We have observed thermalization by elastic collisions of magnetically trapp
ed metastable helium atoms. Our method directly samples the reconstruction
of a thermal energy distribution after the application of a RF knife. The r
elaxation time of our sample toward equilibrium gives an elastic collision
rate constant of alpha similar to5 x 10(-9) cm(3)/s at a temperature of 1 m
K. This value is close to the unitarity limit.