Material Properties

Forms of Ionizing Radiation

Ionizing radiation is categorized by the nature of the particles or electromagnetic waves that create the ionizing effect. These particles/waves have different ionization mechanisms, and may be grouped as:

• Directly ionizing. Charged particles (atomic nuclei, electrons, positrons, protons, muons, etc.) can ionize atoms directly by fundamental interaction through the Coulomb force if it carries sufficient kinetic energy. These particles must be moving at relativistic speeds to reach the required kinetic energy. Even photons (gamma rays and X-rays) can ionize atoms directly (despite they are electrically neutral) through the Photoelectric effect and the Compton effect, but secondary (indirect) ionization is much more significant.
  • Alpha radiation. Alpha radiation consist of alpha particles at high energy/speed. The production of alpha particles is termed alpha decay. Alpha particles consist of two protons and two neutrons bound together into a particle identical to a helium nucleus. Alpha particles are relatively large and carry a double positive charge. They are not very penetrating and a piece of paper can stop them. They travel only a few centimeters but deposit all their energies along their short paths.
  • Beta radiation. Beta radiation consist of free electrons or positrons at relativistic speeds. Beta particles (electrons) are much smaller than alpha particles. They carry a single negative charge. They are more penetrating than alpha particles, but thin aluminum metal can stop them. They can travel several meters but deposit less energy at any one point along their paths than alpha particles.
• Indirectly ionizing. Indirect ionizing radiation is electrically neutral particles and therefore does not interact strongly with matter. The bulk of the ionization effects are due to secondary ionizations.
  • Photon radiation (Gamma rays or X-rays). Photon radiation consist of high energy photons. These photons are particles/waves (Wave-Particle Duality) without rest mass or electrical charge. They can travel 10 meters or more in air. This is a long distance compared to alpha or beta particles. However, gamma rays deposit less energy along their paths. Lead, water, and concrete stop gamma radiation. Photons (gamma rays and X-rays) can ionize atoms directly through the Photoelectric effect and the Compton effect, where the relatively energetic electron is produced. The secondary electron will go on to produce multiple ionization events, therefore the secondary (indirect) ionization is much more significant.
  • Neutron radiation. Neutron radiation consist of free neutrons at any energies/speeds. Neutrons can be emitted by nuclear fission or by the decay of some radioactive atoms. Neutrons have zero electrical charge and cannot directly cause ionization. Neutrons ionize matter only indirectly. For example, when neutrons strike the hydrogen nuclei, proton radiation (fast protons) results. Neutrons can range from high speed, high energy particles to low speed, low energy particles (called thermal neutrons). Neutrons can travel hundreds of feet in air without any interaction.

Beta Radiation

Beta radiation consist of free electrons  or positrons at relativistic speeds. These particles are known as the beta particles. Beta particles are high-energy, high-speed electrons or positrons emitted by certain fission fragments or by certain primordial radioactive nuclei such as potassium-40. The beta particles are a form of ionizing radiation also known as beta rays. The production of beta particles is termed beta decay. There are two forms of beta decay, the electron decay (β− decay) and the positron decay (β+ decay). In a nuclear reactor occurs especially the β− decay, because the common feature of the fission products is an excess of neutrons (see Nuclear Stability). An unstable fission fragment with the excess of neutrons undergoes β− decay, where the neutron is converted into a proton, an electron, and an electron antineutrino.

Characteristics of Beta Radiation

Key characteristics of beta radiation are summarized in following points:

• Beta particles are energetic electrons, they are relatively light and carry a single negative charge.
• Their mass is equal to the mass of the orbital electrons with which they are interacting and unlike the alpha particle a much larger fraction of its kinetic energy can be lost in a single interaction.
• Their path is not so straightforward. The beta particles follow a very zig-zag path through absorbing material. This resulting path of particle is longer than the linear penetration (range) into the material.
• Since they have very low mass, beta particles reach mostly relativistic energies.
• Beta particles also differ from other heavy charged particles in the fraction of energy lost by radiative process known as the bremsstrahlung. Therefore for high energy beta radiation shielding dense materials are inappropriate.
• When the beta particle moves faster than the speed of light (phase velocity) in the material it generates a shock wave of electromagnetic radiation known as the Cherenkov radiation.
• The beta emission has the continuous spectrum.
• A 1 MeV beta particle can travel approximately 3.5 meters in air.
• Due to the presence of the bremsstrahlung low atomic number (Z) materials are appropriate as beta particle shields.

