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.     

Parameters of Isotope Shifts for 2s2p~(3,1)P_1→ 2s~(2 1)S_0 Transitions in Heavy Be-Like Ions

The field shift and mass shift parameters of the 2s2p~(3,1)P_1→ 2s~(2 1)S_0 transitions in Be-like ions(70 ≤ Z≤ 92)are calculated using the multi-configuration Dirac–Hartree–Fock and the relativistic configuration interaction methods with the inclusion of the Breit interaction and the leading QED corrections. We find that the mass shift parameters of these two transitions do not change monotonously along the isoelectronic sequence in the high-Z range due to the relativistic nuclear recoil effects. A minimum value exists for the specific mass shift parameters around Z= 80, especially for the 2s2p~(3,1)P_1→ 2s~(2 1)S_0 transition. In addition, the field shifts and mass shifts of these two transitions are estimated using an empirical formula, and their contributions are compared along the isoelectronic sequence.     

Probe the 2s（1/2） and 1d（3/2） state level inversion with electron-nucleus scattering

The neutron-rich even-even nuclei^26–40Mg,^28–46Si,^30–48S, and ^32–56Ar are calculated with the RMF model and the phase-shift electron scattering method. Results show that level inversion of the 2s1/2 and 1d3/2 proton states may occur for the magnesium, silicon, sulphur, and argon isotopes with more neutrons away from the stability line. Calculations show that the variation of the central charge densities for30–48S, and32–56Ar are very sensitive to the 2s1/2 and 1d3/2 proton state level inversion, and the level inversion can lead to a large measurable central charge depletion to the charge density distributions for the neutron-rich isotopes. Calculations also show that the charge density diferences between the isotopes with and without central charge depletion can reveal not only the level inversion of the 2s1/2 and 1d3/2 proton states but also the behavior of the proton wave functions of both states. The results can provide references for the possible study of the nuclear level inversion and nuclear bubble phenomenon with electron scattering of short-lived nuclei at RIKEN or/and GSI in the future. In addition, direct nuclear reaction 44S（n, d）43P or44S（3H, α）43P might also be a possible way to study the 2s1/2 and 1d3/2 proton state level inversion.     

Precision frequency measurement of ~1S_0–~3P_1 intercombination lines of Sr isotopes

We report on frequency measurement of the intercombination(5s2)1S0–(5s5p)3P1transition of the four natural isotopes of strontium,including88Sr(82.58%),87Sr(7.0%),86Sr(9.86%),and84Sr(0.56%).A narrow-linewidth laser that is locked to an ultra-low expansion(ULE)optical cavity with a finesse of 12000 is evaluated at a linewidth of 200 Hz with a fractional frequency drift of 2.8×10-13at an integration time of 1 s.The fluorescence collector and detector are specially designed,based on a thermal atomic beam.Using a double-pass acousto-optic modulator(AOM)combined with a fiber and laser power stabilization configuration to detune the laser frequency enables high signal-to-noise ratios and precision saturated spectra to be obtained for the six transition lines,which allows us to determine the transition frequency precisely.The optical frequency is measured using an optical frequency synthesizer referenced to an H maser.Both the statistical values and the final values,including the corrections and uncertainties,are derived for a comparison with the values given in other works.     

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.     

Theoretical Investigation on Excitation,Ionization and Capture in H（1s, 2s） ＋ H（1s, 2s） Collisions

Cross sections of electron-loss in H（1s）＋ H（1s） collisions and total collisional destruction of H（2s） in H（1s） 4- H（2s） collisions are calculatted by four-body classical-trajectory Monte Caylo （CTMC） method and compared with previous theoretical and experimental data over the energy range of 4-100 keV. For the former a good agreement is obtained within different four-body CTMC calculations, and for the incident energy Ep 〉 10 keV, comparison with the experimental data shows a better agreement than the results calculated by the impact parameter approx- imation. For the latter, our theory predicts the correct experimental behaviour, and the discrepancies between our results and experimental ones are less than 30%. Based on the successive comparison with experiments, the cross sections for excitation to H（2p）, single- and double-ionization and H- formation in H（2s）＋H（2s） collisions are calculated in the energy range of 4-100 keV for the first time, and compared with those in H（1s）＋H（1s） and H（1s）＋U（2s） collisions.     

Study of the process e~+e~- →π~+π~-π~0π~0 at energies s～(1/2)<1 GeV

In an experiment with the Spherical Neutral Detector at VEPP-2M collider the cross section of the process e+e-→π+π-π0π0 was measured.At energies s～(1/2)920 MeV this cross section was measured for the first time.The energy dependence of the cross section is well discribed by the vector dominance model with contributions from ρ,ρ,ρ mesons.The decay probability ρ→π+π-π0π0 was found to be Bρ =(1.60±0.74±0.18)×10-5.The upper limit for the decay ω→π+π-π0π0 was improved by two orders of magnitude compared to the previous measurements and is Bω 2×10-4 at 90% confidence level.     

