cross section

A use of the term cross section, in the physics of particles, is a representation of the probability of an interaction between some particle-of-interest with other particles passing through the vicinity. The probability is represented by an area (the cross section), surrounding the particle-of-interest, chosen such that the probability of some other particle passing through that given area is identical to the probability of some other particle interacting with the particle-of-interest. Portions of physics where the concept is used include nuclear physics (fission and fusion, such as the power generation within stars), in radiative transfer, and in the physics of gases as interacting particles (kinetic theory of gases). The term collision cross section is sometimes used when the interactions are thought of as collisions between particles.

In the mechanics of small particles (quantum mechanics), particles passing at a certain distance of each other may or may not interact, an interaction having some probability whose calculation is the business of quantum mechanics. If a specific region were selected around one particle that includes nearly all points at which another passing particle might interact (so the probability of interacting with a particle passing outside this region is virtually zero), then the cross section is a smaller region sized so the ratio of region sizes matches the probability of an interaction of a particle passing through the larger region. It is a convenient and simplifying method of modeling how many interactions will take place, which is possible if the complicated quantum-mechanical analysis yields a single probability for the interaction (or some relatively simple function).

Given such a cross section, the path of a moving particle can be viewed as a straight, round, tube-shaped volume, whose calculated volume along with the density of the material allows calculation of properties of interest such as how long the particle is likely to move before an interaction (the mean free path).

The differential cross section of some type of particle-scattering incorporates information about the effects of the scattering. It is an indication scattering probability (e.g., of Compton scattering) that a particle will be scattered (by another particle) to a direction within a given solid angle, consisting of a ratio between the rate of change of this cross section with the rate of change of the solid angle into which a particle is scattered. This ratio is typically a function of a number of parameters including the scattering angle (angle between the scattered particle's initial and final trajectory) and the impact parameter (closest distance reached between the centers of the two particles given their initial trajectories).