# How to Work with Particle Scattering and Cross-section Equations

Quantum physicists use large particle accelerators to discover more about particle scattering on the subatomic level. You can think of a scattering experiment in terms of *particles in* and *particles out*. The following figure shows an example where particles are being sent in a stream from the left and interacting with a target; most of them continue on unscattered, but some particles interact with the target and scatter.

Those particles that do scatter do so at a particular angle in three dimensions — that is, you give the scattering angle as a solid angle,

The number of particles scattered into a specific

is proportional to a very important quantity in scattering theory: the differential cross section.

The *differential cross section* is given by

and it’s a measure of the number of particles per second scattered into

per incoming flux. The *incident flux*, J (also called the *current density*), is the number of incident particles per unit area per unit time. So

The differential cross section

has the dimensions of area, so calling it a cross section is appropriate. The cross section is sort of like the size of the bull’s eye when you’re aiming to scatter incident particles through a specific solid angle.

The *differential cross section* is the cross section for scattering to a specific solid angle. The *total cross section,*

is the cross section for scattering of any kind, through any angle. So if the differential cross section for scattering to a particular solid angle is like the bull’s eye, the total cross section corresponds to the whole target.

You can relate the total cross section to the differential cross section by integrating the following: