Theory of Line Broadening in Multiplet Spectra

Abstract

A theory of line broadening in the impact approximation is developed which includes the case of overlapping lines. It is assumed that the collisions which give rise to the broadening do not cause transitions between states with different principal quantum numbers. The theory has been worked out in detail in two cases:(1) the broadening arises only from perturbations of the upper state with arbitrary splitting of the substates. This approximation may be used if the perturbations of the lower state are relatively unimportant (e.g., the higher series members of the Balmer lines), and is exact if the perturbations do not affect the lower state as in the case of the ground state of hydrogen perturbed by electron collisions; (2) complete degeneracy of the initial and final states. This approximation is also valid on the far wing of the line if there is splitting, i.e., for frequencies large compared to the splitting, and is a generalization of Anderson's theory. The formal theory is worked out by two different methods. The method of calculation for nearly degenerate initial and final states with splitting is indicated. Method I is particularly suited for calculating the wing distribution while Method II is more suitable for finding the intensity distribution at the line center for overlapping lines. The line profile is made up of a sum of dispersion profiles and asymmetric terms which arise from interferences when the transition operator is not diagonal. The shift and half-width parameters are found from the roots of a secular equation and depend on the splitting as well as the density, temperature, and the character of the perturbation.

Line Broadening and Mixing in NH3 Inversion Doublets Perturbed by NH3, He, Ar, and H2

“…The latter is obtained using the collisional absorption coefficients α Col in Eqs. [4] or [5] after convolution by the Doppler profile α Dop and accounting for the Fourier transform apparatus function F App ; i.e.,…”

Self-broadening of the hydrogen Balmerαline

“…In impact broadening, the duration of the collision is assumed to be small compared to the interval between collisions, and the results describe the line within a few line widths of center. The impact theories of pressure broadening (Baranger 1958a,b;Kolb & Griem 1958) are based on the assumption of sudden collisions (impacts) between the radiator and perturbing atoms, and are valid when frequency displacements ∆ω = ω − ω 0 and gas densities are sufficiently small. One outcome of our unified approach is that we may evaluate the difference between the impact limit and the general unified profile, and establish with certainty the region of validity of an assumed Lorentzian profile.…”

Importance of collisions with charged particles for stellar UV line shapes: $\ion{Cd}{iii}$

“…Advanced calculation of the Stark broadening parameters using the strong-coupling quantum-mechanical method (Baranger 1958a(Baranger , 1958b(Baranger , 1958cKolb & Griem 1958;Griem 1974;Dimitrijević et al 1981;Seaton 1988;Ralchenko et al 1999;Zeng-xin et al 1999) is so complicated that only a limited amount of data for spectral lines originating from lowlying transitions can be calculated adequately. On the other hand, the semi-classical method (Sahal-Bréchot 1969a, 1969bDimitrijević et al 1991; see also a review of obtained results in Dimitrijević 1997) needs a large amount of atomic data, energy levels and oscillator strengths.…”