# What does it mean that the Rutherford's cross section is infinite?

I'm studying elastic scattering and I read that the Rutherford's differential cross section is defined as:

$$\left( \frac{d \sigma}{d \Omega} \right)_R = \frac{Z^2}{4} r_o^2 z^2 \frac{(m_ec / \beta p)^2}{\sin^4(\theta/2)}$$

And the total cross section is defined as:

$$\sigma_T = \int_0^{2 \pi} d \phi \int_0^\pi \frac{d \sigma}{d \Omega} \sin \theta d \theta$$

For the Rutherford's cross section the total cross section equals infinity ($(\sigma_T)_R = \infty$).

What does this mean physically? The cross section is the probability of interaction per unit of surface. Does this mean that we are considering as an interaction even when the particle continues its path as if nothing happens (i.e. $\theta=0$)?