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Neutron Cross-Section

The neutron cross-section of a chemical element refers to the likelihood that a neutron will interact with the chemical element. The neutron interaction with most elements is weak, meaning that most of the beam, but not all, will pass straight through a sample which is typically a solid object composed of one or more chemical elements. The neutrons which do not pass straight through the sample interact with the material in various ways with a probability described by the cross-section for each type of interaction. For each interaction, the larger the cross-section, the more neutrons will be removed from the direct beam.

Unlike the X-ray cross-sections of elements which are largely proportional to the atomic number of the element, neutron cross sections do not follow a similar simple relation. For this reason, it turns out that we can use neutrons to distinguish neighboring atoms in the periodic table or even isotopes of the same chemical element! This is one of the advantages of using neutrons in an experiment. 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 interactions each varying between chemical elements (isotopes) in the samples.

Below we describe the types of interaction (for which corresponding cross-sections can be described by theoretical models) which are relevant to neutron experiments on condensed matter.

At the top is an illustration showing the comparison between neutron beam and X-ray cross-sections for the same elements, which can be very different in size. For example, neutron beams have a very large cross-section for hydrogen, but with x-ray, the cross-section of hydrogen becomes very small. The same goes for lithium and chlorine, among others. The X-ray cross-section, usually scales with the atomic number of the element, meaning that it is large for copper and extremely large for lead, compared to the neutron beam cross sections. Deuterium, Carbon and Aluminium are approximately the same. At the bottom is an illustration showing the comparison between neutron beam and x-ray cross-sections for the same elements as mentioned earlier. In this illustration the cross-sections are divided based on their interaction. For example, while the coherent scattering cross section is very small, the incoherent one is much larger for a neutron beam. The absorption cross section is negligible for most elements shown, but large for lithium and chlorine.

Figure 1 a; Neutrons and X-ray total cross-sections for different elements. b; Partial neutron cross-section for different elements. Each of the partial cross-sections represent the chance for a specific interaction between the element and a neutron

Absorption

When a neutron passes through an object there is a chance that one of the atoms in the object will absorb it. This chance is called the absorption cross-section or capturing cross-section. When a neutron is absorbed by an atom it is incorporated into the atom nucleus. Depending on the isotope that captured it, this either creates a new stable isotope or an unstable isotope which then decays into a stable isotope over time by emitting other particles in the process. Some elements like for example Boron has an enormous absorption cross-section and is therefore an excellent choice to incorporate in neutron shielding.

Scattering

When a neutron beam passes through an object there is a chance that the flight direction of some neutrons will be changed. This is called scattering since neutrons in a beam passing through the object are scattered into one or several new directions. The chance of this happening is expressed by the total neutron scattering cross-section which is the sum of the coherent and incoherent scattering cross-sections as described below. The neutron can interact both with the nucleus of an atom in the object – we call that nuclear scattering. But since the neutron has a spin it can also be scattered by the magnetic moment of atoms in the object and we call that magnetic scattering. Below we will only describe nuclear scattering In most neutron scattering experiments a large portion of the neutron beam is transmitted and not scattered.

Coherent Scattering

If the object contains ordered atoms in repeated patterns, some of the neutrons are scattered coherently, which means they create interference patterns with constructive interference in particular scattering directions. The scattering direction depends on the (average) distances between the atoms (or planes of atoms) in the sample, thus coherent scattering carries structural information about the sample. Some of the coherently scattered neutrons will have transferred or received energy when scattering from the sample - a process which is called inelastic coherent neutron scattering.

Incoherent Scattering

“Incoherent scattering of neutrons result from randomness of the atoms in the object we study. Even in a sample containing only a single isotope there will can be variations over time of the nuclear spin moment direction in each atom which will give incoherent scattering. Furthermore the randomness in a composite sample can be due to random chemical or isotopic variations (impurities) or random variations of atomic distances in the object. The incoherent scattering cross-section is the likelihood that the neutron will be scattered by some randomness in the sample. The effect of the incoherent scattering cross-section is that of the neutrons will be scattered from the object in a random direction without interference. Some of the incoherently scattered neutrons will have transferred or received energy when scattering from the sample - a process which is called inelastic incoherent neutron scattering. In many experiments the incoherent scattering is just background noise in the experiment, but in some experiments like QENS, the incoherent scattering carries useful information about the sample.

Referred from:

Article
Neutron Transmission