An isolated line-shape model based on the Keilson and Storer function for velocity changes. I. Theoretical approaches

This paper presents new results for the modeling of isolated line shapes from the Doppler to the collisional regime, thus including the effects of confinement (Dicke narrowing) and of the speed dependence of collisional parameters. They are obtained within a classical description of the time evolution of the autocorrelation function of the optical transition moment, combined with the use of the Keilson and Storer model for the changes in the radiator translational velocity. A purely numerical solution to the subsequent differential equations, which uses discretized grids for the radiating-molecule velocity vector, is first described. An alternative approach, using projections onto generalized Laguerre polynomials (for the velocity modulus) and spherical harmonics (for the velocity orientation), is also presented. A first test of these approaches is made in the particular case of the Q(1) Raman line of the fundamental band of pure H(2) at room temperature (others will be presented in paper II). It is shown that the two models lead to exactly the same results, as expected, and to satisfactory agreement with measured values of the linewidth at various densities.