Dicke narrowing and collisional broadening of spectral lines in dilute molecular gases

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Abstract
A unified description of pressure broadening and Dicke or diffusional narrowing of spectral lines is presented from the point of view of a quantum mechanical kinetic theory. The present description of Dicke narrowing includes the correlation between collision‐induced changes in the internal energy levels and the molecular velocity. The spectral line shape function is expressed in terms of relaxation coefficients which are directly proportional to generalized collision cross sections obtained from a linearized kinetic collision (super)operator. Liouville space techniques are utilized to obtain exact expressions for the collision cross sections in terms of S‐matrix elements in the total‐J representation. These generalized cross sections are then simplified through the introduction of the coupled states and the infinite‐order sudden approximations. The description of the generalized cross sections is valid for any linear molecule in a multiplet‐Σ electronic state, infinitely dilute in a bath of structureless perturbers. Using the Hund’s case (b) coupling scheme for the molecular wave function, the equivalence of the scattering dynamics for paramagnetic and diamagnetic molecules is emphasized. All dependence of the generalized collision cross sections on the nonzero electronic spin of open shell molecules is contained inWigner 6‐j symbols, which multiply spin‐independent S‐matrix elements. Explicit expressions for a diamagnetic molecule in a 1Σ electronic state are also presented. Connections between the present theory and earlier theoretical treatments of pressure broadening are made.