatively. Our result…
We employ the closed-shell perturbed relativistic coupled-cluster (RCC) theory developed by us earlier [Phys. Rev. A {\bf 77}, 062516 (2008)] to evaluate the ground state static electric dipole polarizabilities (αs) of several atomic systems. In this work, we have incorporated a class of higher order many-body effects in our calculations that had not been taken into account in the above paper. We highlight their importance in improving the accuracy of $α$. We also calculate the ground state αs of the inert gas atoms and several iso-electronic singly and doubly charged ions in order to make a c…
We have estimated the size of the light-shifts due to parity nonconservation (PNC) interactions in different isotopes of Ba+ and Ra+ ions based on the work of Fortson [Phys. Rev. Lett. 70, 2383 (1993)]. We have used the nuclear spin independent (NSI) amplitudes calculated earlier by us [Phys. Rev. Lett. 96, 163003 (2006); Phys. Rev. A 78, 050501(R) (2008)] and we have employed the third order many-body perturbation theory (MBPT(3)) in this work to estimate the nuclear spin dependent (NSD) amplitudes in these ions. Ra+ is found to be more favourable than Ba+ for measuring both the NSI and NSD P…
Relativistic third-order MBPT is applied to obtain energies of ions with two valence electrons in the no virtual-pair approximation (NVPA). A total of 302 third-order Goldstone diagrams are organized into 12 one-body and 23 two-body terms. Only third-order two-body terms and diagrams are presented here, owing to the fact that the one-body terms are identical to the previously studied third-order terms in monovalent ions. Dominant classes of diagrams are identified. The model potential is a Dirac-Hartree-Fock $V^{N-2}$ potential, and B-spline basis functions in a cavity of finite radius are emp…
Static dipole polarizabilities are calculated in the ground and metastable states of Sr$^+$, Ba$^+$ and Ra$^+$ using the relativistic coupled-cluster method. Trends of the electron correlation effects are investigated in these atomic ions. We also estimate the Stark and black-body radiation shifts from these results for these systems for the transitions proposed for the optical frequency standards and compare them with available experimental data.
Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency stan…
Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole $C_6$ and three-dipole $C_9$ dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The $C_6$ and $C_9$ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated $C_6$ coefficients for the considered alkaline-earth atoms among themselves are compared with the previously …
Atomic properties of the 24 low-lying ns, np, nd, nf, and ng states in Th IV ion are calculated using the high-precision relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements, oscillator strengths, transition rates, and lifetimes. Scalar polarizabilities of the ground and six excited states (5f_j, 6d_j, 7p_j, and 7s), and tensor polarizabilities of the 5f_j, 6d_j, 7p_{3/2} states of Th IV are e…
We present electric dipole polarizabilities ($α_d$) of the alkali-metal negative ions, from H$^-$ to Fr$^-$, by employing four-component relativistic many-body methods. Differences in the results are shown by considering Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and DC Hamiltonian with the lower-order quantum electrodynamics interactions. At first, these interactions are included self-consistently in the Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are incorporated over the DHF wave functions in the second-order many-body perturbation …
We report our successful implementation of the full fledged relativistic equation of motion coupled cluster (EOMCC) method. This method is employed to compute the principal ionization potentials (IPs) of closed-shell rare gas atoms, He-like ions, Be-like ions along with Na+, Al+, K+, Be, and Mg. Four component Dirac spinors are used in the calculations and the one and two electron integrals are evaluated using the Dirac Coulomb Hamiltonian. Our results are in excellent agreement with those available measurements, which are taken from the National Institute of Science and Technology database (N…
Investigating Roles of Triple Excitations for High-precision Determination of Clock Properties of Alkaline Earth Metal Singly Charged Ions
Atomic, Molecular and Optical Physics Division, Physical Research Laboratory（物理研究实验室原子、分子与光学物理分部）；Indian Institute of Technology Gandhinagar（甘地纳加尔印度理工学院）
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 est…
Stark shifts of potassium and rubidium D1 lines have been measured with high precision by Miller et al [1]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the 4p_j-3d_j' transitions in K and for the 5p_j-4d_j' transitions in Rb to high precision. The 4p_1/2-3d_3/2 and 5p_1/2-4d_3/2 transitions contribute on the order of 90% to the respective polarizabilities of the np_1/2 states in K and Rb, and the remaining 10% can be accurately calculated using the relativistic all-order method. Therefore, the co…
