The main aim of this paper is to present accurate energy levels of the ground [Xe]$4f^{12}$ and first excited [Xe]$4f^{11}5d$ configurations of Er$^{2+}$. The energy level structure of the Er$^{2+}$ ion was computed using the multiconfiguration Dirac-Hartree-Fock and relativistic configuration interaction (RCI) methods, as implemented in the GRASP2018 program package. The Breit interaction, self-energy and vacuum polarization corrections were included in the RCI computations. The zero-first-order approach was used in the computations. Energy levels with the identification in $LS$ coupling for all (399) states belonging to the [Xe]$4f^{12}$ and [Xe]$4f^{11}5d$ configurations are presented. Electric dipole (E1) transition data between the levels of these two configurations are computed. The accuracy of the these data are evaluated by studying the behaviour of the transition rates as functions of the gauge parameter as well as by evaluating the cancellation factors. The core electron correlations were studied using different strategies. Root-mean-square deviations obtained in this study for states of the ground and excited configurations from the available experimental or semi-empirical data are 649 cm$^{-1}$, and 747 cm$^{-1}$, respectively.
In this comment, through our independent calculations, we assess that the recently reported results of El-Maaref et al. [{\em Indian J. Phys.} {\bf 91} 1029 (2017)] for energy levels, oscillator strengths, radiative rates, and lifetimes are inaccurate and unreliable for several levels and transitions of S-like Sc~VI.
Energy levels, Landé $g$-factors and radiative lifetimes are reported for the lowest 182 levels of the 3d$^4$, 3d$^3$4s and 3d$^3$4p configurations of Fe~V, Co~VI and Ni~VII. Additionally, radiative rates ($A$-values) have been calculated for the E1, E2 and M1 transitions among these levels. The calculations have been performed in a quasi-relativistic approach (QR) with a very large {\em configuration interaction} (CI) wavefunction expansion, which has been found to be necessary for these ions. Our calculated energies for all ions are in excellent agreement with the available measurements, for…
Energy levels, radiative rates and lifetimes are reported for four S-like ions, namely Sc~VI, V VIII, Cr IX, and Mn~X. Two independent atomic structure codes, namely the general-purpose relativistic atomic structure package ({\sc grasp}) and the flexible atomic code ({\sc fac}), have been adopted for calculating the energy levels, with differing amounts of configuration interaction. This is mainly to make some assessment of accuracy. However, the {\sc grasp} alone is used for calculating the remaining parameters. Results are reported for varying number of levels of these ions, and for calculat…
We report calculations of energy levels and radiative rates ($A$-values) for transitions in Cr-like Co IV and Ni V. The quasi-relativistic Hartree-Fock (QRHF) code is adopted for calculating the data although GRASP (general-purpose relativistic atomic structure package) and flexible atomic code (FAC) have also been employed for comparison purposes. No radiative rates are available in the literature to compare with our results, but our calculated energies are in close agreement with those compiled by NIST for a majority of the levels. However, there are discrepancies for a few levels of up to 3…
We report calculations of energy levels, radiative rates, oscillator strengths and line strengths for transitions among the lowest 231 levels of Ti VII. The general-purpose relativistic atomic structure package ({\sc grasp}) and flexible atomic code ({\sc fac}) are adopted for the calculations. Radiative rates, oscillator strengths and line strengths are provided for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2) transitions among the 231 levels, although calculations have been performed for a much larger number of levels (159,162). In add…
Results for energy levels, radiative rates and electron impact excitation (effective) collision strengths for transitions in Be-like Cl XIV, K XVI and Ge XXIX are reported. For the calculations of energy levels and radiative rates the General-purpose Relativistic Atomic Structure Package ({\sc grasp}) is adopted, while for determining the collision strengths and subsequently the excitation rates, the Dirac Atomic R-matrix Code ({\sc darc}) is used. Oscillator strengths, radiative rates and line strengths are listed for all E1, E2, M1 and M2 transitions among the lowest 98 levels of the $n \le$…
Lanthanide elements play important roles as an opacity source in the ejected material from neutron star mergers. Accurate and complete atomic data are necessary to evaluate the opacities and to analyze the observed data. In this paper, we perform extended, ab-initio atomic calculations from Pr II (Z=59) to Gd II (Z=64). By using multiconfiguration Dirac-Hartree-Fock and relativistic configuration-interaction methods, implemented in the general-purpose relativistic atomic structure package GRASP2K, we calculate the energy levels and transition data of electric dipole transitions. These computat…
Energy levels and radiative rates (A-values) for four types of transitions (E1, E2, M1, and M2) are reported for an astrophysically important Mg-like ion Si~III, whose emission lines have been observed in a variety of plasmas. For the calculations, well-known and widely-used GRASP code has been adopted, and results are listed for transitions among the 141 levels of the 3$\ell3\ell'$ and 3$\ell$4$\ell$ configurations. Experimental energies are available for only the lowest 58 levels but there is no major discrepancy with theoretical results. Similarly, the A-values and lifetimes show a satisfac…
The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the transition rates between the nine lowest levels of radium. The dominant rates were then used to evaluate the radiative lifetimes. The decay of the metastable $ 7s7p ^3 P_0 $ state through 2-photon E1M1 and hyperfine induced channels is also studied.
