Uncertainty evaluation of the isotope shift factors for 2s2p~(3,1)P_1~o–2s~2 ~1S_0 transitions in B Ⅱ

Accurate isotope shift factors of the 2s2p~(3,1)P_1~o–2s~2 ~1S_0 transitions in B II, obtained with the multi-configuration Dirac–Hartree–Fock and the relativistic configuration interaction methods, are reported. We found a linear correlation relation between the mass shift factors and the energies for the transitions concerned, considering all-order electron correlations. This relation is important for estimating the uncertainty in the calculation of isotope shift factors. These atomic data can be used to extract the nuclear mean-square charge radii of the boron isotopes with halo structures or to resolve the high precise spectroscopy of B II in astronomical observation.     

Isotope shift of the 2s ~2S_(1/2)→ 2p ~2P_(1/2,3/2) transitions of Li-like Ca ions

The mass-and field-shift parameters of the two 2 s ~2 S_(1/2)→2 p ~2 p_(1/2,3/2) transitions in the Li-like Ca ions are calculated by using multi-configuration Dirac-Hartree-Fock(MCDHF) and the relativistic configuration interaction(RCI) methods with the inclusion of the transverse photon(Breit) interaction,vacuum polarization and self-energy corrections.In addition,the mass shift and field shift of these two transitions are calculated,where the field shift is calculated by using the evaluated value δr~2 obtained by [Atomic Data and Nuclear Data Tables 99 69(2013)].It is found that the mass shift of Li-like Ca ions is greater than the field shift.     

Weak- and hyperfine-interaction-induced 1s2s ~1S_0→ 1s~2 ~1S_0 E1 transition rates of He-like ions

Weak- and hyperfine-interaction-induced 1s2s1S0→ 1s2 1S0E1 transition rates for the isoelectronic sequence of Helike ions have been calculated using the multi-configuration Dirac–Hartree–Fock(MCDHF) and relativistic configuration interaction methods. The results should be helpful for the future experimental investigations of parity non-conservation effects.     

Forbidden transition properties of fine-structure 2p~3 ~4S_(3/2)–2p~3 ~2D_(3/2,5/2) for nitrogen-like ions

Based on relativistic wave functions from multiconfiguration Dirac–Hartree–Fock and configuration interaction calculations, E2 and M1 transition probabilities of 2p~3 ~4S_(3/2)–2 p~3 ~2D_(3/2,5/2) are investigated in the nitrogen-like sequence with7 ≤ Z ≤ 16. The contributions of the electron correlations, Breit interaction, and the quantum electrodynamic(QED) effects on the transition properties are analyzed. The present results can be used for diagnosing plasma. In addition, several N-like ions can also be recommended as a promising candidate for a highly charged ion(HCI) clock with a quality factor(Q) of transition as high as 10~(20).     

Calculations of atomic polarizability for beryllium using MCDHF method

Based on the fully relativistic multiconfiguration Dirac-Hartree-Fock(MCDHF) method and the corresponding program package GRASP2018,a new program for calculating the polarizabilities is developed.As the first application,the static electric-dipole polarizabilities of the ground state 2 s~2 ~1 S_0 and excited state 2 s2 p ~3 P_0 of beryllium are calculated.By means of these polarizabilities,the blackbody radiation(BBR) shift of the 2 s2 p ~3 P_0→2 s~2 ~1 S_0 clock transition is determined.The present results agree very well with other available theoretical results.     

Dirac R-matrix calculations of photoionization cross sections of Ni Ⅻ and atomic structure data of Ni 

We performed R-matrix calculations for photoionization cross sections of the two ground state configuration 3s~23p~5(~2P_(3/2,1/2)~o) levels and 12 excited states of Ni Ⅻ using relativistic Dirac Atomic R-matrix Codes(DARC) across the photon energy range between the ionizations thresholds of the corresponding states and well above the thresholds of the last level of the Ni XIII target ion. Generally, a good agreement is obtained between our results and the earlier theoretical photoionization cross sections. Moreover, we have used two independent fully relativistic GRASP and FAC codes to calculate fine-structure energy levels, wavelengths, oscillator strengths, transitions rates among the lowest 48 levels belonging to the configuration(3s~23p~4, 3s3p~5, 3p~6, 3s~23p~33d) in Ni XIII. Additionally, radiative lifetimes of all the excited states of Ni XIII are presented. Our results of the atomic structure of Ni XIII show good agreement with other theoretical and experimental results available in the literature. A good agreement is found between our calculated lifetimes and the experimental ones.Our present results are useful for plasma diagnostic of fusion and astrophysical plasmas.     

