Marie Guitou

Inelastic Mg+H collision data for non-LTE applications in stellar atmospheres

Rate coefficients for inelastic Mg+H collisions are calculated for all transitions between the lowest seven levels and the ionic state (charge transfer), namely Mg(3s(2) S-1, 3s3p P-3, 3s3p P-1, 3s4s S-3, 3s4s S-1, 3s3d D-1, 3s4p P-3)+H(1s) and Mg+(3s S-2)+H-. The rate coefficients are based on cross-sections from full quantum scattering calculations, which are themselves based on detailed quantum chemical calculations for the MgH molecule. The data are needed for non-LTE applications in cool astrophysical environments, especially cool stellar atmospheres, and are presented for a temperature range of 500-8000 K. From consideration of the sensitivity of the cross-sections to various uncertainties in the calculations, most importantly input quantum chemical data and the numerical accuracy of the scattering calculations, a measure of the possible uncertainties in the rate coefficients is estimated.

Mg line formation in late-type stellar atmospheres - I. The model atom

Context. Magnesium is an element of significant astrophysical importance, often traced in late-type stars using lines of neutral magnesium, which is expected to be subject to departures from local thermodynamic equilibrium (LTE). The importance of Mg, together with the unique range of spectral features in late-type stars probing different parts of the atom, as well as its relative simplicity from an atomic physics point of view, makes it a prime target and test bed for detailed ab initio non-LTE modelling in stellar atmospheres. Previous non-LTE modelling of spectral line formation has, however, been subject to uncertainties due to lack of accurate data for inelastic collisions with electrons and hydrogen atoms. Aims. In this paper we build and test a Mg model atom for spectral line formation in late-type stars with new or recent inelastic collision data and no associated free parameters. We aim to reduce these uncertainties and thereby improve the accuracy of Mg non-LTE modelling in late-type stars. Methods. For the low-lying states of Mg i, electron collision data were calculated using the R-matrix method. Hydrogen collision data, including charge transfer processes, were taken from recent calculations by some of us. Calculations for collisional broadening by neutral hydrogen were also performed where data were missing. These calculations, together with data from the literature, were used to build a model atom. This model was then employed in the context of standard non-LTE modelling in 1D (including average 3D) model atmospheres in a small set of stellar atmosphere models. First, the modelling was tested by comparisons with observed spectra of benchmark stars with well-known parameters. Second, the spectral line behaviour and uncertainties were explored by extensive experiments in which sets of collisional data were changed or removed. Results. The modelled spectra agree well with observed spectra from benchmark stars, showing much better agreement with line profile shapes than with LTE modelling. The line-to-line scatter in the derived abundances shows some improvements compared to LTE (where the cores of strong lines must often be ignored), particularly when coupled with averaged 3D models. The observed Mg emission features at 7 and 12 μm in the spectra of the Sun and Arcturus, which are sensitive to the collision data, are reasonably well reproduced. Charge transfer with H is generally important as a thermalising mechanism in dwarfs, but less so in giants. Excitation due to collisions with H is found to be quite important in both giants and dwarfs. The R-matrix calculations for electron collisions also lead to significant differences compared to when approximate formulas are employed. The modelling predicts non-LTE abundance corrections ΔA(Mg) NLTE−LTE in dwarfs, both solar metallicity and metal-poor, to be very small (of order 0.01 dex), even smaller than found in previous studies. In giants, corrections vary greatly between lines, but can be as large as 0.4 dex. Conclusions. Our results emphasise the need for accurate data of Mg collisions with both electrons and H atoms for precise non-LTE predictions of stellar spectra, but demonstrate that such data can be calculated and that ab initio non-LTE modelling without resort to free parameters is possible. In contrast to Li and Na, where only the introduction of charge transfer processes has led to differences with respect to earlier non-LTE modelling, the more complex case of Mg finds changes due to improvements in the data for collisional excitation by electrons and hydrogen atoms, as well as due to the charge transfer processes. Grids of departure coefficients and abundance corrections for a range of stellar parameters are planned for a forthcoming paper.

