Determination of the Phase Shifts Leading to the Broadening and Shift of Spectral Lines

Abstract

The classical theory of collisional broadening and shift parameters (β, δ) of an isolated spectral line was used to obtain simple analytical formulas for calculating both β and δ. These formulas were obtained under the assumption that the short range interaction is effective only in the broadening while the long range is effective in the shift of the spectral line. These parameters β and δ depend on the limiting phase shifts responsible for broadening η0b and shift η0δ. It was found that the values of η0b and shift η0δ are not equal to each other as was proposed by Weisskopf η0b = η0δ = 1. The two limiting values of η were obtained by numerical evaluation, using different inverse power potentials. By introducing these parameters into the approximated formulas for β and δ using van-der Waals and Lennard–Jones potential it was found that the results of calculations of (β and δ) for different atomic transitions perturbed by different inert gases are in close agreement with the corresponding numerical earlier results based on the Lindholm–Foly theory. The relations between the two parameters ρ0b and ρ0δ for different, interactions were also obtained.