Unified theories of the pressure broadening and shift of spectral lines. I. General formulation for multipole interactions

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Abstract
General expressions are presented for the line profile produced by an emitting atom embedded in a sea of randomly distributed identical perturbers, on the assumption that the interaction between the emitter and a perturber is of the type 1/Rp, where p>or=3. The motion of each perturber relative to the emitter is treated classically and the trajectory of the perturber is assumed to be a straight line. Results are given for the case in which all emitter-perturber interactions are assumed to be additive; when the emitter is subject to the linear Stark effect, additional results are obtained that do not depend on the assumption of scalar additivity. The profile can be expressed in terms of the Fourier transform of a 'universal' function of a single dimensionless variable that may be evaluated once and for all, since it does not depend explicitly on any particular parameters associated with the spectral line or with the perturbing gas. The properties of this function are studied in detail, and for p>or=4, it is shown that it may be represented very accurately by a semi-empirical analytic function of relatively simple form. It is also shown that certain features of the line profile can depend appreciably on whether or not the correct average over a Maxwellian distribution of velocities of the perturbers is carried out. The use of the semi-empirical universal functions means that profiles can be generated extremely quickly for a particular case, and these can be used as a starting point for a more detailed assessment of the additional physical effects involved that are not included in the present model. Explicit results are given for the cases p=4 and 5; these are relevant to the analysis of the broadening of atomic and molecular lines by molecules.

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