# Neutron Beam Attenuation

When a neutron beam hits the material of a sample, the beam intensity will be exponentially damped with the path length (l) the beam travels in the material

*I* = *I*_{0}* • exp(-μ•I)*

In the relation above, I_{0} is the intensity of the incoming neutron beam when it hits the sample and μ is the attenuation coefficient of the sample material.

The attenuation coefficient is a measure of how much of the neutron beam a certain material will stop per unit of length of the material the beam passes through. The attenuation coefficient can be calculated as the sum of all neutron interaction cross-sections in the material weighted by the density of the material as described mathematically in the relation below.

Here, μ is the attenuation coefficient, N_{i} is the number of a given chemical element (isotope) i in the sample volume V, n_{i} is the atomic density N_{i}/V, and σi is the cross-section of the given element (isotope).

In parts of the sample where the attenuation coefficient is high, less intensity will be transmitted. Thus if we shine a neutron beam on the sample and record the transmitted intensity the parts of the sample containing elements with high neutron cross-sections would be dark on the image since the attenuation coefficient would be high, while elements with a low cross-section would be brighter on the image since more neutrons can pass through there.

When we are talking about the cross-section in neutron radiography or imaging we are in fact referring to the total cross-section which covers many types of neutron interaction which each varies between chemical elements (isotopes) in the samples. The relevant interactions for thermalized neutrons are classified as either absorption or scattering. The total attenuation coefficient for a neutron ray is the sum of attenuation coefficients for each type of interaction

*μ = μ _{absorption}*+

*μ*

_{scattering}