Context. Abundances of s- and r-process elements in Sun-like stars constrain nucleosynthesis in extreme astrophysical events, such as compact binary mergers and explosions of highly magnetised rapidly rotating massive stars. Aims. We measure solar abundances of yttrium (Y) and europium (Eu) using 3D non-local thermal equilibrium (NLTE) models. We use the model to determine the abundance of Y, and also explore the model's ability to reproduce the solar centre-to-limb variation of its lines. In addition, we determine the Eu abundance using solar disc-centre and integrated flux spectra. Methods. We developed an NLTE model of Eu and updated our model of Y with collisional data from detailed quantum-mechanical calculations. We used the IAG spatially resolved high-resolution solar spectra to derive the solar abundances of Y across the solar disc and of Eu for integrated flux and at disc centre using a set of carefully selected lines and a 3D radiation-hydrodynamics model of the solar atmosphere. Results. We find 3D NLTE solar abundances of A(Y)(3D NLTE) = 2.30 +/- 0.03(stat) +/- 0.07(syst) dex based on observations at all angles and A(Eu) = 0.57 +/- 0.01(stat) +/- 0.06(syst) dex based on the integrated flux and disc-centre intensity. 3D NLTE modelling offers the most consistent abundances across the solar disc, and resolves the problem of severe systematic bias in Y and Eu abundances inherent to 1D LTE, 1D NLTE, and 3D LTE modelling.

Context. Abundances of s- and r-process elements in Sun-like stars constrain nucleosynthesis in extreme astrophysical events, such as compact binary mergers and explosions of highly magnetised rapidly rotating massive stars. Aims. We measure solar abundances of yttrium (Y) and europium (Eu) using 3D non-local thermal equilibrium (NLTE) models. We use the model to determine the abundance of Y, and also explore the model's ability to reproduce the solar centre-to-limb variation of its lines. In addition, we determine the Eu abundance using solar disc-centre and integrated flux spectra. Methods. We developed an NLTE model of Eu and updated our model of Y with collisional data from detailed quantum-mechanical calculations. We used the IAG spatially resolved high-resolution solar spectra to derive the solar abundances of Y across the solar disc and of Eu for integrated flux and at disc centre using a set of carefully selected lines and a 3D radiation-hydrodynamics model of the solar atmosphere. Results. We find 3D NLTE solar abundances of A(Y)$_{\textrm{3D NLTE}}$=$2.30 \pm 0.03_{\textrm{stat}} \pm 0.07_{\textrm{syst}}$ dex based on observations at all angles and A(Eu)$_{\textrm{3D NLTE}}$=$0.57 \pm 0.01_{\textrm{stat}} \pm 0.06_{\textrm{syst}}$ dex based on the integrated flux and disc-centre intensity. 3D NLTE modelling offers the most consistent abundances across the solar disc, and resolves the problem of severe systematic bias in Y and Eu abundances inherent to 1D LTE, 1D NLTE, and 3D LTE modelling.

The cross sections and rate coefficients for inelastic processes in low-energy collisions of yttrium and hydrogen atoms and ions are calculated. Three ionic states of Y+ + H− are considered. Calculations of non-adiabatic nuclear dynamics in all molecular symmetries of each ionic state are performed. Inelastic processes due to non-adiabatic transitions between 65 different states of the YH quasimolecule are considered. In total, 1,796 inelastic processes are treated and their cross sections for collision energy range from 0.001 to 100 eV and rate coefficients for temperatures from 1,000 to 10,000 K are calculated and analyzed. Inelastic processes with large rate coefficients are important for treating Non-LTE effects in astrophysical modeling.

ABSTRACT This paper reports the results of investigations of inelastic processes in B + H and B+ + H− collisions with accounting for the fine structure. The calculations of the cross-sections and rate coefficients for excitation, de-excitation, ion-pair formation, and mutual neutralization processes (240 in total) are performed by using the quantum asymptotic method, which is modified in this paper for accounting of the fine structure, and by the multichannel approach within the framework of the Born–Oppenheimer formalism. It is found that accounting for the fine structure may change the rate coefficients significantly, and the rates calculated with accounting for the fine structure cannot be obtained by a simple redistribution of the non-relativistic rates. The processes important for non-local thermodynamic equilibrium modelling of stellar atmospheres are designated.

Utilizing a simplified quantum model approach, the low-energy inelastic collision processes between yttrium atoms (ions) and hydrogen atoms have been studied. Rate coefficients corresponding to the mutual neutralization, ion-pair formation, excitation, and de-excitation processes for the above collision systems have been provided in the temperature range of 1000-10 000 K. Three ionic states and 73 covalent states are considered in calculations for the collisions of yttrium atoms with hydrogen atoms, which include six molecular symmetries and 4074 partial inelastic reaction processes. For the collisions of yttrium ions with hydrogen atoms, one ionic state and 116 covalent states are included, which are related to three molecular symmetries and 13 572 partial inelastic collision processes. It is found that the rate coefficients for the mutual neutralization process have a maximum at T = 6000 K, which is an order of magnitude higher than those of other processes. Notably, the positions of optimal windows for the collisions of yttrium atoms and ions with hydrogen atoms are found near electronic binding energy -2 eV (Y) and -4.4 eV (Y+), respectively. The scattering channels located in or near these optimal windows have intermediate-to-large rate coefficients (greater than 10(-12) cm(3) s(-1)). The reported data should be useful in the study of non-local thermodynamic equilibrium modelling.

Inelastic processes rate coefficients for low-energy Sr + H, Sr+ + H−, Sr+ + H, and Sr2+ + H− collisions are calculated using the multichannel quantum model approach. A total of 31 scattering channels of SrH+ and 17 scattering channels of SrH are considered. The partial cross sections and the partial rate coefficients are hence calculated for 1202 partial processes in total. Using new quantum data for Sr ii + H i collisions, we updated the model atom of Sr ii and performed the non-local thermodynamic equilibrium (non-LTE) calculations. We provide the non-LTE abundance corrections for the Sr ii resonance lines in two grids of model atmospheres, which are applicable to very metal-poor ([Fe/H] ≤−2) dwarfs and giants.

The cross sections and rate coefficients for inelastic processes in low-energy collisions of nickel atoms and positive ions with hydrogen atoms and negative ions are calculated for the collisional energy range 10−4–100 eV and for the temperature range 1000–10,000 K. 74 covalent and three ionic states correlated to 11 molecular symmetries are considered. 3380 partial inelastic processes are treated in total. The study of nickel–hydrogen collisions is performed by the quantum model methods within the Born–Oppenheimer formalism. The electronic structure of the collisional quasimolecule is calculated by the semiempirical asymptotic method for each considered molecular symmetry. For nuclear dynamic calculations the simplified method in combination with the Landau–Zener model is used. Nuclear dynamics within each considered symmetry is treated separately, and the total rate coefficients for each inelastic process have been summed over all symmetries. The largest values of the rate coefficients (exceeding 10−8 cm3 s−1) correspond to the mutual neutralization processes in collisions Ni+(3d 9 2 D) + H−(1s 2 1 S) (the ground ionic state being the initial state), as well as in Ni+(3d 84s 4,2 F) + H−(1s 2 1 S) (the first excited and the second excited ionic states being the initial states) collisions. At the temperature of 6000 K, the rate coefficients with large magnitudes have the values from the ranges (1.35−5.87) × 10−8 cm3 s−1 and (1.02−6.77) × 10−8 cm3 s−1, respectively. The calculated rate coefficients with large and moderate values are important for non–local thermodynamic equilibrium stellar atmosphere modeling.

ABSTRACT We present a new model atom of Zn i-Zn ii based on the most up-to-date photoionization cross-sections, electron-impact excitation rates, and rate coefficients for the Zn i + H i and Zn ii + H− collisions. The latter were calculated using the multichannel quantum asymptotic treatment based on the Born–Oppenheimer approach. Non-LTE analysis was performed for the first time for lines of Zn i and Zn ii in the ultraviolet (UV) spectra of two very metal-poor reference stars: HD 84937 and HD 140283. We found consistent non-LTE abundance from the resonance Zn i 2138 Å line, the subordinate lines, and the lines of Zn ii. In both stars, non-LTE leads to 0.17 dex higher average abundance from Zn i, while, for Zn ii lines, non-LTE corrections are minor and do not exceed 0.06 dex. Using lines of Zn i in the high-resolution spectra, we determined the non-LTE abundances for a sample of 80 stars in the −2.5 ≤ [Fe/H] ≤ 0.2 metallicity range. The [Zn/Fe] versus [Fe/H] diagram reveals a dip, with [Zn/Fe] ≃ 0.3 in the most metal-poor stars, a close-to-solar value for [Fe/H] ∼−1.2, and increasing [Zn/Fe] up to 0.3 in the thick disc stars. The close-to-solar metallicity stars have subsolar [Zn/H] ≃ −0.1, on average. Non-LTE abundances of zinc were derived for the first time for seven reference F- to B-type stars. We provide a grid of the non-LTE abundance corrections.

