Theory of evaporative cooling with energy-dependent elastic scattering cross section and application to metastable helium

The kinetic theory of evaporative cooling developed by Luiten [Phys. Rev. A 53, 381 (1996)] is extended to include the dependence of the elastic scattering cross section on collision energy. We introduce a simple approximation by which the transition range between the low-temperature limit and the unitarity limit is described as well. Applying the modified theory to our measurements on evaporative cooling of metastable helium, we find a scattering length \a\=10(5) nm.