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Shielding of Beta Radiation – Electrons

Beta radiation ionizes matter weaker than alpha radiation. On the other hand the ranges of beta particles are longer and depends strongly on initial kinetic energy of particle. Some have enough energy to be of concern regarding external exposure. A 1 MeV beta particle can travel approximately 3.5 meters in air. Such beta particles can penetrate into the body and deposit dose to internal structures near the surface. Therefore greater shielding than in case of alpha radiation is required.

Materials with low atomic number Z are appropriate as beta particle shields. With high Z materials the bremsstrahlung (secondary radiation – X-rays) is associated. This radiation is created during slowing down of beta particles while they travel in a very dense medium. Heavy clothing, thick cardboard or thin aluminium plate will provide protection from beta radiation and prevents of production of the bremsstrahlung.

See also more theory: Interaction of Beta Radiation with Matter

See also calculator: Beta activity to dose rate 

Shielding of Beta Radiation – Positrons

The coulomb forces that constitute the major mechanism of energy loss for electrons are present for either positive or negative charge on the particle and constitute the major mechanism of energy loss also for positrons. Whatever the interaction involves a repulsive or attractive force between the incident particle and orbital electron (or atomic nucleus), the impulse and energy transfer for particles of equal mass are about the same. Therefore positrons interact similarly with matter when they are energetic. The track of positrons in material is similar to the track of electrons. Even their specific energy loss and range are about the same for equal initial energies.

At the end of their path, positrons differ significantly from electrons. When a positron (antimatter particle) comes to rest, it interacts with an electron (matter particle), resulting in the annihilation of the both particles and the complete conversion of their rest mass to pure energy (according to the E=mc² formula) in the form of two oppositely directed 0.511 MeV gamma rays (photons).

Therefore any positron shield have to include also a gamma ray shield. In order to minimize the bremsstrahlung a multi-layered radiation shield is appropriate. Material for the first layer must fulfill the requirements for negative beta radiation shielding. First layer of such shield may be for example a thin aluminium plate (to shield positrons), while the second layer of such shield may be a dense material such as lead or depleted uranium.

See also: Shielding of Gamma Radiation

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The shape of this energy curve depends on what fraction of the reaction energy (Q value-the amount of energy released by the reaction) is carried by the electron or neutrino.Basic materials for beta particles shielding.

 

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Radiation

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Conservation of momentum and kinetic energy

where:

m_n = mass of the neutron

m_T = mass of the target nucleus T

v_n,i = initial neutron speed

v_n,f = final neutron speed

v_T,i = initial target speed

v_T,f = final target speed

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Glossary

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Key Characteristics of Elastic Scattering

• Elastic scattering is the most important process for slowing down neutrons.

• Total kinetic energy of the system is conserved in elastic scattering.

• In this process, energy lost by the neutron is transferred to the recoiling nucleus.

• Maximum energy transfer is occurred with an head-on collision.

• Kinetic energy of the recoiled nucleus depends on the recoiled angle φ of the nucleus.

• Elastic scattering cross-sections for light elements are more or less independent of neutron energy up to 1 MeV.

• For intermediate and heavy elements, the elastic cross-section is constant at low energy with some specifics at higher energy.

• A good approximation is, σ_s = const, for all elements, that are of importance.

• At low energy, σ_s can be described by the one-level Breit-Wigner formula.

• Nearly all elements have scattering cross-sections in the range of 2 to 20 barns.

• The important exception is for water and heavy water.

• If the kinetic energy of an incident neutron is large compared with the chemical binding energy of the atoms in a molecule, the chemical bound can be ignored.

• If the kinetic energy of an incident neutron is of the order or less than the chemical binding energy, the cross-section of the molecule is not equal to the sum of cross-sections of its individual nuclei.

• Scattering of slow neutrons by molecules is greater than by free nuclei.

• Therefore one nucleus microscopic cross-sections do not describe the process correctly, while the macroscopic cross-section (Σs) has a precise meaning.

Elastic Scattering Cross-section

To be an effective moderator, the probability of elastic reaction between neutron and the nucleus must be high. In terms of cross-sections, the elastic scattering cross section of a moderator’s nucleus must be high.

