I am currently reading myself into the topic of scattering experiments and (differential cross sections) and stumbled across the following problem which I really dont know how to solve (this is $\textbf{not}$ any kind of homework assignement, I just want to solve this problem :D).
An $\alpha$-particle with energy $E_\alpha=7\,$MeV scatters at an Al-foil. Now I have to show that the integrated cross section $\sigma_{int}(\theta,180^\circ)=\int_0^{2\pi}\int_\theta^{\pi}\frac{d\sigma}{d\Omega}\sin\theta'd\theta'd\phi$ for a particle thats scattered in the range $[\theta,180^\circ]$ is given by
$$\sigma_{int}=\pi\left(\frac{Z_{Al}Z_\alpha\hbar c}{2E_\alpha}\right)^2 \cot^2\left(\frac{\theta}{2}\right).$$
To start things of I dont even know how to calculate the differential cross section in this case? Is this Rutherford-scattering?
Any help or advice is very much appreciated!