Inelastic processes in low-energy Cu + H and Cu+ + H- collisions, 306 partial processes in total, are investigated taking fine-structure effects into account. We use the asymptotic approach to model the adiabatic potentials and adapt a recently proposed method to include the copper fine structure. The nuclear dynamics is performed by the multichannel analytical approach and the Landau-Zener model. The rate coefficients are calculated for the temperature range of 1000-10000 K. The largest rate coefficient is obtained for the mutual neutralization process Cu+ + H- -> Cu(3d(10)5s S-2(1/2)) + H with a value of 3.81 x 10(-8) cm(3) s(-1) at a temperature of 6000 K . It is shown that the practice to redistribute LS-coupling rate coefficients among fine-structure sublevels can give rates that deviate significantly from those calculated in the JJ-coupling scheme, that is with account for the fine-structure effects.

Motivated by the controversy over the surface metallicity of the Sun, we present a re-analysis of the solar photospheric oxygen (O) abundance. New atomic models of O and Ni are used to perform Non-Local Thermodynamic Equilibrium (NLTE) calculations with 1D hydrostatic (MARCS) and 3D hydrodynamical (Stagger and Bifrost) models. The Bifrost 3D MHD simulations are used to quantify the influence of the chromosphere. We compare the 3D NLTE line profiles with new high-resolution, R = 700 000, spatially-resolved spectra of the Sun obtained using the IAG FTS instrument. We find that the O I lines at 777 nm yield the abundance of log A(O) = 8.74 +/- 0.03 dex, which depends on the choice of the H-impact collisional data and oscillator strengths. The forbidden [O I] line at 630 nm is less model-dependent, as it forms nearly in LTE and is only weakly sensitive to convection. However, the oscillator strength for this transition is more uncertain than for the 777 nm lines. Modelled in 3D NLTE with the Ni I blend, the 630 nm line yields an abundance of log A(O) = 8.77 +/- 0.05 dex. We compare our results with previous estimates in the literature and draw a conclusion on the most likely value of the solar photospheric O abundance, which we estimate at log A(O) = 8.75 +/- 0.03 dex.

We have constructed a new K I model atom using currently available atomic data. We have performed calculations for K I by abandoning the assumption of local thermodynamic equilibrium (non-LTE) for the Sun and three moderately metal-poor dwarf stars. To take into account the inelastic processes in collisions with hydrogen atoms, for the first time we have used the rate constants calculated by including the fine structure of K I levels and analyzed the influence of their application on the non-LTE results compared to the use of the rate constants calculated for combined levels. In agreement with the non-LTE studies available in the literature, K I is subject to overrecombination, which leads to a strengthening of spectral lines and negative abundance corrections. The non-LTE effects are shown to weaken when using new collisional data. We reached the same conclusion when comparing the non-LTE corrections calculated for the Ca II 8662 Å line in model atmospheres with $$\textrm{[Fe/H]}={-}4.5$$ using the Ca II $$+$$ H I collision rates derived with and without allowance for the fine structure of Ca II levels. However, the effect is very small for the other two triplet lines, Ca II 8498 and 8542 Å. The solar non-LTE abundance $$\log\varepsilon_{\textrm{K}}=5.09\pm 0.08$$ derived from five lines is consistent with the meteoritic one within 0.01 dex. Despite the fact that in the atmospheres of the program stars the departures from LTE are larger than those in the Sun, the differential abundance [K/H] is almost independent of which collisional data set is used: the one calculated with or without allowance for the fine structure of K I levels.

We performed the non-local thermodynamic equilibrium (non-LTE) calculations for Ti I-II with the updated model atom that includes quantum-mechanical rate coefficients for inelastic collisions with hydrogen atoms. We have calculated for the first time the rate coefficients for bound-bound transitions in inelastic collisions of titanium atoms and ions with hydrogen atoms and for the charge-exchange processes: Ti I + H <-> Ti II + H- and Ti II + H <-> Ti III + H-. The influence of these data on non-LTE abundance determinations has been tested for the Sun and four metal-poor stars. For Ti I and Ti II, the application of the derived rate coefficients has led to an increase in the departures from LTE and an increase in the titanium abundance compared to that, obtained with approximate formulas for the rate coefficients. In metal-poor stars, we have failed to achieve consistent non-LTE abundances from lines of two ionization stages. The known in the literature discrepancy in the non-LTE abundances from Ti I and Ti II lines in metal-poor stars cannot be solved by improvement of the rates of inelastic processes in collisions with hydrogen atoms in non-LTE calculations with classical model atmospheres.