 

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Elastic Scattering

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Elastic Scattering Cross-section

To be an effective moderator, the probability of elastic reaction between neutron and the nucleus must be high. In terms of cross-sections, the elastic scattering cross section of a moderator’s nucleus must be high.

 

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See also:

Elastic Scattering

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E = mc² Meaning

At the beginning of the 20th century, the notion of mass underwent a radical revision. Mass lost its absoluteness. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc². In words, energy equals mass multiplied by the speed of light squared. Because the speed of light is a very large number, the formula implies that any small amount of matter contains a very large amount of energy. The mass of an object was seen to be equivalent to energy, to be interconvertible with energy, and to increase significantly at exceedingly high speeds near that of light. The total energy of an object was understood to comprise its rest mass as well as its increase of mass caused by increase in kinetic energy.

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. It was found the rest mass an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E = mc²) this binding energy is proportional to this mass difference and it is known as the mass defect.

E=mc² represents the new conservation principle – the conservation of mass-energy.

, where m is the small amount of mass and c is the speed of light.

What that means? If the nuclear energy is generated (splitting atoms, nuclear fusion), a small amount of mass (saved in the nuclear binding energy) transforms into the pure energy (such as kinetic energy, thermal energy, or radiant energy).

Example:

The energy equivalent of one gram (1/1000 of a kilogram) of mass is equivalent to:

• 89.9 terajoules
• 25.0 million kilowatt-hours (≈ 25 GW·h)
• 21.5 billion kilocalories (≈ 21 Tcal)
• 85.2 billion BTUs

or to the energy released by combustion of the following:

• 21.5 kilotons of TNT-equivalent energy (≈ 21 kt)
• 568,000 US gallons of automotive gasoline

Any time energy is generated, the process can be evaluated from an E = mc² perspective.

 

See also:

Nuclear Energy

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 compound nucleus is formed. This is the very important feature, because the mode of decay of such compound nucleus does not depend on the way 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 σ_γ.

• 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 simply be captured, or it may cause nuclear fission. For fissionable materials we thus divide the absorption cross section as σ_a = σ_γ + σ_f.

Neutron Absorption Cross-section

The likelihood of a neutron absorption is represented by the absorption cross section as σ_a. The relative likelihoods of an absorption reaction or a neutron scattering are represented by dividing the total cross section into scattering and absorption cross sections:

σ_t = σ_s + σ_a

Given a collision, σ_a / σ_t is the probability that the neutron will be
absorbed and σ_s / σ_t is the probability that the neutron will be scattered.

Table of cross-sections.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data LibraryHydrogen. Neutron absorption and scattering. Comparison of cross-sections.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Xenon – 135. Neutron absorption and scattering. Comparison of cross-sections.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

 

See also:

See also:

Neutron Reactions

See also:

Neutron Absorption Cross-section

The likelihood of a neutron absorption is represented by the absorption cross section as σ_a. The relative likelihoods of an absorption reaction or a neutron scattering are represented by dividing the total cross section into scattering and absorption cross sections:

σ_t = σ_s + σ_a

Given a collision, σ_a / σ_t is the probability that the neutron will beabsorbed and σ_s / σ_t is the probability that the neutron will be scattered.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Hydrogen. Neutron absorption and scattering. Comparison of cross-sections.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Xenon – 135. Neutron absorption and scattering. Comparison of cross-sections.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Table of cross-sections.

 

See also:

Neutron Absorption

Neutron Capture – Radiative Capture

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 σ_γ.

The radiative capture is a reaction, in which the incident neutron is completely absorbed and 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 also on the target energy (temperature). In fact the energy in the center-of-mass system determines this probability.

Neutron Capture at Small Neutron Flux

It must be noted we have to distinguish between radiative captures at small neutron flux and at high neutron flux. At small neutron flux, as in a nuclear reactor, the compound nucleus has time to decay between two neutron captures. The most usual capture reactions that occur inside a power reactor are below:

Neutron Capture at High Neutron Flux

At very high flux the atomic nuclei do not necessarily have enough time to decay via beta particle emission between neutron captures. This happens inside stars, where a really tremendous flux may be reached. As a result of many capture reactions without beta decay the mass number rises by a large amount, while the atomic number stays the same. Only afterwards, the highly unstable nuclei decay via many β− decays to stabilize itself.

