In a Rutherford Scattering experiment the impact parameter $b$ can be easily related to the scattering cross section. A theoretical relation between the impact parameter $b$ (or the differential scattering cross section $(d\sigma)/(d\theta)$ and scattering angle has been deduced by Rutherford in the form $b=f(\theta)$ or $(d\sigma)/(d\theta)=f(\theta)$. This relation can be deduced starting from the conservation laws of momentum and energy for the incoming charged particles.
a) Why in the Rutherford experiments the metal sheet is thin?
b) What conclusion can be deduced from the fact that the theoretical is experimentally verified in the majority of cases?
c) Experimentally for $\alpha$ particles scattered by $Au$ nuclei, the above relation $b=f(\theta)$ is not true for small angles $\theta$. How do you explain this?
d) Under which other conditions the above relation $b=f(\theta)$ is not verified?
a) The metallic sheet is thin to minimize the probability of multiple scattering.
b) This is a proof that the mass and charge of the nucleus is concentrated in a very small volume and also a proof of the fact that the interaction between the incoming (projectile) particles and the target nuclei is electrostatic (Coulomb type interaction) for moderate kinetic energies.
c) For small scattering angles the impact parameter has large values and because of this the nucleus charge is shielded by the atom electrons.
d) The relation $b=f(\theta)$ fails also for big incoming kinetic energies when nuclear interaction forces can become significant (the incoming $\alpha$ particle “enters” the target $Au$ nuclei).