Inelastic Mg+H collision processes at low energies

Full quantum scattering calculations of cross sections for low-energy near-threshold inelastic Mg+H collisions are reported, such processes being of interest for modelling of Mg spectral lines in stellar atmospheres. The calculations are made for three transitions between the ground and two lowest excited Mg states, Mg(3s(2) (1)S(0)), Mg(3s3p (3)P) and Mg(3s3p (1)P). The calculations are based on adiabatic potentials and nonadiabatic couplings for the three low-lying (2)Sigma(+) and the first two (2)Pi states, calculated using large active spaces and basis sets. Non-adiabatic regions associated with radial couplings at avoided ionic crossings in the (2)Sigma(+) molecular potentials are found to be the main mechanism for excitation. Cross sections of similar order of magnitude to those obtained in Li+H and Na+H collisions are found. This, together with the fact that the same mechanism is important, suggests that as has been found earlier for Li and Na, processes such as ion pair production may be important in astrophysical modelling of Mg, and motivates continued study of this system including all states up to and including the ionic limit.

Model estimates of inelastic calcium-hydrogen collision data for non-LTE stellar atmospheres modeling

Aims. Inelastic processes in low-energy Ca + H and Ca+ + H- collisions are treated for the states from the ground state up to the ionic state with the aim to provide rate coeffcients needed for non-LTE modeling of Ca in cool stellar atmospheres. Methods. The electronic molecular structure was determined using a recently proposed model approach that is based on an asymptotic method. Nonadiabatic nuclear dynamics were treated by means of multichannel formulas, based on the Landau-Zener model for nonadiabatic transition probabilities. Results. The cross sections and rate coeffcients for inelastic processes in Ca + H and Ca+ + H- collisions were calculated for all transitions between 17 low-lying covalent states plus the ionic state. It is shown that the highest rate coeffcient values correspond to the excitation, de-excitation, ion-pair formation, and mutual neutralization processes involving the Ca(4s5s 1;3S) and the ionic Ca+ + H- states. The next group with the second highest rate coeffcients includes the processes involving the Ca(4s5p 1;3P), Ca(4s4d 1;3D), and Ca(4s4p 1P) states. The processes from these two groups are likely to be important for non-LTE modeling.

Calcium-hydrogen interactions for collisional excitation and charge transfer

The accurate highly correlated ab initio calculations for ten low lying covalent Σ+2 states of CaH molecule, and one ionic Ca+H- state, are performed using large active space and extended basis set, with special attention to the long-range (6-20 Å) region where a number of avoided crossings between ionic and covalent states occur. These states are further transformed to a diabatic representation using a numerical diabatization scheme based on the minimization of derivative coupling. This results in a smooth diabatic Hamiltonian which can be easily fit to an analytic form. The diagonal elements of the diabatic potentials were then empirically corrected to reproduce experimental dissociation energies. Though the emphasis is on the asymptotic region, the obtained spectroscopic constants are in good agreement with available experimental and theoretical data. The resulting analytical Hamiltonian, after back transformation to adiabatic representation, is used to obtain cross sections for different inelastic processes using both the multichannel and the branching probability current approaches. It is shown that while for most intense transitions both approaches provide very close results, the multichannel approach underestimates the cross sections of weak transitions, as a consequence of the short-range avoided crossings that are accounted for only in the branching probability current method.

Mg2H2: New insight on the Mg–Mg bonding and spectroscopic study

The six dimensional potential energy surface of the electronic ground state X̃(1)Σ(g)(+) of Mg(2)H(2) has been generated by the coupled-cluster approach with single, double and perturbative triple excitations [CCSD(T)] combined with the aug-cc-pCVTZ basis set for Mg atoms and the aug-cc-pVTZ basis set for the H atoms. The analytical representation of this surface was used in variational calculations of the rovibrational energies of Mg(2)H(2), Mg(2)D(2), and HMg(2)D for J = 0 and 1. For Mg(2)H(2), the rotational constant B(0) is computed to be 0.1438 cm(-1), and the fundamental anharmonic wavenumbers are calculated to be ν(1) = 1527.3 cm(-1) (Σ(g)(+)), ν(2) = 275.3 cm(-1) (Σ(g)(+)), ν(3) = 1503.6 cm(-1) (Σ(u)(+)), ν(4) = 312.9 cm(-1) (Π(g)), and ν(5) = 256.5 cm(-1) (Π(u)). In addition, the electronic ground states of Mg(2)H, MgH(2), Mg(2), and MgH have been investigated in order to compute the bonding energies of Mg(2)H(2) and to explain the strength of the Mg-Mg bond in this tetra-atomic molecule. The nature of the low-lying excited states of Mg(2)H(2) is also studied.

