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
0nσdx
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
0e
-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
-24cm
2. This unusually-named
unit has its origin in an
experiment which had an
expected value for cross-section on the order of 10
-26cm
2, but which yielded a cross-section of order 10
-24cm
2, as big as the
metaphorical "side of a
barn".