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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Contributions of strong collisions in the theory of spectral lines

S. Günter

Published Jul 1, 1993• 14 citations
Publisher

Abstract

Contributions of strong electron-atom collisions to shift and width of spectral lines are treated via partial summation of the three-particle T matrix. Therefore, besides the width, the shift of spectral lines may be calculated also, avoiding an often-used cutoff procedure for strong collisions. As an example, shift and width of the hydrogen Lyman-\ensuremath{\alpha} line have been calculated.

DOI
10.1103/physreve.48.500

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Contributions of strong electron-atom collisions to shift and width of spectral lines are treated via partial summation of the three-particle T matrix. Therefore, besides the width, the shift of spectral lines may be calculated also, avoiding an often-used cutoff procedure for strong collisions. As an example, shift and width of the hydrogen Lyman-\ensuremath{\alpha} line have been calculated.
The broadening of spectral lines due to dipole-dipole interactions with ground-state atoms of the same element is calculated with the impact and classical path approximations. Summation over all contributing intermediate states accounts for the multiplicity of the levels involved and results in a width proportional to the geometrical mean of absorption and emission oscillator strengths. Higher multipole interactions are shown to be almost always negligible, and for Lyman-$\ensuremath{\alpha}$ the iterated solution of the time-dependent Schr\"odinger equation describing the collisions is extended to fourth order. Estimated errors of its calculated width and of the widths of other lines are about 5% in the validity regime of the impact approximation, apart from any uncertainties in oscillator strengths and statistical weight factors.
The contribution from electron scattering to the width and shift of the ${\mathrm{H}}_{\mathrm{\ensuremath{\alpha}}}$ and ${\mathrm{Ly}}_{\mathrm{\ensuremath{\beta}}}$ lines of neutral hydrogen is evaluated. Elements of the S matrix for electron-atom scattering calculations are obtained from close-coupling calculations including pseudostates, either of the variational or the optical potential type. The convergence of sums over angular-momentum variables is discussed. Results are compared with some other calculations and with experiment where possible.
In this paper general expressions for the width and shift of atomic lines produced by fast electron collisions are obtained. We use the recent quantum-mechanical theories developed to explain the pressure line shape in the impact approximation. Only isolated and Lorentzian lines are analyzed. The calculations are performed by expanding the scattering matrix up to the second Born approximation. The contributions of both elastic and inelastic virtual collisions are calculated. Degenerate and nondegenerate atomic states are considered.
The theory of line width due to dissipative interactions, such as collisions, is examined for the case of weakly coupled systems (weak collisions). It is shown that the apparent paradox that the width of the energy of the total system is of the order of Avogadro's number is resolved by a substraction procedure. The width of a spectral line is the difference in widths of the two macroscopic states before and after the transition. This should be contrasted to the case of natural line width where the width of the line is the sum of the widths of the two states involved. The physical reason for the difference in sign is discussed.
The SSS matrices for Stark broadening of the n=1n=1n=1 and n=2n=2n=2 levels of hydrogen based on the straight-line classical-path model are calculated numerically. The interaction terms (excluding exchange) are included to all orders, and time ordering of the operators in the SSS matrix is retained. The resultant values for the impact-broadening operator $\ensuremath{\Phi}$ are presented. These results are compared with previous approximations based on the same model. The effect of the present calculations on the center and near wings of the Lyman-$\ensuremath{\alpha}$ line profile is considered.
A universal formula is derived for the spectral line profile of atoms. It describes the whole spectrum, including collisional, intermediate, and quasistatic frequency ranges in the case when optical collisions take place with impurity particles in a strong electromagnetic field which influences the collision dynamics. A new physical effect is predicted: it is manifested by a dependence of the collisional shift of an absorption (stimulated emission) line profile on the intensity of an electromagnetic field.