I was reviewing the following question.
"A key result of the α particle scattering experiment of Geiger and Marsden was that the number of particles scattered into a given angle was proportional to the thickness of the target. Explain why this shows that the scattering is of single atoms or nuclei,and not due to multiple scattering off many atoms."
The answer was given as We know that N(θ > 90) is proportional to the number of target nuclei and proportional to t, the thickness of the target. If multiple scattering was occurring our path would consist of a series of small angle scatterings due to the Coulomb field of the nucleus. On average the scattering will be small. For multiple interactions, it should be distributed as a Gaussian with mean 0 and width σ ∝ t. Increasing the thickness will only increase the number of small scattering which will not generally add but will also cancel each other. As a result the angular distribution will be a Gaussian with width proportional to √t which cannot explain the Geiger and Marsden observation.
I was fairly satisfied with this answer however there was one particular aspect I didn't understand which is in bold above. Coulomb collision and the inverse square law don't seem to give any specific satisfactory answers as to WHY small angle scatterings occur? So my question is, why does the coulomb force give small angle scattering?
I believe there is a fundamental piece of mathematics I am missing here. Any direction would be much appreciated.