  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.
