  In this note we study Boltzmann's collision kernel for inverse power law
interactions $U_s(r)=1/r^{s-1}$ for $s>2$ in dimension $ d=3 $. We prove the
limit of the non-cutoff kernel to the hard-sphere kernel and give precise
asymptotic formulas of the singular layer near $\theta\simeq 0$ in the limit $
s\to \infty $. Consequently, we show that solutions to the homogeneous
Boltzmann equation converge to the respective solutions.
