tupos, i think you've completely understood what it is that was asked.
I was curious to why the Rutherford cross section tends to infinity. I think we're all aware that the its not the complete picture, but i wanted to know why it broke down so catastrophically in the small angle region...
The Rutherford differential cross section \frac{d\sigma}{d\Omega} goes like
cosec(\vartheta)^4
which means at \vartheta=0 the differential cross section is infinite, which is ok.
My question is, given that the differential cross section is proportional to the probability per unit solid...