Probe the 2s_(1/2) and 1d_(3/2) state level inversion with electron-nucleus scattering

The neutron-rich even-even nuclei26–40Mg,28–46Si,30–48S,and32–56Ar are calculated with the RMF model and the phase-shift electron scattering method.Results show that level inversion of the 2s1/2and 1d3/2proton states may occur for the magnesium,silicon,sulphur,and argon isotopes with more neutrons away from the stability line.Calculations show that the variation of the central charge densities for30–48S,and32–56Ar are very sensitive to the 2s1/2and 1d3/2proton state level inversion,and the level inversion can lead to a large measurable central charge depletion to the charge density distributions for the neutron-rich isotopes.Calculations also show that the charge density diferences between the isotopes with and without central charge depletion can reveal not only the level inversion of the 2s1/2and 1d3/2proton states but also the behavior of the proton wave functions of both states.The results can provide references for the possible study of the nuclear level inversion and nuclear bubble phenomenon with electron scattering of short-lived nuclei at RIKEN or/and GSI in the future.In addition,direct nuclear reaction44S(n,d)43P or44S(3H,α)43P might also be a possible way to study the 2s1/2and 1d3/2proton state level inversion.     

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.     

Theoretical Investigation of Decay Process in a Doubly Excited 2s^2 ^1S0 State of He-Like Ions

In the framework of multi-configuration Dirac-Fock theory, a detailed calculation is performed for the decay rates and the energies of the doubly excited 2s^2 ^1So state of He-like ions, of which atomic number Z ranges from 6 to 92. The 2s^2 ^1So - ls ^2S1/2 Auger decay is predominant at low Z regime, whereas the 2s^2 ^1So - 1s2p ^1,3P1 two-electron one-photon transitions become quite important in moderate and high Z regimes. For heavy ions with Z ≥ 72, the contribution of 2s^2 ^1So - 1s2s ^3S1 M1 transition is significant. The Breit interaction considerably enhances the 2s^2 ^1So - 1s ^2S1/2 Auger rate at high Z regime.     

Vector correlations study of the reaction N(~2D) + H_2(X~1Σ_g~+) →NH(a~1?) + H(~2S) with different collision energies and reagent vibration excitations

Vector correlations of the reaction N(2D)+ H2(X1Σ+g) → NH(a1?)+ H(2S) are studied based on a recent DMBESEC PES for the first excited state of NH2[J. Phys. Chem. A 114 9644(2010)] by using a quasi-classical trajectory method.The effects of collision energy and the reagent initial vibrational excitation on cross section and product polarization are investigated for v = 0–5 and j = 0 states in a wide collision energy range(10–50 kcal/mol). The integral cross section could be increased by H2 vibration excitation remarkably based on the DMBE-SEC PES. The different phenomena of differential cross sections with different collision energies and reagent vibration excitations are explained. Particularly,the NH molecules are scattered mainly in the backward hemisphere at low vibration quantum number and evolve from backward to forward direction with increasing vibration quantum number, which could be explained by the fact that the vibrational excitation enlarges the H–H distance in the entrance channel, thus enhancing the probability of collision between N atom and H atom. A further study on product polarization demonstrates that the collision energy and vibrational excitation of the reagent remarkably influence the distributions of P(θr), P(φr), and P(θr, φr).     

Mid-infrared luminescence of Dy~(3+)-doped Ga_2S_3–Sb_2S_3–CsI chalcohalide glasses

The mid-infrared(MIR) luminescent properties of Dy~(3+) ions in a new chalcohalide glass host, Ga_2S_3–Sb_2S_3–CsI,are investigated; and the suitability of the doped glass for MIR fiber lasers is evaluated. The Dy~(3+)-doped chalcohalide glasses exhibit good thermal stability and intense MIR emissions around 2.96 μm and 4.41 μm. These emissions show quantum efficiencies(η) as high as ~60%, and have relatively large stimulated emission cross sections(σem). The low phonon energy(~307 cm~(-1)) of the host glass accounts for the intense MIR emissions, as well as the high η. These favorable thermal and emission properties make the Dy~(3+)-doped Ga_2S_3–Sb_2S_3–CsI glasses promising materials for MIR fiber amplifiers or lasers.     

