Cross section

There are two types of cross section: 'microscopic' and 'macroscopic'.

Microscopic

• assume the neutron flux f is the total number of neutrons passing through a unit area which is normal to their direction of travel per second
  

  f = nv

  n per unit volume v is the neutron speed

• If there is a total number of atoms in a target of N, then the interaction rate, F will be proportional to N and proportional to f.
  
  F µ f N, or
  F = s f N
  
  where the proportionality factor s is the microscopic cross section.

Macroscopic

This is the total cross section of all the nuclei in a unit volume of material (S).

S = s × (number of nuclei per unit volume) m^-1

S = 1 / l

where l is the mean free path - the average distance a neutron (or other particle) travels without interacting.