Cross section

1.

A section formed by a plane cutting through an object, usually at right angles to an axis.

2.

(Physics) A measure of the probability of an encounter between particles that will result in the occurrence of a particular atomic or nuclear reaction.

3.

(Statistics) A sample ment to be representative of a whole population.

In physics, a measure of the likelihood of a specific interaction between two or more particles. Cross-sections have the units of area, and are usually represented by the greek letter sigma (σ).

The simplest and most common usage for cross-section is to calculate the probability of interaction between a fast-moving incident particle and a mass of slow-moving target particles. In this case, the probability for an individual particle to undergo the specified interaction in a small distance dx is simply nσdx, where n is the number of target particles per unit volume. If there are N₀ particles in the incident beam, then N₀nσdx incident particles will undergo the interaction. Now, if an incident particle is effectively removed from the incident beam by undergoing the specified interaction, a simple differential equation results, and we see that the number of particles remaining in the incident beam after having travelled a distance x is N=N₀e^-nσx. This is, of course, similar to the exponential decay law for radioisotopes, and we thus define a quantity analogous to the mean life: the mean free path λ=(nσ)^-1.

Cross-sections are in very common use in particle and nuclear physics, where the standard unit is the barn (b), defined as 10^-24cm². This unusually-named unit has its origin in an experiment which had an expected value for cross-section on the order of 10^-26cm², but which yielded a cross-section of order 10^-24cm², as big as the metaphorical "side of a barn".