Since the process entails a succession of many rapid neutron captures, it is called the r-process. The r-process is a nucleosynthesis process that occurs in core-collapse supernovae and is responsible for the creation of approximately half of the neutron-rich atomic nuclei heavier than iron.

Uranium 238. Comparison of cross-sections.Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data LibraryXenon – 135. Neutron absorption and scattering. Comparison of cross-sections.Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data LibraryHydrogen. Neutron absorption and scattering. Comparison of cross-sections.Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data LibraryGadolinium 155 and 157. Comparison of radiative capture cross-sections.
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Neutron Capture and Fuel Breeding

In reactor calculations, the neutron capture reaction is as important as the fission reaction. Its impact on the neutron balance is evident. But this reaction is of importance also from another point of view. Fissionable nuclei or even fissile nuclei may capture a neutron, this capture leads to formation of unstable nuclei with higher neutron number. Such unstable nuclei undergo a nuclear decay, which may lead to formation of another fissile nuclei. This process is also referred to as the nuclear transmutation and is responsible for new fuel breeding in nuclear reactors.

 

Radiative Capture Cross-section

The likelihood of a neutron radiative capture is represented by the radiative capture cross section as σ_γ. As usual, the cross-section can be divided into three regions according to the incident neutron energy.

• 1/v Region
• Resonance Region
• Fast Neutrons Region

1/v Region

In the common case, the cross section is usually much larger at low energies than at high energies. For thermal neutrons (in 1/v region), also radiative capture cross-sections increase as the velocity (kinetic energy) of the neutron decreases. Therefore the 1/v Law can be used to determine shift in capture cross-section, if the neutron is in equilibrium with a surrounding medium. This phenomenon is due to the fact the nuclear force between the target nucleus and the neutron has a longer time to interact.

Resonance Region

The largest cross-sections are usually at neutron energies, that lead to long-lived states of the compound nucleus. The compound nuclei of these certain energies are referred to as nuclear resonances and its formation is typical in the resonance region. The widths of the resonances increase in general with increasing energies. At higher energies the widths may reach the order of the distances between resonances and then no resonances can be observed. The narrowest resonances are usually compound states of heavy nuclei (such as fissionable nuclei).

Since the mode of decay of the compound nucleus does not depend on the way the compound nucleus was formed, the nucleus sometimes emits a gamma ray (radiative capture) or sometimes emits a neutron (scattering). In order to understand the way, how a nucleus will stabilize itself, we have to understand the behaviour of compound nucleus.

The compound nucleus emits a neutron only after one neutron obtains an energy in collision with other nucleon greater than its binding energy in the nucleus. It have some delay, because the excitation energy of the compound nucleus is divided among several nucleons. It is obvious the average time that elapses before a neutron can be emitted is much longer for nuclei with large number of nucleons than when only a few nucleons are involved. It is a consequence of sharing the excitation energy among a large number of nucleons.

This is the reason the radiative capture is comparatively unimportant in light nuclei but becomes increasingly important in the heavier nuclei.

The lifetime of a compound nucleus is inversely proportional to its total width. Narrow resonances therefore correspond to capture while the wider resonances are due to scattering.

Table of cross-sections.

Radiative Capture Cross-section – region of resonances of 238U nuclei.
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data LibraryEnergy levels of compound state. For neutron absorption reaction on ²³⁸U the first resonance E1 corresponds to the excitation energy of 6.67eV. E0 is a base state of ²³⁹U.Radiative capture and elastic scattering cross-sections in ¹⁶O and ²³⁸U.

Example:

Source: R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).

The first resonance in ²³⁸U at 6.67 eV, which corresponds to the first virtual level in ²³⁹U, has a total width of only 0.027 eV, and the mean life of this state is 2.4×10^-14s. By contrast, the resonance observed at 443 keV in ¹⁶O, which corresponds to the first virtual state in ¹⁷O, has a total width of 41 keV, giving a mean lifetime of 1.5×10^-21s. Thus it is highly likely that the compound state in ²³⁹U decays at least to some extent by gamma ray emission, while compound state in ¹⁷O must decay primarily by nucleon emission. The 443-keV resonance in ¹⁶O is clearly a scattering resonance, whereas the 6.67-eV resonance in ²³⁸U is in part a capture resonance.

