= Angular exchange for elastic collisions
{title2=$(C,r,\omega,\sigma)\leftrightarrow(C,r,\sigma,\omega)$}
Write incoming relative velocity as $r\omega$ and outgoing relative velocity as $r\sigma$. For isotropic scattering, the product measure $dC\,r^2dr\,d\omega\,d\sigma$ is invariant under exchanging the two angular variables. This gives the pre/post-collision weak identities. Keeping $\sigma$ fixed and sending only the velocities to the outgoing pair is not invertible: that map discards the incoming angular direction.
Back to article page
