Other
Scientific paper
Oct 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998phdt........18b&link_type=abstract
PhD thesis, Univ. Queensland , (1998)
Other
7
Atomic Data, Line Profiles, Solar Abundances
Scientific paper
In this thesis the theory of collisional broadening by neutral hydrogen of Anstee and O'Mara (1991,1992,1995) for s-p and p-s transitions of neutrals is extended and applied to both p-d, d-p, d-f and f-d transitions of neutral atoms, and the broadening of transitions of ions. The interaction between a ground state hydrogen atom with a generic neutral atom, is considered using Rayleigh-Schrödinger perturbation theory. The usual second order expression for the interaction energy between the two atoms involves an infinite sum over virtual states of the two-atom system, and an energy denominator which is the energy debt incurred when the two atom system makes a transition from the state of interest to a virtual state. Unsöld (1927,1955) showed that the expression for the in teraction energy can be greatly simplified if the variable energy debt incurred in making a transition from the state of interest to a virtual state is replaced by a fixed debt Ep. Closure can then be used to complete the sum over the virtual states leading to an expression for the interaction energy in terms of diagonal matrix elements of V2 (where V is the electrostatic interaction between the two atoms), and Ep. This is commonly referred to as the Unsöld approximation. It is the most important approximation in the development of the treatment of spectral line broadening presented in this thesis. Expressions for the interaction energy between a ground state hydrogen atom and a generic neutral atom in both d- and f-states are presented. Adiabatic potential curves calculated from code written to compute these expressions are presented. For interactions of neutral atoms, the Unsöld value of Ep=-4/9 atomic units is used throughout. Code was written to compute line broadening cross-sections for p-d, d-p, d-f and f-d transitions of neutral atoms, using the semi-classical procedure of Roueff (1974) adapted for these transitions. Firstly, the dependence of cross-sections on regions of the potential curves is examined. It is concluded that as found by Anstee and O'Mara (1991,1992) for s-p and p-s transitions, line broadening is insensitive to close collisions and most sensitive to intermediate range interactions. Evidence for this conclusion is presented. The influence of the use of the approximate value of Ep=-4/9 for the energy denominator on the broadening of neutral atom transitions is fully investigated. The dependence on the choice of Ep is shown to be small over the domain of expected values. Line broadening cross-section results are presented for selected specific transitions. Results are also presented in tabular form for cross-sections for general p-d, d-p, d-f and f-d transitions. The cross-sections are tabulated with effective principal quantum number for each state, for a relative perturber velocity of 104 m/s. The cross-sections are fitted to a power law relationship with velocity, of the form σ(v) ∝ vα. The velocity parameter α is similarly tabulated. The extent of the tables is such that most transitions corresponding to these angular momentum states, that will be astrophysically important, should fall within the tables. The results are tested by application to solar spectra. The data is applied to strong lines and abundances for these elements derived and compared with meteoritic abundances. The derived elemental abundances are found to be consistent with meteoritic and currently accepted values, to within the uncertainties in the f-values. Finally, the theory is extended to the broadening of spectral lines of singly ionised atoms. Required modifications to the current interaction potentials are presented. The use of the Unsöld approximation requires a slightly modified approach for ions. A method is presented for calculation of Ep that is suitable for the upper and lower states of strong transitions. Dispersion coefficients C6 and subsequent energy denominators E_p are presented for selected states of ionised atoms. Using these results, broadening cross-sections are presented for the resonance transitions of Ca^+, Mg^+ and Ba^+, and the infrared 4p-3d triplet of Ca+. The triplet lines are tested in the solar spectra, by comparison with empirically determined cross-sections. The calculations for other transition s are compared with both theoretical calculations and empirical determinations by other workers.
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