# Interactions of Neutrons with Matter

Neutrons have zero electrical charges and cannot directly cause ionization. Neutrons ionize matter only indirectly. For example, when neutrons strike the hydrogen nuclei, proton radiation (fast protons) results. This reaction is known as scattering. Neutrons can also be absorbed. Most absorption reactions result in the loss of a neutron coupled with the production of one or more gamma rays since the resulting nucleus is usually unstable.

Neutrons are neutral particles. Therefore they travel in straight lines, deviating from their path only when they collide with a nucleus to be scattered into a new direction or absorbed. Neither the electrons surrounding (atomic electron cloud) a nucleus nor the electric field caused by a positively charged nucleus affect a neutron’s flight. In short, neutrons collide with nuclei, not with atoms. A very descriptive feature of the transmission of neutrons through bulk matter is the mean free path length (λ – lambda), which is the mean distance a neutron travels between interactions. It can be calculated from the following equation:

λ=1/Σ

Neutrons may interact with nuclei in one of the following ways:

## Types of Interactions of Neutrons with Matter

Elastic Scattering Reaction
Generally, a neutron scattering reaction occurs when a target nucleus emits a single neutron after a neutron-nucleus interaction. No energy is transferred into nuclear excitation in an elastic scattering reaction between a neutron and a target nucleus.
Inelastic Scattering Reaction
In an inelastic scattering reaction between a neutron and a target nucleus, some energy of the incident neutron is absorbed into the recoiling nucleus, and the nucleus remains in the excited state. Thus while momentum is conserved in an inelastic collision, the kinetic energy of the “system” is not conserved.
Neutron Absorption
The neutron absorption reaction is the most important type of reactions that take place in a nuclear reactor. The absorption reactions are reactions where the neutron is completely absorbed, and the compound nucleus is formed. This is a very important feature because the decay mode of such a compound nucleus does not depend on how the compound nucleus was formed. Therefore a variety of emissions or decays may follow. The most important absorption reactions are divided by the exit channel into two following reactions:

• Radiative Capture. Most absorption reactions result in the loss of a neutron coupled with the production of one or more gamma rays. This is referred to as a capture reaction, and it is denoted by σγ.
• Neutron-induced Fission Reaction. Some nuclei (fissionable nuclei) may undergo a fission event, leading to two or more fission fragments (nuclei of intermediate atomic weight) and a few neutrons. In a fissionable material, the neutron may be captured, or it may cause nuclear fission. For fissionable materials, we thus divide the absorption cross-section as σa = σγ + σf.
The neutron capture is one of the possible absorption reactions that may occur. In fact, for non-fissionable nuclei, it is the only possible absorption reaction. Capture reactions result in the loss of a neutron coupled with the production of one or more gamma rays. This capture reaction is also referred to as a radiative capture or (n, γ) reaction, and its cross-section is denoted by σγ.

The radiative capture is a reaction in which the incident neutron is completely absorbed, and the compound nucleus is formed. The compound nucleus then decays to its ground state by gamma emission. This process can occur at all incident neutron energies, but the probability of the interaction strongly depends on the incident neutron energy and the target energy (temperature). The energy in the center-of-mass system determines this probability.

Nuclear Fission
Nuclear fission is a nuclear reaction in which the nucleus of an atom splits into smaller parts (lighter nuclei). The fission process often produces free neutrons and photons (in the form of gamma rays) and releases a large amount of energy. In nuclear physics, nuclear fission is either a nuclear reaction or a radioactive decay process. The case of the decay process is called spontaneous fission, and it is a very rare process.
Neutron Emission
Although the neutron emission is usually associated with nuclear decay, it must also be mentioned in connection with neutron nuclear reactions. Some neutrons interact with a target nucleus via a compound nucleus. Among these compound nuclei, reactions are reactions in which a neutron is ejected from the nucleus, and they may be referred to as neutron emission reactions. The point is that compound nuclei lose their excitation energy in a way, which is identical to radioactive decay. A very important feature is that the mode of decay of the compound nucleus does not depend on how the compound nucleus was formed.
Charged Particle Ejection
Charged particle reactions are usually associated with the formation of a compound nucleus, which is excited to a high energy level, that such compound nucleus can eject a new charged particle. At the same time, the incident neutron remains in the nucleus. After the new particle is ejected, the remaining nucleus is completely changed but may or may not exist in an excited state depending upon the mass-energy balance of the reaction. This type of reaction is more common for charged particles as incident particles (such as alpha particles, protons, and so on).

