Parametrization of Absorption-Line Profiles

Abstract

The parametrization $\ensuremath{\sigma}(E)=C+\ensuremath{\Sigma}\stackrel{}{K}\frac{[(\frac{1}{2}{\ensuremath{\Gamma}}_{K}){B}_{K}+(E\ensuremath{-}{E}_{K}){A}_{K}]}{[{(E\ensuremath{-}{E}_{K})}^{2}+{(\frac{1}{2}{\ensuremath{\Gamma}}_{K})}^{2}]}$ for attenuation cross sections (particularly photo-ionization) is discussed, with attention to the following details: prescriptions for exact calculation of profile parameters, in which the effects of distortions are separated from the effects of multiple scatterings; the validity of assuming independent (noninterfering) resonances; the specific case of autoionizing lines; connections with alternative parametrizations; the prohibition on negative cross sections assured by unitarity; behavior at threshold; and the applicability of this parametrization to emission lines.