We define solid angle, flux and the scattering angle and flux and cross section are defined.
The definition of cross section is formulated in probabilistic terms. This interpretation turns out to be useful for interpretation of the cross section as an area, and also for quantum mechanical problems.
An important class of two particle scattering is when the forces are central, {\it i.e.} the potential depends on the separation \(\vec r_1-\vec r_2\) between the particles: \[ V(\vec r_1, \vec r_2)= V(\vec r_1-\vec r_2).\] The two particle elastic scattering problem becomes equivalent to scattering of a particle, of reduced mass, from a potential \(V(\vec r)\), with \(\vec r= \vec r_1-\vec r_2,\) in the centre of mass frame.
Rutherford formula\begin{eqnarray}\sigma(\theta)&=& \frac{1}{4} \left( \frac{k}{2E} \right)^{2} \frac{1}{\sin^{4} \left(\frac{\theta}{2} \right)}\end{eqnarray}for Coulomb scattering is derived in classical echanics.
The cross section is measured by measuring the intensity of beam, scattered from a thin foil, in the forward direction as a function of thickness of the foil.
It is shown that the total cross section from a hard sphere of radius \(R\) is \(\pi R^2\)
A formula for differential cross section is derived making use of relation of the scattering angle with the impact parameter.
For scattering of particles, we explain which area is scattering cross section.
The definition of scattering cross section for waves is given and the interpretation as an area is explained.
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