Context. The pursuit of more realistic spectroscopic modelling and consistent abundances has led us to begin a new series of papers designed to improve current solar and stellar abundances of various atomic species. To achieve this, we have begun updating the three-dimensional (3D) non-local thermodynamic equilibrium (non-LTE) radiative transfer code, MULTI3D, and the equivalent one-dimensional (1D) non-LTE radiative transfer code, MULTI 2.3. Aims. We examine our improvements to these codes by redetermining the solar barium abundance. Barium was chosen for this test as it is an important diagnostic element of the s-process in the context of galactic chemical evolution. New BaII + H collisional data for excitation and charge exchange reactions computed from first principles had recently become available and were included in the model atom. The atom also includes the effects of isotopic line shifts and hyperfine splitting. Methods. A grid of 1D LTE barium lines were constructed with MULTI 2.3 and fit to the four BaII lines available to us in the optical region of the solar spectrum. Abundance corrections were then determined in 1D non-LTE, 3D LTE, and 3D non-LTE. A new 3D non-LTE solar barium abundance was computed from these corrections. Results. We present for the first time the full 3D non-LTE barium abundance of A(Ba) = 2.27 +/- 0.02 +/- 0.01, which was derived from four individual fully consistent barium lines. Errors here represent the systematic and random errors, respectively.

Rate coefficients for inelastic processes in low-energy Co + H, Co + + H − , Co + + H , and Co 2 + + H − collisions are estimated using the quantum simplified model. Considerations include 44 triplet and 55 quintet molecular states of CoH, as well as 91 molecular states of CoH + . The estimations provide the rate coefficients for the 4862 partial processes (mutual neutralization, ion-pair formation, excitation, and de-excitation) in the neutral CoH system, and for the 8190 partial processes in the ionized CoH + system, 13 , 052 processes in total. At T = 6000 K, the rate coefficients with the largest values around 6 × 10 − 8 cm 3 s − 1 correspond to the mutual neutralization processes into the Co ( e 2 F ) + H and Co + ( g 5 F ) + H final channels in the neutral and ionized systems, respectively. Among the excitation and de-excitation processes in Co + H and in Co + + H collisions, at T = 6000 K, the largest rate coefficients have values around 7 × 10 − 9 cm 3 s − 1 and correspond to the processes Co ( y 2 S ∘ ) + H → Co ( e 2 F ; v 4 D ∘ ) + H and Co + ( h 3 P ) + H → Co + ( g 3 P ; g 5 P ; g 5 F ) + H , respectively. The calculations single out inelastic processes important for non-local thermodynamic equilibrium (NLTE) modelling of Co I and Co II spectra in stellar atmospheres. The test NLTE calculations are carried out, and it is found that the new collision rates have a strong effect on the line formation and NLTE abundance corrections.

Context. The pursuit of more realistic spectroscopic modelling and consistent abundances has led us to begin a new series of papers designed to improve current solar and stellar abundances of various atomic species. To achieve this, we have begun updating the three-dimensional (3D) non-local thermodynamic equilibrium (non-LTE) radiative transfer code, MULTI3D, and the equivalent one-dimensional (1D) non-LTE radiative transfer code, MULTI 2.3. Aims. We examine our improvements to these codes by redetermining the solar barium abundance. Barium was chosen for this test as it is an important diagnostic element of the s-process in the context of galactic chemical evolution. New Ba II + H collisional data for excitation and charge exchange reactions computed from first principles had recently become available and were included in the model atom. The atom also includes the effects of isotopic line shifts and hyperfine splitting. Methods. A grid of 1D LTE barium lines were constructed with MULTI 2.3 and fit to the four Ba II lines available to us in the optical region of the solar spectrum. Abundance corrections were then determined in 1D non-LTE, 3D LTE, and 3D non-LTE. A new 3D non-LTE solar barium abundance was computed from these corrections. Results. We present for the first time the full 3D non-LTE barium abundance of A(Ba) = 2.27 ± 0.02 ± 0.01, which was derived from four individual fully consistent barium lines. Errors here represent the systematic and random errors, respectively.

