Editing Cross section (physics) (section)

=== Elastic collision of two hard spheres ===
The following equations apply to two hard spheres that undergo a perfectly elastic collision.{{sfn | Taylor | 2005 | pp=564,574}} Let {{math|''R''}} and {{math|''r''}} denote the radii of the scattering center and scattered sphere, respectively. The differential cross section is
: <math>
\frac{d\sigma}{d\Omega} = \frac{R^2}{4},
</math>
and the total cross section is
: <math>
\sigma_\text{tot} = \pi \left(r + R\right)^2.
</math>
In other words, the total scattering cross section is equal to the area of the circle (with radius {{math|''r'' + ''R''}}) within which the center of mass of the incoming sphere has to arrive for it to be deflected.