The case of neutron-induced charged particle reactions is not so common, but there are some neutron-induced charged particle reactions, that are of importance in the reactivity control and also in the detection of neutrons.

## Neutron cross-section

The extent to which neutrons interact with nuclei is described in terms of quantities known as cross-sections. Cross-sections are used to express the likelihood of particular interaction between an incident neutron and a target nucleus. It must be noted this likelihood does not depend on real target dimensions. In conjunction with the neutron flux, it enables the calculation of the reaction rate, for example, to derive the thermal power of a nuclear power plant. The standard unit for measuring the microscopic cross-section (σ-sigma) is the barn, equal to 10-28 m2. This unit is very small. Therefore barns (abbreviated as “b”) are commonly used. The microscopic cross-section can be interpreted as the effective ‘target area’ that a nucleus interacts with an incident neutron.

A macroscopic cross-section is derived from microscopic and the material density:

Σ=σ.N

Here σ, which has units of m2, is referred to as the microscopic cross-section. Since the units of N (nuclei density) are nuclei/m3, the macroscopic cross-section Σ has units of m-1. Thus, it is an incorrect name because it is not a correct unit of cross-sections.

Neutron cross-sections constitute a key parameter of nuclear fuel. Neutron cross-sections must be calculated for new fuel assemblies, usually in two-Dimensional models of the fuel lattice.

The neutron cross-section is variable and depends on:

• Target nucleus (hydrogen, boron, uranium, etc.) Each isotope has its own set of cross-sections.
• Type of the reaction (capture, fission, etc.). Cross-sections are different for each nuclear reaction.
• Neutron energy (thermal neutron, resonance neutron, fast neutron). For a given target and reaction type, the cross-section is strongly dependent on the neutron energy. In the common case, the cross-section is usually much larger at low energies than at high energies. This is why most nuclear reactors use a neutron moderator to reduce the neutron’s energy and thus increase the probability of fission, essential to produce energy and sustain the chain reaction.
• Target energy (temperature of target material – Doppler broadening) This dependency is not so significant. Still, the target energy strongly influences the inherent safety of nuclear reactors due to a Doppler broadening of resonances.

## Law 1/v

Absorption cross-sections increase for thermal neutrons (in 1/v region) as the neutron’s velocity (kinetic energy) decreases. Therefore the 1/v law can determine a shift in absorption cross-section if the neutron is in equilibrium with a surrounding medium. This phenomenon is because the nuclear force between the target nucleus and the neutron has a longer time to interact.

This law is applicable only for absorption cross-section and only in the 1/v region.

Example of cross-sections in 1/v region:

The absorbtion cross-section for 238U at 20°C = 293K (~0.0253 eV) is:

.

The absorption cross-section for 238U at 1000°C = 1273K is equal to:

This cross-section reduction is caused only due to the shift of temperature of the surrounding medium.

## Resonance neutron capture

The absorption cross-section is often highly dependent on neutron energy. Note that nuclear fission produces neutrons with a mean energy of 2 MeV (200 TJ/kg, i.e., 20,000 km/s). The neutron can be roughly divided into three energy ranges:

• Fast neutron. (10MeV – 1keV)
• Resonance neutron (1keV – 1eV)
• Thermal neutron. (1eV – 0.025eV)

The resonance neutrons are called resonance for their special behavior. At resonance energies, the cross-section can reach peaks more than 100x higher than the base value of the cross-section. At these energies, the neutron capture significantly exceeds the probability of fission. Therefore it is very important (for thermal reactors) to quickly overcome this range of energy and operate the reactor with thermal neutrons, increasing the probability of fission.

A Doppler broadening of resonances is a very important phenomenon, which improves reactor stability. The prompt temperature coefficient of most thermal reactors is negative, owing to a nuclear Doppler effect. Although the absorption cross-section depends significantly on incident neutron energy, the shape of the cross-section curve also depends on the target temperature.

Nuclei are located in atoms that are themselves in continual motion owing to their thermal energy. As a result of these thermal motions, neutrons impinging on a target appear to the target’s nuclei to have a continuous spread in energy. This, in turn, affects the observed shape of resonance. The resonance becomes shorter and wider than when the nuclei are at rest.

Although the shape of a resonance changes with temperature, the total area under the resonance remains essentially constant. But this does not imply constant neutron absorption. Despite the constant area under resonance, a resonance integral, which determines the absorption, increases with increasing target temperature. This, of course, decreases coefficient k (negative reactivity is inserted).

## Typical cross-sections of materials in the reactor

The following table shows neutron cross-sections of the most common isotopes of the reactor core.

Neutron Energy

Neutron

Free Neutron