Macroscopic cross-sections

Nuclear reactors are macroscopic media where neutrons are propagated. It is, therefore, worthwhile to define macroscopic entities characteristic of neutronic properties of the medium. We consider a homogeneous mixture of different nuclei i in number N. Let n_i the number of nuclei i per unit volume (usually cm³). Let $\sigma_{i}^{(\alpha)}$ be the cross-section of type $(\alpha)$( for example fission, absorption, capture or scattering) of nucleus i. The macroscopic cross-section is defined as:

$$\Sigma^{(\alpha)}(cm^{-1})\ =10^{-24}\ \overset{N}{\sum_{i}} n_{i}\sigma _{i}^{(\alpha)}(barns)$$ (4.6)

The mean free path for reaction $\alpha$ is simply

$$\Lambda^{(\alpha)}=\frac{1}{\Sigma^{(\alpha)}}$$ (4.7)