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 N

_{0} particles in the

incident beam, then N

_{0}nσdx

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=N

_{0}e

^{-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

^{-24}cm

^{2}. This unusually-named

unit has its origin in an

experiment which had an

expected value for cross-section on the order of 10

^{-26}cm

^{2}, but which yielded a cross-section of order 10

^{-24}cm

^{2}, as big as the

metaphorical "side of a

barn".