State-to-state dynamics of F(~2P) + HO(~2Π) → O(~3P) + HF(~1Σ~+)reaction on 1~3A〞 potential energy surface

State-to-state time-dependent quantum dynamics calculations are carried out to study F(~2P) + HO(~2Π) → O(~3P) +HF(~1Σ~+) reaction on 1~3A〞 ground potential energy surface(PES). The vibrationally resolved reaction probabilities and the total integral cross section agree well with the previous results. Due to the heavy–light–heavy(HLH) system and the large exoergicity, the obvious vibrational inversion is found in a state-resolved integral cross section. The total differential cross section is found to be forward–backward scattering biased with strong oscillations at energy lower than a threshold of 0.10 eV, which is the indication of the indirect complex-forming mechanism. When the collision energy increases to greater than 0.10 eV, the angular distribution of the product becomes a strong forward scattering, and almost all the products are distributed at θ_t = 0°. This forward-peaked distribution can be attributed to the larger J partial waves and the property of the F atom itself, which make this reaction a direct abstraction process. The state-resolved differential cross sections are basically forward-backward symmetric for v' = 0, 1, and 2 at a collision energy of 0.07 eV; for a collision energy of 0.30 eV,it changes from backward/sideward scattering to forward peaked as v increasing from 0 to 3. These results indicate that the contribution of differential cross sections with more highly vibrational excited states to the total differential cross sections is principal, which further verifies the vibrational inversion in the products.     

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).     

Excitation and decay dynamics of 1s2s inner-shell double-vacancy states of neon atoms

The photo-excitation and Auger decay processes of inner-shell double vacancy states 1s2s2p^6（1,3^S）3s3p of neutral neon atoms have been studied theoretically. Multi-configuration Dirac-Fock （MCDF） calculations have been carried out, with electron correlation effects taken into consideration. The relaxation of core and excited orbitals and configuration interaction are found to be crucial to creating the double vacancy states by single photo-absorption. The predominant decay paths for the double vacancy states turn out to be of the LLM Auger decay to 1s 2s^22p^53s（3p）, KLL Auger decay to 1s^22s2p^43s3p, and KLM Auger decay to 1s^22p^63s（3p）. They lead to further Auger decay, creating the neon ions of multiple charge states. For both double and single vacancy states the spectator type of Auger process is dominated in all the Auger decay processes. Theoretical Anger electron spectra are presented for further investigations, experimental and theoretical.     

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.     

S-wave resonance contributions to B_((s))~0→η_c(2S)π~+π~- in the perturbative QCD factorization approach

By employing the perturbative QCD(PQCD) factorization approach, we study the quasi-two-body B_((s))~0→η_c(2S)π~+π~- decays, where the pion pair comes from the S-wave resonance f_0(X). The Breit-Wigner formula for the f_0(500) and f_0(1500) resonances and the Flatt′e model for the f_0(980) resonance are adopted to parameterize the time-like scalar form factors in the two-pion distribution amplitudes. As a comparison, Bugg's model is also used for the wide f_0(500) in this work. For decay rates, we found the following PQCD predictions:(a)-B(B_s~0 →ηc(2S)f_0(X)[π~+π~-]s)= 2.67_(-1.08)~(+1.78) ×10~(-5) when the contributions from f_0(980) and f_0(1500) are all taken into account;(b)B(B~0→η-c(2S)f_0(500)[π~+π~-]s) = 1.40_(-0.56)~(+0.92) ×10~(-6) in the Breit-Wigner model and 1.53_(-0.61)~(+0.97) ×10~(-6) in Bugg's model.     

Formation of hydrogen atom in 2s state in proton–sodium inelastic scattering

The inelastic collision of protons with sodium atoms are treated for the first time within the framework of the coupledstatic and frozen core approximations. The method is used for calculating partial and total cross-sections with the assumption that only two channels(elastic and hydrogen formation in 2s state) are open. In each case, the calculations are carried out for seven values of the total angular momentum l(0≤ l≤ 6). The target is described using the Clementi Roetti wave functions within the framework of the one valence electron model. We use Lipmann–Swinger equation to solve the derived equations of the problem, then apply an iterative numerical method to obtain the code of computer to calculate iterative partial cross-sections. This can be done through calculating the reactance matrix at different values of considered energies to obtain the transition matrix that gives partial and total cross sections. The present results for total hydrogen(2s state)formation cross sections are in agreement with results of other available ones in wide range of incident energy.     

Molecule opacities of X~2Σ~+, A~2Π, and B~2Σ~+ states of CS~+

Carbon sulfide cation(CS~+) plays a dominant role in some astrophysical atmosphere environments. In this work, the rovibrational transition lines are computed for the lowest three electronic states, in which the internally contracted multireference configuration interaction approach(MRCI) with Davison size-extensivity correction(+Q) is employed to calculate the potential curves and dipole moments, and then the vibrational energies and spectroscopic constants are extracted. The Frank–Condon factors are calculated for the bands of X~2~+Σ~+–A~2Π and X~2Σ~+–B~2Σ~+systems, and the band of X~2Σ~+–A~2Π is in good agreement with the available experimental results. Transition dipole moments and the radiative lifetimes of the low-lying three states are evaluated. The opacities of the CS~+ molecule are computed at different temperatures under the pressure of 100 atms. It is found that as temperature increases, the band systems associated with different transitions for the three states become dim because of the increased population on the vibrational states and excited electronic states at high temperature.