Consider a general inverse-power interparticle force of the form
$$
F(r)=\frac{K}{r^p}
$$
where $K$ is a constant and $p$ is a positive integer number.
(a) Determine expressions for the scattering angle $\chi$, for the differential scattering cross section $\sigma(\chi, \epsilon)$, for the total scattering cross section $\sigma_t$, and for the momentum transfer cross section $\sigma_m$.
(b) Calculate $\chi, \sigma(\chi, \epsilon), \sigma_t$, and $\sigma_m$ for the case of Maxwell molecules, for which $p=5$.