Continuous Versus Average Cross Section
Cross sections depend strongly on the incoming particle speed. In the case of a beam with multiple particle speeds, the reaction rate R is integrated over the whole range of energy:
Where σ(E) is the continuous cross section, Φ(E) the differential flux and N the target atom density.
In order to obtain a formulation equivalent to the mono energetic case, an average cross section is defined:
Where Φ= Φ(E) dE is the integral flux.
Using the definition of the integral flux Φ and the average cross section σ, the same formulation as before is found:
Read more about this topic: Neutron Cross Section
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