Doppler Broadening

In general, Doppler broadening is the broadening of spectral lines due to the Doppler effect caused by a distribution of kinetic energies of molecules or atoms. In reactor physics a particular case of this phenomenon is the thermal Doppler broadening of resonances caused by the thermal motion of the target particle in the nuclear fuel.

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

Nuclei are located in atoms which are themselves in continual motion owing to their thermal energy. As a result of these thermal motions neutrons impinging on a target appears to the nuclei in the target to have a continuous spread in energy. This, in turn, has an effect on 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 absorbtion. Despite the constant area under resonance, a resonance integral, which determines the absorbtion, increases with increasing target temperature. This, of course, decreases coefficient k (negative reactivity is inserted).

Fast Neutrons Region

The radiative capture cross-section at energies above the resonance region drops rapidly to very small values. This rapid drop is caused by the compound nucleus, which is formed in more highly-excited states. In these highly-excited states it is more likely that one neutron obtains an energy in collision with other nucleon greater than its binding energy in the nucleus. The neutron emission becomes dominant and gamma decay becomes less important. Moreover, at high energies, the inelastic scattering and (n,2n) reaction are highly probable at the expense of both elastic scattering and radiative capture.

 

See also:

See also:

Neutron Reactions

See also:

Neutron Capture Cross-section

The likelihood of a neutron radiative capture is represented by the radiative capture cross section as σ_γ. As usual, the cross-section can be divided into three regions according to the incident neutron energy.

• 1/v Region
• Resonance Region
• Fast Neutrons Region

1/v Region

In the common case, the cross section is usually much larger at low energies than at high energies. For thermal neutrons (in 1/v region), also radiative capture cross-sections increase as the velocity (kinetic energy) of the neutron decreases. Therefore the 1/v Law can be used to determine shift in capture cross-section, if the neutron is in equilibrium with a surrounding medium. This phenomenon is due to the fact the nuclear force between the target nucleus and the neutron has a longer time to interact.

Resonance Region

The largest cross-sections are usually at neutron energies, that lead to long-lived states of the compound nucleus. The compound nuclei of these certain energies are referred to as nuclear resonances and its formation is typical in the resonance region. The widths of the resonances increase in general with increasing energies. At higher energies the widths may reach the order of the distances between resonances and then no resonances can be observed. The narrowest resonances are usually compound states of heavy nuclei (such as fissionable nuclei).

Since the mode of decay of the compound nucleus does not depend on the way the compound nucleus was formed, the nucleus sometimes emits a gamma ray (radiative capture) or sometimes emits a neutron (scattering). In order to understand the way, how a nucleus will stabilize itself, we have to understand the behaviour of compound nucleus.

The compound nucleus emits a neutron only after one neutron obtains an energy in collision with other nucleon greater than its binding energy in the nucleus. It have some delay, because the excitation energy of the compound nucleus is divided among several nucleons. It is obvious the average time that elapses before a neutron can be emitted is much longer for nuclei with large number of nucleons than when only a few nucleons are involved. It is a consequence of sharing the excitation energy among a large number of nucleons.

This is the reason the radiative capture is comparatively unimportant in light nuclei but becomes increasingly important in the heavier nuclei.

The lifetime of a compound nucleus is inversely proportional to its total width. Narrow resonances therefore correspond to capture while the wider resonances are due to scattering.

Example:

Source: R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).

The first resonance in ²³⁸U at 6.67 eV, which corresponds to the first virtual level in ²³⁹U, has a total width of only 0.027 eV, and the mean life of this state is 2.4×10^-14s. By contrast, the resonance observed at 443 keV in ¹⁶O, which corresponds to the first virtual state in ¹⁷O, has a total width of 41 keV, giving a mean lifetime of 1.5×10^-21s. Thus it is highly likely that the compound state in ²³⁹U decays at least to some extent by gamma ray emission, while compound state in ¹⁷O must decay primarily by nucleon emission. The 443-keV resonance in ¹⁶O is clearly a scattering resonance, whereas the 6.67-eV resonance in ²³⁸U is in part a capture resonance.

σ_γ

Table of cross-sections.

Radiative Capture Cross-section – region of resonances of 238U nuclei.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Energy levels of compound state. For neutron absorption reaction on ²³⁸U the first resonance E1 corresponds to the excitation energy of 6.67eV. E0 is a base state of ²³⁹U.Radiative capture and elastic scattering cross-sections in ¹⁶O and ²³⁸U.

