Rutherford Scattering Cross-Section

(3.83) |

Assuming that the scattering is azimuthally symmetric (i.e., symmetric in ), we can write . Now, the probability per unit time of a collision having an impact parameter in the range to is

(3.84) |

Furthermore, we can write

(3.85) |

provided that and are related according to the two-particle scattering law, Equation (3.82). It follows that

Equation (3.82) yields

Finally, Equations (3.82), (3.86), and (3.87) can be combined to give the so-called

It is immediately apparent, from the previous formula, that two-particle Coulomb collisions are dominated by small-angle (i.e., small ) scattering events.