E. W. Smith

Correlation effects in the theory of combined Doppler and pressure broadening. I - Classical theory

Abstract A classical Fourier amplitude theory of combined Doppler and pressure broadening in the impact approximation is developed which treats phase changes changes due ti translation and collision on an equal basis. Radiator motion is accounted for properly by including speed dependence in the collision frequency and velocity dependence in the distribution function for phase shifts and final velocities as the result of a collision. The resulting theory is shown to be equivalent to a previous kinetic equation formulation of the problem. The one-perturber and classical analogue of the quantum one-interacting-level approximations are derived. In the latter case, a simple expression for the line shape in terms of speed dependent width and shift functions is obtained without approximation. Correlation effects are investigated by means of model speed dependent width and shift functions calculated for an inverse power interaction using straight line trajectories. The model shows no departure from a Voigt profile for the r -3 interaction and for the r -6 and r -12 interactions the resulting profile is narrower in the core than the Voigt and in general asymmetric. Analysis of correlated profiles as Voigt profiles is shown under some conditions to lead to non-linear density dependence in the width and shifts resulting in extra- polation anomalies and to significant errors in temperatures inferred from Doppler widths. Results are compared with previous work.

Absorption and dispersion in the O2 microwave spectrum at atmospheric pressures

Calculations are performed for absorption and phase dispersion at various frequencies within the 60 GHz band of O2 from low pressures where the spectral lines are isolated, to atmospheric pressures where they merge to form a continuum band. A perturbation theory proposed by Rosenkranz was tested and found to be valid for pressures up to 100 kPa (1 atm). The ’’line coupling coefficients’’, which describe the transfer of excitation from one radiating state to another, are also studied and various methods for evaluating these coefficients are analyzed and compared with experimental data. It is found that dispersion measurements are extremely sensitive to these coefficients and an experimental procedure for systematically measuring them is outlined; it is shown that such measurements can provide a very sensitive test for theoretical calculations of inelastic transition amplitudes.

A semiclassical theory for spectral line broadening in molecules

A semiclassical S‐matrix theory is developed and applied to spectral line broadening in linear molecules perturbed by atoms. This theory uses curved classical trajectories determined by the isotropic part of the atom–molecule interaction and the S‐matrix is treated to all orders in the interaction. Numerical calculations can be made rather easily even for high quantum numbers. The theory is least accurate for very low quantum numbers, but even then calculations agree to within 10% with close coupling results where comparisons could be made. Comparisons were also made with other theoretical approaches using model potentials and with experiment using ab initio potential surfaces.

The Broadening of He I lines including ion dynamic corrections, with application to λ4471Å☆

Abstract A theory is developed for the broadening of He I lines with forbidden components which is valid at low densities (where the forbidden line is reasonably well isolated). This theory takes into account the effects of dynamic ion broadening. Application to λ4471A gives good agreement with experiment and with a recent calculation of Lee; reasons for agreement with Lee are discussed in detail. Comprehensive tables for 4471A are presented. These have been extended further into the line wings than previous tabulations. Static ion theory is found to be adequate for densities greater than ∼ 5 × 10 15 cm −3 . A simple numerical profile for allowed lines, taking into account dynamic ion effects, is also presented.

Experimental studies of mercury molecules

Optically excited fluorescence spectra in pure mercury vapor have been studied over the spectral range 240–600 nm for temperatures between 400–1000 K and densities between 5×1016–2×1019 cm−3. Absorption measurements were made over the spectral range 253–334 nm, and both structured and continuum bands were observed. Several types of two photon experiments were also performed in order to probe the excited states of the mercury dimer. In addition, the mercury spectrum from mercury vapor–noble gas mixtures has also been studied for noble gas pressures up to 1 atm.

HYDROGEN STARK BROADENING CALCULATIONS WITH THE UNIFIED CLASSICAL PATH THEORY

Abstract The unified theory has been generalized for the case of upper and lower state interaction by introducing a more compact tetradic notation. The general result is then applied to the Stark broadening of hydrogen. The thermal average of the time development operator for upper and lower state interaction is presented. Except for the time ordering it contains the effect of finite interaction time between the radiator and perturbers to all orders, thus avoiding a Lewis type cutoff. A simple technique for evaluating the Fourier transform of the thermal average has been developed. The final calculations based on the unified theory and on the one-electron theory are compared with measurements in the high and low electron density regime. The unified theory calculations cover the entire line profile from the line center to the static wing and the simpler one-electron theory calculations provide the line intensities only in the line wings.

A theoretical analysis of mercury molecules

A theoretical analysis of experimental observations on bound–free electronic transitions in mercury molecules is presented. Potential curves and A values are derived for these transitions and the possibility of emission from a mercury trimer is also discussed briefly. These data are then used to produce a simple model for an optically pumped 335 nm mercury laser. A table is given which predicts the small signal gain at 335 nm as a function of temperature, density, and the excimer density in the vapor.

Unified Theory Calculations of Stark Broadened Hydrogen Lines Including Lower State Interactions

Report on calculations of hydrogen Stark broadening on the basis of the unified classical path theory which has been extended to include lower state interactions in the final line profile. A detailed comparison with experiments in the density range 10-13-10-17 cm-3 is given.

An impact theory for Doppler and pressure broadening—I. General theory

Abstract A quantum-mechanical impact theory for the combined effects of Doppler and pressure broadening is developed from quantum radiation theory. The results are compared with other semiclassical theories and certain simplifying approximations relevant to cases of experimental and theoretical interest are discussed.

Pressure broadening of the O2 microwave spectrum

The pressure broadened half‐widths of the 60 GHz microwave spectrum in O2 have been calculated for low pressures where the lines do not overlap. Both self‐broadening and foreign gas broadening by noble gases have been calculated using various semiempirical potential surfaces. Agreement with experimental results is quite good. Differences with various other theoretical calculations are discussed.