Configuration interaction (CI) calculations in atoms with two valence electrons, carried out in the V(N-2) Hartree-Fock potential of the core, are corrected for core-valence interactions using many-body perturbation theory (MBPT). Two variants of the mixed CI+MBPT theory are described and applied to obtain energy levels and transition amplitudes for Be, Mg, Ca, and Sr.
We employ semiclassical theoretical analysis to study laser cooling of free atoms using three-level cascade transitions, where the upper transition is much weaker than the lower one. This represents an alternate cooling scheme, particularly useful for group II atoms. We find that temperatures below the Doppler limits associated with each of these transitions are expected. The lowest temperatures arise from a remarkable increase in damping and reduced diffusion compared to two-level cooling. They are reached at the two-photon resonance, where there is a crossing between the narrow and the parti…
The ab initio quasirelativistic Hartree-Fock method developed specifically for the calculation of spectral parameters of heavy atoms and highly charged ions is used to derive transition data for multicharged tungsten ion. The configuration interaction method is applied to include electron correlation effects. The relativistic effects are taken into account in the Breit-Pauli approximation for quasirelativistic Hartree-Fock radial orbitals. The energy level spectra, radiative lifetimes $τ$, Lande $g$-factors are calculated for the $\mathrm{4p^64d^2}$, $\mathrm{4p^64d4f}$ and $\mathrm{4p^54d^3}$…
Multiconfiguration Dirac-Hartree-Fock electric quadrupole (E2) and magnetic dipole (M1) transition probabilities are reported for transitions between levels of 3d^5 in [Fe IV]. The accuracy of the ab initio energy levels and the agreement in the length and velocity forms of the line strength for the E2 transitions are used as indicators of accuracy. The present E2 and M1 transition probabilities are compared with earlier Breit-Pauli results and other theories. An extensive set of transition probabilites with indicators of accuracy are reported in Appendices A and B. Recommended values of A(E2)…
Magnetic quadrupole and electric octupole transitions from the configurations $4p^54d^{N+1}$ and $4p^64d^{N-1}4f$ were calculated along with magnetic dipole, electric dipole and electric quadrupole radiative transitions in quasirelativistic Hartree-Fock approximation. Their significance in determining the metastable level radiative lifetimes was investigated along several isoelectronic sequences for the ions from $Z=50$ to $Z=92$. Strontium-like ions, zirconium-like ions, molybdenum-like ions and rhodium-like ions were studied comprehensively. Remaining isoelectronic sequences with the ground …
We calculate ionization energies and fundamental vibrational transitions for H$_2^+$, D$_2^+$, and HD$^+$ molecular ions. The NRQED expansion for the energy in terms of the fine structure constant $α$ is used. Previous calculations of orders $mα^6$ and $mα^7$ are improved by including second-order contributions due to the vibrational motion of nuclei. Furthermore, we evaluate the largest corrections at the order $mα^8$. That allows to reduce the fractional uncertainty to the level of $7\cdot10^{-12}$ for fundamental transitions and to $4\cdot10^{-12}$ for the ionization energies.
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 …
The atomic states of the W IX (W8+) tungsten ion lying below the W9+ ionisation threshold have been studied theoretically, employing the multiconfiguration Dirac-Hartree-Fock method with configuration interaction. The level electronic structures and their energies are presented. The electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) radiative transitions have been computed in order to calculate the radiative lifetimes of given states. Transition wavelengths, energies, and decay rates are also presented for selected high-intensity E1 transitions. …
We present absolute frequency measurement of the unperturbed P7 P7 O$_2$ B-band transition with relative standard uncertainty of $2\times10^{-11}$. We reached the level of accuracy typical for Doppler-free techniques, with Doppler-limited spectroscopy. The Doppler-limited shapes of the P7 P7 spectral line were measured with a frequency-stabilized cavity ring-down spectrometer referenced to an $^{88}$Sr optical atomic clock by an optical frequency comb.
The ab initio quasirelativistic Hartree-Fock method developed specifically for the calculation of spectral parameters of heavy atoms and highly charged ions was applied to determine atomic data for tungsten ions. The correlation effects were included by adopting configuration interaction method. The Breit-Pauli approximation for quasirelativistic Hartree-Fock radial orbitals was employed to take into account relativistic effects. The energy level spectra, radiative lifetimes, Lande factors $g$ were calculated for the $\mathrm{4p^64d}$, $\mathrm{4p^64f}$ and $\mathrm{4p^54d^2}$ configurations o…
We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in Be-like Ti XIX. The GRASP (General-purpose Relativistic Atomic Structure Package) is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac Atomic R-matrix Code (DARC) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 98 levels of the n <= 4 configurations. Additionally, theoretical lifetim…
We report calculations of collision strengths and effective collision strengths for 26 allowed transitions among the $n \le$ 5 degenerate levels of atomic hydrogen for which the close-coupling (CC) and Born approximations have been used. Results are listed over a wide range of energies (up to 50~Ryd) and temperatures (up to 10$^7$~K), sufficient for applications over a variety of plasmas, including fusion. Similar results have also been calculated for deuterium, but they negligibly differ with those of hydrogen.
The complex internal atomic structure involved in radiative transitions has an effect on the spectrum of fluctuations (noise) of the transmitted light. A degenerate transition has different properties in this respect than a pure two-level transition. We investigate these variations by studying a certain transition between two degenerate atomic levels for different choices of the polarization state of the driving laser. For circular polarization, corresponding to the textbook two-level atom case, the optical spectrum shows the characteristic Mollow triplet for strong laser drive, while the corr…
Energies, wavelengths, transition probabilities, and oscillator strengths have been calculated for the 4s24p2-4s4p3, 4s24p2-4s24p4d and 4s4p3-4p4 allowed transitions in heavy Ge-like ions with Z=59-63. The fully relativistic Multiconfiguration Dirac-Fock (MCDF) method taking into account both the correlations within the n=4 complex and the quantum electrodynamic (QED) effects have been used in the calculations. MCDFGME code is used to calculate electron impact excitation cross sections for the 4s24p2-4s4p3 and 4s24p2-4s24p4d transitions with plane-wave Born approximation. The results of Pr XXV…
Branching fractions were measured for electric dipole transitions from the 5p upper levels to the 5s levels in neutral krypton atoms. The measurements were made with a wall-stabilized electric arc and a 2m monochromator for the spectral lines in the visible, and with a hollow cathode lamp and the NIST 2m-Fourier transform spectrometer for the lines in the near infrared. A semi-empirical calculation, based on accurately known lifetimes for six upper levels, was used to calculate lifetimes for which accurate measurements do not exist. This resulted in a complete set of lifetimes for all 5p level…
Previously reported works on the spectrum of Cs VII are critically studied using supplementary spectrograms recorded on a 3 m normal incidence vacuum spectrograph in the wavelength region 300-1240 A at the Antigonish laboratory (Canada). We confirmed the results of the earlier work of Gayasov and Joshi on this spectrum. Our analysis is supported by extended calculations with the pseudo-relativistic Hartree-Fock (HFR) method with superposition of configuration interactions implemented in Cowan's suite of codes. In this critical evaluation, in addition to the accurate energy levels of Cs VII wit…
Energy levels and radiative rates are reported for transitions in Br-like W XL, calculated with the general-purpose relativistic atomic structure package ({\sc grasp}). Configuration interaction (CI) has been included among 46 configurations (generating 4215 levels) over a wide energy range up to 213 Ryd. However, for conciseness results are only listed for the lowest 360 levels (with energies up to $\sim$ 43 Ryd), which mainly belong to the 4s$^2$4p$^5$, 4s$^2$4p$^4$4d, 4s$^2$4p$^4$4f, 4s4p$^6$, 4p$^6$4d, 4s4p$^5$4d, 4s$^2$4p$^3$4d$^2$, and 4s$^2$4p$^3$4d4f configurations, and provided for fo…
We report on calculations of energy levels, radiative rates, oscillator strengths, and line strengths for transitions among the lowest 253 levels of the (1s$^2$2s$^2$2p$^6$) 3s$^2$3p$^5$, 3s3p$^6$, 3s$^2$3p$^4$3d, 3s3p$^5$3d, 3s$^2$3p$^33d^2$, 3s$^2$3p$^4$4s, 3s$^2$3p$^4$4p and 3s$^2$3p$^4$4d configurations of Ti VI. The general-purpose relativistic atomic structure package ({\sc grasp}) and flexible atomic code ({\sc fac}) are adopted for the calculations. Radiative rates, oscillator strengths and line strengths are reported for all electric dipole (E1), magnetic dipole (M1), electric quadrup…
We excite the 717 nm electric quadrupole 6$D_{3/2} $ $\leftrightarrow$ 7$S_{1/2}$ transition in a laser-cooled $^{232}$Th$^{3+}$ ion crystal. The transition frequency and the lifetime of the metastable 7$S_{1/2}$ level are measured to be 417 845 964(30) MHz and 0.60(7) s, respectively. We subsequently employ the 7$S_{1/2}$ level to drive the ions with nanosecond-long 269 nm laser pulses into the 7$P_{1/2}$ level. The latter is connected to the 7$S_{1/2}$ electronic level within the $^{229}$Th nuclear isomer manifold by the strongest available electron-bridge transition, forming a basis for its…
The measured radiative rates of the 2s22p2 3P1,2 - 2s2p3 5S°2 intercombination transitions in neutral carbon reported in the literature are critically evaluated by comparing them with theoretical and semi-empirical results. The experimental and theoretical values are compared for the carbon isoelectronic sequence from neutral carbon to nine-times ionized phosphorous. We find strong support for the currently recommended theoretical data on C I and conclude that the published measurements for this transition in neutral carbon cannot be trusted. The reasons for the discrepancies are not clear, an…
We report calculations of energy levels, radiative rates and electron impact excitation cross sections and rates for transitions in He-like Kr XXXV. The GRASP (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac Atomic R-matrix Code (DARC) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1, and M2 transitions among the lowest 49 levels. Additionally, theoretical lifetimes are listed for all 49 le…
Energy levels, radiative rates and lifetimes are reported for F-like Sc~XIII and Ne-like Sc~XII and Y~XXX for which the general-purpose relativistic atomic structure package ({\sc grasp}) has been adopted. For all three ions limited data exist in the literature but comparisons have been made wherever possible to assess the accuracy of the calculations. In the present work the lowest 102, 125 and 139 levels have been considered for the respective ions. Additionally, calculations have also been performed with the flexible atomic code ({\sc fac}) to (particularly) confirm the accuracy of energy l…
The electron correlation effects and Breit interaction as well as Quantum Electro-Dynamics (QED) effects were expected to have important contribution to the energy level and transition properties of heavy highly charged ions. The ground states [Ne]$3s^{2}3p^{6}3d^{2}$ and first excited states [Ne]3s$^{2}3p^{5}3d^{3}$ of W$^{54+}$ ion have been studied by using Multi-Configuration Dirac-Fock method with the implementation of Grasp2K package. A restricted active space was employed to investigate the correlation contribution from different models. The Breit interaction and QED effects were taken …
Energy levels and transition rates for electric-dipole, electric-quadrupole, electric-octupole, magnetic-dipole, and magnetic-quadrupole transitions among the levels arising from the $n\ \leq$ 5 configurations in B-like Kr XXXII are calculated by using two state-of-the-art methods, namely, the multi-configuration Dirac-Hartree-Fock (MCDHF) approach and the second-order many-body perturbation theory (RMBPT). Our results are compared with several available experimental and other theoretical values. Electron-impact excitation (EIE) collision strengths are calculated via the independent process an…
