\section{The collision integrals}

To extend the implementation of the Enskog solutions to more advanced potential models, the collision integrals must be evaluated for those potentials. This requires a combination of numerical root solving and integration that will be described in this section. The final objective is to evaluate the integral

\begin{equation}
    W_{\ell, r} = 2 \int_0^\infty \int_0^\infty \exp{\lrp-g^2\rrp} g^{2r + 3} \lsp 1 - \cos^\ell\lrp\chi\lrp g, b\rrp\rrp\rsp \pfrac{b}{\sigma} \d \pfrac{b}{\sigma} \d g
    \label{eq:kin_dimless_collision_integral}
\end{equation}

for an arbitrary spherically symmetric potential.

%\input{kinetic_gas/dynamics}

\input{kinetic_gas/numerics}
\input{kinetic_gas/validation}