Semiempirical Formulas for the Electron-Impact Widths and Shifts of Isolated Ion Lines in Plasmas

Abstract

Using the Bethe-Born approximation for excitation and deexcitation cross sections with semiempirical effective Gaunt factors as proposed by Van Regemorter and Seaton, and extrapolating to below threshold energies, an "optical" cross section is obtained which agrees on the average to within a factor of 1.5 with measured Stark widths for ratios of initial electron energies to threshold energies from about 0.5 to 50. At low values of this ratio, inelastic collisions causing allowed dipole transitions are almost negligible, indicating that most of the broadening is then due to elastic collisions and, probably to a lesser extent, also to superelastic collisions and inelastic collisions involving higher multipole interactions. Comparison of this semiempirical cross section with quasiclassical estimates shows that the dependence on two parameters (namely, the Coulomb parameter and the relative size of the dipole matrix elements) not accounted for in the semiempirical effective Gaunt factors is generally weak in line-broadening applications. Line shifts are estimated from the widths using a dispersion relation, and from an expression valid for large perturber energies. Over the whole energy range considered, the ratio of the shift $d$ of the maximum to the (half) half width $\mathcal{w}$ is found to vary between about 0.7 and 1.4 for lines where there is no cancellation between contributions to the shift from various levels. For other lines this ratio is smaller, in reasonable agreement with experiments. The measurements are also consistent (though not conclusively) with the existence of an additional blue shift (plasma polarization shift) corresponding typically to $\Delta \left(\frac{d}{\mathcal{w}}\right)\approx 0.15$.