Reaction Rates

If the total path length of all the neutrons in a cubic centimeter in a second is known, (neutron flux ( Φ)), and if the probability of having an interaction per centimeter path length is also known (macroscopic cross section (∑)), multiply them together to get the number of interactions taking place in that cubic centimeter in one second. This value is known as the reaction rate and is denoted by the symbol R. The reaction rate can be calculated by the equation shown below.

(1-1)

where:
R = reaction rate (reactions/sec)
1 = neutron flux (neutrons/cm²-sec)
∑ = macroscopic cross section (cm^-1)

Substituting the fact that ∑ = N ) into Equation (1-1) yields the equation below.

where:
σ = microscopic cross section (cm²)
N = atom density (atoms/cm³)

The reaction rate calculated will depend on which macroscopic cross section is used in the calculation. Normally, the reaction rate of greatest interest is the fission reaction rate.