Collision kernel and interatomic potential

We present a detailed study of the influence of the form and strength of the interatomic potential on the one-dimensional elastic collision kernel W($v_z^{\mathcal{’}}$,$v_z$), a quantity of interest in the study of the effects of velocity-changing collisions on laser spectroscopic line shapes. We find that the absolute magnitudes of collision kernels are very sensitive while normalized collision kernels are moderately sensitive to the potential form used. This indicates the importance of employing realistic interatomic potentials and reliable differential cross sections in the accurate determination of collision kernels. For the case of the Lennard-Jones (12,6) potential, we found a universal semiclassical Lennard-Jones (SCLJ) analytical model function, which is the combination of a semiclassical expression for small to medium scattering angles and a classical expression for large scattering angles, capable of providing correct average quantum-mechanical behaviors of differential cross sections for all scattering angles. This greatly facilitates the (often time-consuming) numerical evaluation of the collision kernel integrals and exhibits the correct collision kernel line profiles. It is found that the SCLJ collision kernel consists of a strongly peaked forward diffractive zone (small-angle scatterings), reflecting the nature of velocity resonance, as well as a broad wing region due to large-angle scatterings. Ambiguities associated with the drawbacks of the hard-sphere model, the small-angle classical long-range model, and the classical Lennard-Jones model are analyzed and clarified. While our analysis is confined to the Na-Ar and Ar-Ar systems, the conclusions derived from this study are general and are expected to be also applicable to other systems where both the long- and short-range interactions play essential roles in velocity-changing collisions.