Neutron Cross Section - Mean Free Path

Mean Free Path

The “mean free path” λ of a random particle is the average length between two interactions. The total length L that non perturbed particles travel during a time interval dt in a volume dV is simply the product of the length l covered by each particle during this time with the number of particles N in this volume:

Noting v the speed of the particles and n is the number of particles per unit volume:

It follows:

Using the definition of the neutron flux Φ

It follows:

This average length L is however valid only for unperturbed particles. To account for the interactions, L is divided by the total number of reactions R to obtain the average length between each collision λ:

From #Microscopic versus macroscopic cross section:

It follows:

where λ is the mean free path and Σ is the macroscopic cross section.