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Classical differential cross section = MACRO-m3c-diff

Scattering events can be described in terms of total cross sections [Compare with the total cross section described elsewhere (link type: `compared'; target: a macroscopic module)], differential cross sections or double differential cross sections [Compare with the double differential cross section described elsewhere (link type: `compared'; target: a macroscopic module)] Cross sections contain all information about momentum, energy (electronic, vibrational and rotational) and angular momentum transfer.

The differential cross section $d \sigma_p$ is defined as the number of events of a particular type p per unit of time, divided by the total flux F, where F is the number of particles crossing a unit of transverse area per unit of time.

For the process of elastic scattering sketched in figure MACRO-m3c-diff-F1, the differential cross section per unit solid angle is given by  
[unfold details]

\begin{displaymath}
\big( \frac{d \sigma}{d \Omega} \big)_{el} = \Sigma_{b_i} \frac{b}{\sin \theta} \vert\frac{db}{d \theta}\vert,
\end{displaymath}
where $\theta$ is the angle over which the particle incoming with an impact parameter b is scattered.

Thus the differential cross section can be calculated if the deflection function $\theta (b)$ is known.