Stability of the HgS molecule and spectroscopy of its low lying electronic states

Large scale Multireference Configuration Interactions (MRCI) and energy consistent relativistic pseudopotential (for the Hg atom) have been used to investigate the electronic structure, stability and spectroscopy of the low lying electronic states of the HgS molecule. The relative position of the two lowest electronic states, X and a, was found to be very sensitive to the quality of the basis set. Spin–orbit effects were taken into account leading to accurate spectroscopic data useful for the identification of the molecule. T 0 between the lowest components of the two states, X and a, has been evaluated to be 0.142 eV (3.5 kcal mol−1). Dipole moment functions were calculated for the lowest states; the rather large dipole moment of the X state makes possible the detection of vibrational transitions with a calculated ω e equal to 364 cm−1. Transitions between the X and the A states are predicted in the far IR domain with a  cm−1. The predissociation of the X and A states has been analysed and it has been shown that for the X state only the vibrational levels below v = 11 are stable; higher levels are predissociated by the a state. The effective dissociation energy of the X state of HgS can thus be estimated to be 0.47 eV (6.5 kcal mol−1). For the A state, the levels with v > 8 are predissociated by the dissociative b state.

Physisorbed H2@Cu(100) surface: Potential and spectroscopy

Using an embedding approach, a 2-D potential energy function has been calculated to describe the physisorption interaction of H2 with a Cu(100) surface. For this purpose, a cluster model of the system calculated with highly correlated wavefunctions is combined with a periodic Density-Functional-Theory method using van der Waals-DF2 functional. Rotational and vibrational energy levels of physisorbed H2, as well as D2 and HD, are calculated using the 2D embedding corrected potential energy function. The calculated transitions are in a very good agreement with Electron-Energy-Loss-Spectroscopy observations.

Inelastic cross sections for low-energy Mg + H collisions

Quantum calculations of cross sections for the inelastic processes in Mg + H collisions are improved. It is shown that the largest cross section among the endothermic processes with the value of approximately 80 A2 corresponds to the process of the ion-pair formation: Mg(3s4s1 S)+H → Mg+ + H−. The mechanism of the process is based on nonadiabatic transitions between the MgH(2Σ+) molecular states, which provide the main mechanism for inelastic processes in Mg + H collisions. On the other hand, nonadiabatic transitions between MgH(2II) states affect some cross sections rather significantly. For example, transitions between the MgH(2II) states increase the cross section for the excitation process Mg(3s3p 1P)+H → Mg(3s3d 1D)+H almost by an order of magnitude as compared to the cross section obtained within the MgH(2Σ+) symmetry.

Mg-H collision rates for non-LTE determination of stellar atmospheric parameters

Non-LTE (Local Thermodynamical Equilibrium) modeling implies competition between radiative and collisional processes. The influence of inelastic hydrogen atoms collisions, dominant in cold atmospheres has been and remains to be a significant source of uncertainty for stellar abundance analysis. In the particular case of Mg atoms, a large number of electronic states of the MgH molecule as well as the associated couplings that mix the states during the collision were calculated by high level quantum chemical methods and then used in full quantum scattering calculations. This allows to treat the excitation processes between the seven lowest atomic states of magnesium in collision with hydrogen atoms, as well as the ion-pair production and the mutual neutralization processes. The detailed mechanisms involved during the collision process have been analysed in detail. Our calculations show that the usual approximate Drawin formula leads to errors by factors up to 105. As was already found in Li+H and Na+H collisions, excitation processes were found to be less important than charge transfer processes. However, unlike Li and Na, Mg has different spin terms, singlet and triplet, leading both to doublet molecular MgH electronic states. Collisional rates between spin-allowed and optically spin-forbidden atomic states are found to be of the same order of magnitude although optically spin-forbidden states are only collisionally coupled. Thus we may expect consequences on non-LTE calculations.