Doppler Broadening

In general, Doppler broadening is the broadening of spectral lines due to the Doppler effect caused by a distribution of kinetic energies of molecules or atoms. In reactor physics a particular case of this phenomenon is the thermal Doppler broadening of resonances caused by the thermal motion of the target particle in the nuclear fuel.

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

Nuclei are located in atoms which are themselves in continual motion owing to their thermal energy. As a result of these thermal motions neutrons impinging on a target appears to the nuclei in the target to have a continuous spread in energy. This, in turn, has an effect on 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 absorbtion. Despite the constant area under resonance, a resonance integral, which determines the absorbtion, increases with increasing target temperature. This, of course, decreases coefficient k (negative reactivity is inserted).

Fast Neutrons Region

The radiative capture cross-section at energies above the resonance region drops rapidly to very small values. This rapid drop is caused by the compound nucleus, which is formed in more highly-excited states. In these highly-excited states it is more likely that one neutron obtains an energy in collision with other nucleon greater than its binding energy in the nucleus. The neutron emission becomes dominant and gamma decay becomes less important. Moreover, at high energies, the inelastic scattering and (n,2n) reaction are highly probable at the expense of both elastic scattering and radiative capture.

Cross-sections of key isotopes

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Xenon – 135. Neutron absorption and scattering. Comparison of cross-sections.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Hydrogen. Neutron absorption and scattering. Comparison of cross-sections.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Gadolinium 155 and 157. Comparison of radiative capture cross-sections.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

 

See also:

Radiative Capture

Neutron Emission

The neutron emission is one of the radioactive decays, by which unstable nuclei may reach the stability. In general, this type of radioactive decay may occur, when nuclei contain significant excess of neutrons or excitation energy. In this type of decay a neutron is simply ejected from the nucleus.

Although the neutron emission is usually associated with nuclear decay, it must be also mentioned in connection with neutron nuclear reactions. Some neutrons interacts with a target nucleus via a compound nucleus. Among these compound nucleus reactions are also reactions, in which a neutron is ejected from nucleus and they may be referred to as neutron emission reactions. The point is that compound nuclei lose its excitation energy in a way, which is identical to the radioactive decay. Very important feature is the fact the mode of decay of compound nucleus does not depend on the way the compound nucleus was formed.
The compound nucleus reactions, in which neutron emission occurs, are:

• Elastic Scattering Reaction. In some cases, if the kinetic energy of an incident neutron just right to form a resonance, the neutron may be absorbed and a compound nucleus may be formed. This interaction is more unusual (in comparison with potential scattering) and is also known as resonance elastic scattering. Due to formation of the compound nucleus, initial and final neutron are not the same and this reactions may be also referred to as one type of neutron emission reaction.

• Inelastic Scattering Reaction. In this case, the connection with neutron emission is more obvious. In an inelastic scattering reaction between a neutron and a target nucleus some energy of the incident neutron is absorbed to the recoiling nucleus and the nucleus remains in the excited state. The neutron is emitted then with a lower kinetic energy. If the kinetic energy of an incident neutron is sufficient the double, triple, or more, neutron emission may take place. These events are referred to as (n, 2n), (n, 3n) or (n, …n) reactions. The probability of such reactions increases with increasing incident neutron energies.

• Nuclear Fission. The fission reaction is very specific reaction and is of importance in many fields of nuclear engineering. It is known the fission reaction produces fission neutrons that are of importance in any chain-reacting system. But not all neutrons are released at the same time following fission. Even the nature of creation of these neutrons is different. From this point of view we usually divide the fission neutrons into two following groups:
  • Prompt Neutrons. Prompt neutrons are emitted directly from fission and they are emitted within very short time of about 10^-14 second.
  • Delayed Neutrons. Delayed neutrons are emitted by neutron rich fission fragments that are called the delayed neutron precursors. These precursors usually undergo beta decay but a small fraction of them are excited enough to undergo neutron emission. The fact the neutron is produced via this type of decay and this happens orders of magnitude later compared to the emission of the prompt neutrons, plays an extremely important role in the control of the reactor.

 

See also:

See also:

Neutron Reactions

See also: