EDP Sciences
Free Access
Issue
A&A
Volume 577, May 2015
Article Number A113
Number of page(s) 9
Section Atomic, molecular, and nuclear data
DOI https://doi.org/10.1051/0004-6361/201525914
Published online 13 May 2015

© ESO, 2015

1. Introduction

Atomic data are the main ingredient for a good non-local thermodynamic equilibrium (non-LTE) description of the interaction of a chemical species with matter and radiation in atmospheres of late-type stars. Huge efforts have been made over the years regarding experimental and theoretical data (see e.g. Henry 1993). Semi-classical or empirical formulae are widely used because they provide rough estimates of collision rates based on oscillator strength for radiatively permitted transitions while no formulae exist to correctly treat the forbidden transitions. The most used of such formulae is the impact parameter method (IPM, Seaton 1962a,b) which implies computing collision cross-sections for weak and strong coupling. A simpler way (but also not as precise) is to use the semi-empirical formulation from van Regemorter (1962) which is an approximation of the IPM using experimental data available at that time. A more recent version that takes into account recent experimental data give a formulation with a dependance on the change of the principal quantum number (Fisher et al. 1996) but this version is not used very often in the literature.

Table 1

Energy levels of Mg i.

thumbnail Fig. 1

Grotrian diagram of Mg i with mean energy levels labeled (top) and with the collision transitions (bottom). Theoretical collision transitions are shown with black lines whereas the calculated ones are shown with grey lines.

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Magnesium is an α-element produced by type II supernovæ of which is important to study its enrichment relative to iron in different stellar populations. The numerous optical lines of Mg i, including the green b triplet, allow the determination of its abundance in many kinds of stars which is why a good description of its atomic data and especially the inelastic collisions are needed. Zatsarinny et al. (2009) lead a very detailed study of angle-differential cross-sections for electron scattering from neutral magnesium using a B-spline R-matrix (BSR) method. However, only results for five collision cross-sections with the ground state were published in this paper, whereas many collision cross-sections were computed. In the present research note, we decided to publish the other data in the form of effective collision strengths useful for non-LTE applications and which concern 369 transitions between excited states.

2. Previous calculations

In Zatsarinny et al. (2009), 37 target states were included in the scattering calculations. The configurations, terms, energy levels, and statistical weights g are given in Table 1. The Grotrian diagram of the energy levels are given in the top panel of Fig. 1. The double excited level 3p21S located above the ionization energy is also included owing to big mixing of this configuration to the ground state. This improves the convergence of the total scattering function. The quality of the model atom description can be assessed from the theoretical oscillator strengths they calculated compared with the NIST1 counterparts. The differences are less than 3%. Accurate oscillator strengths are important for subsequent calculations of collision cross-sections.

The B-spline R-matrix code (Zatsarinny 2006) was used for the scattering calculations. Angle-differential cross-sections for electron-impact excitation are obtained and described in detail in Zatsarinny et al. (2009). In their Fig. 8, they show angle-integrated cross-sections for five transitions with the ground state but cross-sections for 369 transitions were actually obtained and not published. Such cross-sections are extremely important for non-LTE studies. With 37 levels included, there are a total of 666 collision transition possibilities. We present here all the transitions between the first 17 levels up to 3s5p 1P°, and all effective collision strengths for excitation of these levels to the more excited level indicated in Table 1. There are 369 overall (see bottom panel of Fig. 1). Though the cross-section for transitions between highly-excited levels can also be extracted from the BSR calculation, they cannot be considered reliable because of slow partial wave convergence for these levels. In non-LTE calculations, we hardly need detailed cross-sections, but rather thermal average quantities such as effective collision strengths.

3. Effective collision strengths

The collision rate from state i to state j with electrons can be written as (1)where ne is the electron density, gi the statistical weight of the lower level, Eij the transition energy, k the Boltzmann constant, T the temperature of the medium and the constant (2)where a0 is the Bohr radius, is the Rydberg unit of energy, and me the mass of electron. Moreover, we use the effective collision strenght defined as (3)where x = E/kT and xij = Eij/kT are the kinetic energy after excitation and the energy of the transition in unit of kT, σij is the collision cross-section expressed in unit of , and is dimensionless and symmetric with respect to the transition (i.e. ). The resulting effective collision strengths are given in Table 2 for nine temperatures between 500 and 20 000 K. The level indexes in Table 2 refer to the levels in Table 1.

These data will be useful for non-LTE studies of magnesium in stellar atmospheres of cool stars since they come from reliable quantum mechanical calculations. We should mention that such efforts toward calculating and collecting quantum mechanical data for inelastic collisions is extremely important so as to derive reliable non-LTE abundance corrections. Special efforts are also currently underway for computing inelastic collisions with hydrogen atoms (Barklem et al. 2011; Belyaev et al. 2014).

Table 2

Effective collision strengths.


Acknowledgments

T.M. is short-term foreign postdoctoral fellow from FNRS (FRFC convention, Ref: PDR T.0198.13).

References

All Tables

Table 1

Energy levels of Mg i.

Table 2

Effective collision strengths.

All Figures

thumbnail Fig. 1

Grotrian diagram of Mg i with mean energy levels labeled (top) and with the collision transitions (bottom). Theoretical collision transitions are shown with black lines whereas the calculated ones are shown with grey lines.

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