Relationship measurement between ac-Stark shift of ~(40)Ca~+ clock transition and laser polarization direction

Ac-Stark shift of atom levels is caused by an ac-electromagnetic field. As an electromagnetic wave, laser light does induce ac-Stark shift. It is proved experimentally that if the light is linearly polarized, the dynamic polarizability changes with polarization direction. The polarization direction of the linearly-polarized laser is tuned by 720?, and the ac-Stark shifts of the 4S_(1/2),m=±1/2→3D_(5/2,m=±1/2) clock transitions in ~(40)Ca~+ are measured in steps of 10?. The frequency shifts change with laser polarization in a periodical manner and have values opposite to each other.     

Experimental Determination of the Landé g-Factors for 5s~2 ~1S and 5s5p ~3P States of the ~(87)Sr Atom

We present an experimental determination on the Lande g-factors for the 5 s~2 ~1 S_0 and 5 s5 p ~3 P_0 states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the ~(87)Sr optical lattice clock. The Zeeman shift of the 5 s5 p ~3 P_0-5 s~2 ~1 S_0 forbidden transition is measured with the π-polarized andσ~±-polarized interrogations at different magnetic field strengths. Moreover, in the g-factor measurement with the σ~±-transition spectra, it is unnecessary to calibrate the external magnetic field. By this means, the ground state 5 s~2 ~1 S_0 g-factor for the ~(87)Sr atom is-1.306(52) ×10~(-4), which is the first experimental determination to the best of our knowledge, and the result matches very well with the theoretical estimation. The differential g-factorδg between the 5 s5 p~3 P_0 state and the 5 s~2 ~1 S_0 state of the ~(87)Sr atoms is measured in the experiment as well,which are-7.67(36) ×10~(-5) with π-transition spectra and-7.72(43) X 10-5 with σ~±-transition spectra, in good agreement with the previous report [Phys. Rev. A 76(2007) 022510]. This work can also be used for determining the differential g-factor of the clock states for the optical clocks based on other atoms.     

The 4s~24p~3—4s4p~4 transition in Cd ⅩⅥ

The available experimental energies for the 4s~24p~3 and 4s~4p~4 configurations in As Ⅰ—like Sr Ⅵ—Ag Ⅹ Ⅴions are compared with the values calculated using the Hartree—Fock method including configuration interaction and relativistic corrections. Some energy values of the 4s~24p~3 configuration in Rh Ⅹ Ⅲ、Pd Ⅹ Ⅳ and Ag Ⅹ Ⅴ ions are improved and all the energies、wavelengths and transition probabilities of the 4s~24p~3—4s4p~4 transition array in Cd Ⅹ Ⅵ are presented.     

Relativistic calculations of 3s2 1S0-3s3p 1P1 and 3s2 1S0-3s3p 3P1,2 transition probabilities in the Mg isoelectronic sequence

Using the multi-configuration Dirac-Fock self-consistent field method and the relativistic configuration-interaction method,calculations of transition energies,oscillator strengths and rates are performed for the 3s 2 1 S 0-3s3p 1 P 1 spinallowed transition,3s 2 1 S 0-3s3p 3 P 1,2 intercombination and magnetic quadrupole transition in the Mg isoelectronic sequence(Mg I,Al II,Si III,P IV and S V).Electron correlations are treated adequately,including intravalence electron correlations.The influence of the Breit interaction on oscillator strengths and transition energies are investigated.Quantum electrodynamics corrections are added as corrections.The calculation results are found to be in good agreement with the experimental data and other theoretical calculations.     

Transition parameters of Li-like ions(Z = 7–11) in dense plasmas

The energy levels, transition energies, transition probabilities, weighted oscillator strengths, and line strengths of Lilike ions(Z = 7–11) in dense plasmas are investigated in this work. The relativistic effects and electron correlation effects are described by the MCDHF method. The ion sphere model is applied to include the dense plasma screening effect. The ground configuration 1 s~22 s and the excited 1 s~22 p, 1 s~23 l(l = 0–2) are considered. The configuration sets are enlarged until n = 7 where the calculated energy levels have converged. The critical free electron densities of 1 s~23 d states are estimated.Except for 1 s~23 s–1 s~23 p transitions, the transition energies for Δn = 0 increase, and for Δn ≠ 0 decrease with increasing free electron densities. For 1 s~23 s–1 s~23 p transitions, the spectra show blue-shift at lower free electron densities and red-shift at higher free electron densities, and the energy level crossing phenomens are observed at higher free electron densities.     

M1 transition energy and rate in the ground configuration of Ag-like ions with 62 ≤ Z ≤ 94

Systematic calculations and assessments are performed for the magnetic dipole(M1)transition energies and rates between the ²F^o_5/2,7/2 levels in the ground configuration 4d104f along the Ag-like isoelectronic sequence with 62≤Z≤94 based on the second-order many-body perturbation theory implemented in the Flexible Atomic Code.The electron correlations,Breit interaction and quantum electrodynamics effects are taken into account in the present calculations.The accuracy and reliability of our results are evaluated through comprehensive comparisons with available measurements and other theoretical results.For transition energies,our results are in good agreement with the recent experimental data obtained from the electron beam ion traps within 0.18%.The maximum discrepancy between our results and those obtained with the large-scale multiconfiguration Dirac–Hartee–Fock calculations by Grumer et al.[Phys.Rev.A 89062501(2014)]is less than 0.13%along the isoelectronic sequence.Furthermore,the corresponding M1 transition rates are also reported.The present results can be used as the benchmark and useful for spectra simulation and diagnostics of astrophysical and fusion plasmas.     