The radium atom is a promising system for studying parity and time invariance violating weak interactions. However, available experimental spectroscopic data for radium is insufficient for designing an optimal experimental setup. We calculate the energy levels and transition amplitudes for radium states of significant interest. Forty states corresponding to all possible configurations consisting of the $7s$, $7p$ and $6d$ single-electron states as well as the states of the $7s8s$, $7s8p$ and $7s7d$ configurations have been calculated. The energies of ten of these states corresponding to the $6…
We show that by averaging over transitions to multiple hyperfine levels, quadrupole shifts and dominant Zeeman effects exactly cancel whenever the nuclear spin, I, is at least as large as the total electronic angular momentum, J. The average frequency thus defines a frequency reference which is inherently independent of external magnetic fields and electric field gradients. We use Lu+ to illustrate the method although the approach could be readily adapted to other atomic species. This approach practically eliminates the quadrupole and Zeeman shift considerations for many clock candidates.
Energy levels and radiative rates are reported for transitions in Cl-like W LVIII. Configuration interaction (CI) has been included among 44 configurations (generating 4978 levels) over a wide energy range up to 363 Ryd, and the general-purpose relativistic atomic structure package ({\sc grasp}) adopted for the calculations. Since no other results of comparable complexity are available, calculations have also been performed with the flexible atomic code ({\sc fac}), which help in assessing the accuracy of our results. Energies are listed for the lowest 400 levels (with energies up to $\sim$ 98…
We consider the stimulated Raman transition between two long-lived states via multiple intermediate states, such as between hyperfine ground states in the alkali-metal atoms. We present a concise treatment of the general, multilevel, off-resonant case, and we show how the lightshift emerges naturally in this approach. We illustrate our results by application to alkali-metal atoms and we make specific reference to cesium. We comment on some artifacts, due solely to the geometrical overlap of states, which are relevant to existing experiments.
We report calculations of energy levels, radiative rates, and electron impact excitation rates for transitions in Li-like ions with 12 <= Z <= 20. The GRASP (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates, while for determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code DARC is used. Oscillator strengths, radiative rates, and line strengths are reported for all E1, E2, M1, and M2 transitions among the lowest 24 levels of the Li-like ions considered. Collision strengths have b…
We report experimental measurements of the rates of blackbody radiation-induced transitions between high-lying (n>60) S, P and D Rydberg levels of rubidium atoms in a magneto-optical trap using a hybrid field ionization and state-selective depumping technique. Our results reveal significant deviations of the measured transition rates from theory for well-defined ranges of the principal quantum number. We assume that the most likely cause for those deviations is a modified blackbody spectrum inside the glass cell in which the magneto-optical trap is formed, and we test this assumption by instal…
We consider the influence of the near dipole-dipole interaction, underlying the local field, on the dynamics of two-level and V-type three-level atoms exposed to cw-laser radiation. The dipole-dipole interaction between the V-type three-level atoms is shown to give rise to the Poincaré-Andronov-Hopf bifurcation in steady-state solution of the equations of motion. As a result, the populations of the energy levels periodically vary in time. In the framework of the two-level model, dynamical instabilities are proved to be impossible.
We study spectroscopy of artificial solid-state four-level quantum system. This system is formed by two coupled superconducting flux qubits. When multiple driving frequency of the applied microwaves matches the energy difference between any two levels, the transition to the upper level is induced. We demonstrate two types of the multi-photon transitions: direct transitions between two levels and ladder-type transitions via an intermediate level. For the latter transitions, in particular, the inverse population of the excited state with respect to the ground one is realized. These processes can…
