# Mott scattering cross section of an electron by a point spinless particle

In Weinberg QFT volume 2 p.273, the equation (20.6.4) says that the Mott scattering cross section for an electron by a point spinless particle is given by: $$(\frac{d\sigma}{d\Omega})_{Mott}=\frac{e^4}{4E_e^2} \frac{cos^2(\theta/2)}{\sin^4(\theta/2)}$$.

Here, $$\pi-\theta$$ is the scattering angle of the electron in the center of mass frame.

However, all other textbooks say the Mott scattering cross section is :$$\frac{\alpha^2}{4E_e^2} \frac{cos^2(\theta/2)}{\sin^4(\theta/2)}$$ where $$\alpha =\frac{e^2}{4\pi}$$ is the fine structure constant.

Is the Weinberg book wrong? I am quite confused...

$$\alpha=\frac{e^2}{\hbar c}.$$
Your definition of $$\alpha$$ is for natural units in which $$\epsilon_0$$ rather than $$4\pi\epsilon_0$$ is 1.