Time-resolved spectroscopy for 5s~('4)D_(7/2) state transitions undergoing electron–ion recombination in femtosecond laser-produced copper plasma

In the femtosecond laser-produced Cu-plasma, the transient transition dynamics that the excited state 5s~('4)D_(7/2) via electron–ion recombination transfers to 4p~('4)F_(9/2)~0(465.11 nm, Λ1 line) and 4p~('4)D_(7/2)~0(529.25 nm, Λ_2 line) states are investigated by using the time-resolved spectroscopy. The occupation number and relevant lifetime of the excited state 5s~('4)D_(7/2),the temporal evolutions of spectral intensities for Λ_1 line and Λ_2 line emissions are demonstrated to be in direct proportion to the employed laser intensity, which reveals the transient features of transition dynamics clearly differing from that resulted in the traditional collision excitation. Furthermore, some unique characteristics for Λ_1 and Λ_2 transitions stemming from electron–ion recombination are examined in detail.     

Theoretical study of the hyperfine interaction constants,Landé g-factors,and electric quadrupole moments for the low-lying states of the 61Niq+(q=11,12,14,and 15) ions

Highly charged nickel ions have been suggested as candidates for the ultra-precise optical clock, meanwhile the relevant experiment has been carried out. In the framework of the multiconfiguration Dirac–Hartree–Fock(MCDHF)method, we calculated the hyperfine interaction constants, the Landég-factors, and the electric quadrupole moments for the low-lying states in the 61Ni11+,61Ni12+,61Ni14+, and61Ni15+ ions. These states are clock states of the selected clock transitions in highly charged nickel ions(see Fig. 1). Based on discussing the effects of the electron correlations, the Breit interaction, and quantum electrodynamics(QED) effect on these physical quantities, reasonable uncertainties were obtained for our calculated results. In addition, the electric quadrupole frequency shifts and the Zeeman frequency shifts of the clock transitions concerned were analyzed.     

Temperature dependence of line parameters of ~(12)C~(16)O_2 near 2.004 μm studied by tunable diode laser spectroscopy

The absorption spectrum of carbon dioxide at 2.004 μm has been recorded at sample temperatures between 218.0 K and room temperature, by using a high-resolution tunable diode laser absorption spectrometer(TDLAS) combined with a temperature controlled cryogenically cooled absorption cell. The self-, N~(2-), and air-broadening coefficients for nine transitions of ~(12)C~(16)O_2 belonging to the 20012←00001 band in the 4987 cm~(-1)–4998 cm~(-1) region have been measured at different temperatures. From these measurements, we have further determined the temperature dependence exponents of the pressure-broadening coefficients. To the best of our knowledge, the temperature dependence parameters of the collisional broadening coefficients are reported experimentally for the first time for these nine transitions. The measured halfwidth coefficients and the air temperature dependence exponents of these transitions are compared with the available values reported in the literature and HITRAN 2012 database. Agreements and discrepancies are also discussed.     

An optimized ion trap geometry to measure quadrupole shifts of ~(171)Yb~+ clocks

We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the ~(171)Yb ion.This trap will minimize the quadrupole shift due to the harmonic component of the confining potential by an order of magnitude.This will be useful to reduce the uncertainties in the clock frequency measurements of the 6s ~2S_(1/2)→4f~(13)6s~2 ~2F_(7/2)and 6s ~2S_(1/2)→5d~2D_(3/2) transitions,from which we can deduce the precise values of the quadrupole moments(0s) of the 4f~(13)6s~2 ~2F_(7/2) and 5d~2D_(3/2) states.Moreover,it may be able to affirm the validity of the measured 0 value of the4f~(13)6s~2~2F_(7/2) state,for which three independent theoretical studies defer almost by one order of magnitude from the measurement.We also calculate 0s using the relativistic coupled-cluster(RCC) method.We use these 0 values to estimate the quadrupole shift that can be measured in our proposed ion trap experiment.     

The dielectronic recombination process in laser-produced Au plasmas

The calculations of the rate coefficients for dielectronic recombination (DR) along the NiI isoelectronic sequence in the ground state Au^{51+} through Cu-like 3d^9nln′f (n,n′=4,5,6) inner-shell excited configurations are performed using the spin-orbit-split array (SOSA) model. Resonant and nonresonant radiative stabilizing transitions and decays to autoionizing levels followed by radiative cascades are included. Collisional transitions following electron capture are neglected. The trend of the DR rate coefficients and the ratio of dielectronic satellite lines intensities with the change of the electron temperature are discussed.