# regarding the infinite cross section in Rutherford scattering

The differential cross section of Rutherford scattering blows as $\theta\rightarrow 0$. People express this fact as "The Coulombic potential is of long range". But I am seeing the opposite: $\theta \rightarrow 0$ is when the incident particle is not affected by the potential, and therefore a blow when $\theta \rightarrow 0$ means short range potential.

That was first. Secondly, I cannot see how the differential cross section is related to (some kind) of probabilities when infinities are involved.

• It is a well known fact that for Coulomb scattering the total scattering cross-section is infinite. Since the optical theorem connects the total cross-section to the imaginary part of the forward (θ=0) scattering amplitude the latter also becomes infinite. You can find more information on wikipedia, search for optical theorem and Coulomb scattering. May 3, 2014 at 17:11
• Thank you, but that doesn't reconcile the difficulties I have which are described in the question. May 3, 2014 at 17:21
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