11.2: Some terminology for general scattering

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The incident flux (I) of particles with momentum \({\bf p}= \hbar {\bf k}\) is the number of incident particles crossing unit area perpendicular to the beam direction per unit time.

The scattered flux (S) of particles with momentum \({\bf p'} = \hbar {\bf k'}\), is the number of scattered particles scattered into the element of solid angle \(d\Omega\) about the direction \(\theta\), \(\phi\) per unit time per unit solid angle.

The differential cross section is the ratio of the scattered flux in direction \(\theta\), \(\phi\) to the incident flux.

\[\frac{d\sigma}{d\Omega} = S/I \nonumber\]

The total cross section is the ratio of the scattered flux in any direction to the incident flux.

\[\sigma_T = \int \int \frac{d\sigma}{d\Omega} \sin \theta d\theta d\phi \nonumber\]