Cusp Kernels for Velocity-Changing Collisions

TL;DR

This paper introduces the cusp kernel, an analytical model for velocity-changing collisions in optically pumped atoms, which improves upon existing models by better matching real collision kernels and being easier to invert.

Contribution

The paper presents the cusp kernel, a new analytical model for velocity-changing collisions that is more accurate and easier to invert than the traditional Keilson-Storer kernel.

Findings

Cusp kernels better match measured collision kernels.

Cusp kernels are easier to invert for steady-state distributions.

Superpositions of cusp kernels enhance modeling flexibility.

Abstract

We introduce an analytical kernel, the "cusp" kernel, to model the effects of velocity-changing collisions on optically pumped atoms in low-pressure buffer gases. Like the widely used Keilson-Storer kernel [J. Keilson and J. E. Storer, Q. Appl. Math. 10, 243 (1952)], cusp kernels are characterized by a single parameter and preserve a Maxwellian velocity distribution. Cusp kernels and their superpositions are more useful than Keilson-Storer kernels, because they are more similar to real kernels inferred from measurements or theory and are easier to invert to find steady-state velocity distributions.