Inelastic processes in low-energy Ca+ + H and Ca2+ + H- collisions accounting for the fine structure of calcium ions are investigated. The present study is based on ab initio nonrelativistic potentials and on modification of the potentials by switching the representation from the LS to the JJ coupling scheme. The nuclear dynamical study is performed by the multichannel Landau-Zener approach for the collisional energy range 10(-4) to 100 eV. The rate coefficients are calculated for the temperature range 1000 to 10 000 K. It is found that the largest rate coefficients correspond to the neutralization processes into the final channels Ca+ (4f F-2(7/2)degrees), Ca+ (6s(2)S(1/2)), Ca+ (5d(2)D(3/2,5/2)), Ca+ (6p(2)P(1/2,3/2)degrees), and Ca+(7s(2)S(1/2)) + H(1s(2)S(1/2)), at a temperature of 6000 K they have values exceeding 10(-8) cm(3) s(-1), and the reaction mechanism for these processes corresponds to the long-range ionic-covalent interaction. The rate coefficients for the Ca II infrared triplet 849.8/854.2/866.2-nm transitions in collisions with H are found to be small. It is shown that accounting for the fine structure does not lead to a simple redistribution of rate coefficients obtained within the LS coupling scheme between the fine-structure levels.

A method is proposed for calculating the rate constants of inelastic processes occurring during collisions of alkali metal atoms and their positive ions with hydrogen atoms and negative ions, taking into account the sublevels of the fine structure of alkali metal levels. The results of the application of the proposed method are presented in this paper based on the example of the KH and RbH collisional systems.

Context. Iron plays a crucial role in studies of late-type stars. In their atmospheres, neutral iron is the minority species, and lines of Fe I are subject to the departures from local thermodynamic equilibrium (LTE). In contrast, one believes that LTE is a realistic approximation for Fe II lines. The main source of the uncertainties in the non-LTE (NLTE) calculations for cool atmospheres is a treatment of inelastic collisions with hydrogen atoms. Aims. Our aim is to investigate the effect of Fe I + H I and Fe II + H I collisions and their different treatments on the Fe I/Fe II ionisation equilibrium and iron abundance determinations for three Galactic halo benchmark stars (HD 84937, HD 122563, and HD 140283) and a sample of 38 very metal-poor giants in the dwarf galaxies with well known distances. Methods. We performed the NLTE calculations for Fe I–Fe II by applying quantum-mechanical rate coefficients for collisions with H I from recent papers. Results. We find that collisions with H I serve as efficient thermalisation processes for Fe II, to an extent that the NLTE abundance corrections for Fe II lines do not exceed 0.02 dex, in absolute value, for [Fe/H] ≳−3, and reach +0.06 dex at [Fe/H] ~−4. For a given star, different treatments of Fe I + H I collisions lead to similar average NLTE abundances from the Fe I lines, although discrepancies in the NLTE abundance corrections exist for individual lines. By using quantum-mechanical collisional data and the Gaia-based surface gravity, we obtain consistent abundances from the two ionisation stages, Fe I and Fe II, for red giant HD 122563. For turn-off star HD 84937, and subgiant HD 140283, we analyse the iron lines in the visible and the ultra-violet (UV, 1968–2990 Å) ranges. For either Fe I or Fe II, abundances from the visible and UV lines are found to be consistent in each star. The NLTE abundances from the two ionisation stages agree within 0.10 dex and 0.13 dex for two different treatments of Fe I + H I collisions. The Fe I/Fe II ionisation equilibrium is achieved for each star of our stellar sample in the dwarf galaxies, with the exception of stars at [Fe/H] ≲−3.7.

The rate coefficients for 13 806 partial inelastic processes in low-energy Fe+ + H and Fe2+ + H- collisions are calculated by means of a quantum simplified model including 118 quintet molecular states of FeH-: 117 covalent and ground ionic states. The calculations are performed within the (5)Sigma(+), (5)Pi and (5)Delta, molecular symmetries. The largest rate coefficient, with a value of 7.47 x 10(-8) cm(3) s(-1) at T = 6000 K, corresponds to a neutralization process. In addition, 57 partial neutralization processes have rates exceeding a value of 10(-8) cm(3) s(-1) and many processes have rates in the range 10(-9) - 10(-8) cm(3) s(-1). Among (de-)excitation processes, the largest rate coefficient has a value of 5.66 x 10(-9) cm(3) s(-1). Nevertheless, there are many partial (de-)excitation processes with rate coefficients in the range 10(-9) - 10(-8) cm(3) s(-1). Collisional processes with large-valued rates are expected to be important in astrophysical applications.