cross section A convenient way to express the probability of interaction between a projectile and a target particle. A large cross section implies a large probability of interaction. The interaction cross section of a target particle varies with the nature of physical process involved and with energy of incident particle. It may be greater or less than the geometrical cross section of the particle.
Suppose we have a slab of some material whose area is A and whose thickness is dx. If the material contains n atoms per unit volume, there are a total of n Adx atoms in the slab. If each nucleus has an interaction cross section s , for some particle interaction, the aggregate cross section of all the nuclei in the slab is s nA dx. If N is the number of incident particles out of which dN interacts with the nuclei of the slab, then
If the slab is of finite thickness x, then by integrating (c30)
N = No exp [-ns x] (d31)
where No = number of incident particles, N = number of particles which emerge from the slab of thickness x. The cross section has a dimension of area. It can be expressed in m2. More commonly barn* is used as a unit.