Revised Line Profile Function for Hydrogenic Species

Abstract

Analytical series expansions for the hydrogenic spectral line profile functions are derived starting from the three single expressions, obtained by integrating twice the convolution of the Holtsmark, Lorentz and Doppler line profile functions. We get well converging series expansions for the line wings and centers by reducing the number of arguments in the profile function by one, introducing the module of the Holtsmark and Lorentz profiles as a new argument. In the intermediate part of the line, the parabolic cylinder functions expressed via the confluent hypergeometric series, are used. The multi-component Stark splitting of the hydrogenic spectral lines and the modeled stochastic electron transitions in the electric field of the adjacent ions generate wide Doppler plateaux at the line centers, with the characteristic widths estimated from the fit to the characteristic width of the Holtsmark profile. This additional Doppler broadening of the line profile function removes the central dip typical to the Holtsmark profile.

Laboratory Hydrogen-Beta Emission Spectroscopy for Analysis of Astrophysical White Dwarf Spectra

“…Computations of line shapes usually involve the convolution of at least the Holtsmark, Lorentz, and Doppler profiles. The convolution of the Holtsmark and Voigt profiles is reduced to a sum of three integrals with predominant Holtsmark, Lorentz, and Doppler contributions [77,78], respectively, Φ(β) = χ(β) + Λ(β) + ∆(β).…”

“…Here, β indicates the ratio of electric field strength, F, and of normal field strength, F 0 , β = F/F 0 . The three integrals χ(β), Λ(β), and ∆(β) are explicitly listed in Reference [78].…”

Laboratory Hydrogen-Beta Emission Spectroscopy for Analysis of Astrophysical White Dwarf Spectra

“…Computations of line shapes usually involve the convolution of at least the Holtsmark, Lorentz, and Doppler profiles. The convolution of the Holtsmark and Voigt profiles is described by three predominant Holtsmark, Lorentz, and Doppler contributions [73,74], respectively, Φ(β) = χ(β) + Λ(β) + ∆(β).…”

Calculation of atomic structures and radiative properties of fusion plasmas

“…Sapar et Kuusik [45][46][47] donnent pour les ions hydrogénoïdes un développement du profil complet qui prend également en compte l'élargissement ionique, obtenu par convolution d'un profil de Holtsmark (élargissement ionique) et du profil de Voigt :…”