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

Context. Departures from local thermodynamic equilibrium (LTE) distort the calcium abundance derived from stellar spectra in various ways, depending on the lines used and the stellar atmospheric parameters. The collection of atomic data adopted in non-LTE (NLTE) calculations must be sufficiently complete and accurate. Aims. We derive NLTE abundances from high-quality observations and reliable stellar parameters using a model atom built afresh for this work, and check the consistency of our results over a wide wavelength range with transitions of atomic and singly ionised calcium. Methods. We built and tested Ca i and Ca ii model atoms with state-of-the-art radiative and collisional data, and tested their performance deriving the Ca abundance in three benchmark stars: Procyon, the Sun, and Arcturus. We have excellent-quality observations and accurate stellar parameters for these stars. Two methods to derive the LTE / NLTE abundances were used and compared. The LTE / NLTE centre-to-limb variation (CLV) of Ca lines in the Sun was also investigated. Results. The two methods used give similar results in all three stars. Several discrepancies found in LTE do not appear in our NLTE results; in particular the agreement between abundances in the visual and infra-red (IR) and the Ca i and Ca ii ionisation balance is improved overall, although substantial line-to-line scatter remains. The CLV of the calcium lines around 6165 Angs can be partially reproduced. We suspect differences between our modelling and CLV results are due to inhomogeneities in the atmosphere that require 3D modelling.Comment: 17 pages, 11 Figure

Kinematically Complete Study of Low-Energy Electron-Impact Ionization of Argon: Internormalized Cross Sections in Three-Dimensional Kinematics

As a further test of advanced theoretical methods to describe electron-impact single-ionization processes in complex atomic targets, we extended our recent work on Ne(2p) ionization [X. Ren, S. Amami, O. Zatsarinny, T. Pflüger, M. Weyland, W. Y. Baek, H. Rabus, K. Bartschat, D. Madison, and A. Dorn, Phys. Rev. A 91, 032707 (2015)PLRAAN1050-294710.1103/PhysRevA.91.032707] to Ar(3p) ionization at the relatively low incident energy of E0 = 66 eV. The experimental data were obtained with a reaction microscope, which can cover nearly the entire 4π solid angle for the secondary electron emission. We present experimental data for detection angles of 10, 15, and 20⁰ for the faster of the two outgoing electrons as a function of the detection angle of the secondary electron with energies of 3, 5, and 10 eV, respectively. Comparison with theoretical predictions from a B-spline R-matrix (BSR) with pseudostates approach and a three-body distorted-wave (3DW) approach, for detection of the secondary electron in three orthogonal planes as well as the entire solid angle, shows overall satisfactory agreement between experiment and the BSR results, whereas the 3DW approach faces difficulties in predicting some of the details of the angular distributions. These findings are different from our earlier work on Ne(2p), where both the BSR and 3DW approaches yielded comparable levels of agreement with the experimental data

Low-Energy Electron-Impact Ionization of Argon: Three-Dimensional Cross Section

Low-energy (E 0 = 70.8 eV) electron-impact single ionization of a 3p electron in argon has been studied experimentally and theoretically. Our measurements are performed using the so-called reaction microscope technique, which can cover nearly a full 4π solid angle for the emission of a secondary electron with energy below 15 eV and projectile scattering angles ranging from -8° to -30°. The measured cross sections are internormalized across all scattering angles and ejected energies. Several theoretical models were employed to predict the triple-differential cross sections (TDCSs). They include a standard distorted-wave Born approximation (DWBA), a modified version to account for the effects of postcollision interaction (DWBA-PCI), a hybrid second-order distorted-wave plus R-matrix (DWB2-RM) method, and the recently developed B-spline R-matrix with pseudostates (BSR) approach. The relative angular dependence of the BSR cross sections is generally found to be in reasonable agreement with experiment, and the importance of the PCI effect is clearly visible in this low-energy electron-impact ionization process. However, there remain significant differences in the magnitude of the calculated and the measured TDCSs

Polarization correlations for electron-impact excitation of the resonant transitions of Ne and Ar at low incident energies

The electron-polarized-photon coincidence method is used to determine linear and circular polarization correlations in vacuum ultraviolet (VUV) for the differential electron-impact excitation of neon and argon resonance transitions at impact energies of 25 and 30 eV at small scattering angles up to 40. The circular polarization correlation is found to be positive in the case of Ne at 25 eV and supports the prediction of the present B-spline R-matrix theory concerning the violation of a long-established propensity rule regarding angular momentum transfer in electron-impact excitation of S→P transitions. Comparisons with the results from the present relativistic distorted-wave approximation and an earlier semirelativistic distorted-wave Born model are also made. For the case of Ar, at 25 and 30 eV, the circular polarization measurements remain in agreement with theory, but provide limited evidence as to whether or not the circular polarization at small scattering angles is also positive. For the linear polarizations, much better agreement with theory is obtained than in earlier measurements carried out by S. H. Zheng and K. Becker

Theoretical and Experimental Investigation of (e, 2e) Ionization of Argon 3p in Asymmetric Kinematics at Intermediate Energy

The field of electron-impact ionization of atoms, or (e, 2e), has provided significant detailed information about the physics of collisions. For ionization of hydrogen and helium, essentially exact numerical methods have been developed which can correctly predict what will happen. For larger atoms, we do not have theories of comparable accuracy. Considerable attention has been given to ionization of inert gases and, of the inert gases, argon seems to be the most difficult target for theory. There have been several studies comparing experiment and perturbative theoretical approaches over the last few decades, and generally qualitative but not quantitative agreement is found for intermediate energy incident electrons. Recently a nonperturbative method, the B-spline R-matrix (BSR) method, was introduced which appears to be very promising for ionization of heavier atoms. We have recently performed an experimental and theoretical investigation for ionization of argon, and we found that, although the BSR gave reasonably good agreement with experiment, there were also some cases of significant disagreement. The previous study was performed for 200-eV incident electrons and ejected electron energies of 15 and 20 eV. The purpose of the present work is to extend this study to a much larger range of ejected electron energies (15-50 eV) to see if theory gets better with increasing energy as would be expected for a perturbative calculation. The experimental results are compared with both the BSR and two different perturbative calculations

Theoretical and Experimental Investigation of (e, 2e) Ionization of Argon 3p in Asymmetric Kinematics at Intermediate Energy

The field of electron-impact ionization of atoms, or (e, 2e), has provided significant detailed information about the physics of collisions. For ionization of hydrogen and helium, essentially exact numerical methods have been developed which can correctly predict what will happen. For larger atoms, we do not have theories of comparable accuracy. Considerable attention has been given to ionization of inert gases and, of the inert gases, argon seems to be the most difficult target for theory. There have been several studies comparing experiment and perturbative theoretical approaches over the last few decades, and generally qualitative but not quantitative agreement is found for intermediate energy incident electrons. Recently a nonperturbative method, the B-spline R-matrix (BSR) method, was introduced which appears to be very promising for ionization of heavier atoms. We have recently performed an experimental and theoretical investigation for ionization of argon, and we found that, although the BSR gave reasonably good agreement with experiment, there were also some cases of significant disagreement. The previous study was performed for 200-eV incident electrons and ejected electron energies of 15 and 20 eV. The purpose of the present work is to extend this study to a much larger range of ejected electron energies (15-50 eV) to see if theory gets better with increasing energy as would be expected for a perturbative calculation. The experimental results are compared with both the BSR and two different perturbative calculations