Material Properties

Key Characteristics of Inelastic Scattering

• During an inelastic scattering the neutron is absorbed and then re-emitted.

• The reaction occurs via compound nucleus.

• While momentum is conserved in an inelastic collision, kinetic energy of the “system” is not conserved.

• Some energy of the incident neutron is absorbed to the recoiling nucleus and the nucleus remains in the excited state.

• The nucleus gives up excitation energy by emitting one or more gamma rays.

• General notation: A(n, n’)A* or A(n, 2n’)B; Example: 14O(n, n’)14O*.

• Inelastic scattering is a threshold reaction and occurs above a threshold energy.

• Inelastic scattering cross section is relatively small for light nuclei.

• For hydrogen nucleus, inelastic scattering does not occur, because it does not have excited states.

• Inelastic scattering plays an important role in slowing down neutrons especially at high energies and by heavy nuclei (e.g. ²³⁸U).

• Inelastic scattering may be significant for heterogeneous reactors with highly enriched fuel (e.g. in fast neutron reactors).

Inelastic Scattering Cross-section

 

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Neutron Reactions

See also:

Inelastic Scattering Cross-section

 

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Inelastic Scattering

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Nuclear Reactions – Basic Classification

A nuclear reaction is considered to be the process in which two nuclear particles (two nuclei or a nucleus and a nucleon) interact to produce two or more nuclear particles or ˠ-rays (gamma rays). Thus, a nuclear reaction must cause a transformation of at least one nuclide to another. Sometimes if a nucleus interacts with another nucleus or particle without changing the nature of any nuclide, the process is referred to a nuclear scattering, rather than a nuclear reaction.

In order to understand the nature of nuclear reactions, the classification according to the time scale of of these reactions has to be introduced. Interaction time is critical for defining the reaction mechanism.

There are two extreme scenarios for nuclear reactions (not only neutron nuclear reactions):

• A projectile and a target nucleus are within the range of nuclear forces for the very short time allowing for an interaction of a single nucleon only. These type of reactions are called the direct nuclear reactions.
• A projectile and a target nucleus are within the range of nuclear forces for the time allowing for a large number of interactions between nucleons. These type of reactions are called the compound nucleus reactions.

In fact, there is always some non-direct (multiple internuclear interaction) component in all reactions, but the direct reactions have this component limited.

Compound Nucleus Reactions

  The compound nucleus model (idea of compound nucleus formation) was introduced by Danish physicist Niels Bohr in 1936. This model assumes that incident particle and the target nucleus become indistinguishable after the collision and together constitute the particular excited state of nucleus – the compound nucleus. To become indistinguishable the projectile has to suffer collisions with constituent nucleons of the target nucleus until it has lost its incident energy. In fact many so these collisions lead to a complete thermal equilibrium inside the compound nucleus. The compound nucleus is excited by both the kinetic energy of the projectile and by the binding nuclear energy.

This compound system is a relatively long-lived intermediate state of particle-target composite system and from the definition, the compound nucleus must live for at least several times longer than is the time of transit of an incident particle across the nucleus (~10^-22 s). The time scale of compound nucleus reactions is of the order of 10^-18 s  –  10^-16 s, but lifetimes as long as 10^-14 s have been also observed.

Very important feature and a direct consequence of the thermal equilibrium inside a compound nucleus is the fact the mode of decay of compound nucleus does not depend on the way the compound nucleus is formed. The large number of collisions between nucleons leads to the loss of the information on the entrance channel from the system. The decay mechanism (exit channel) that dominates the decay of C* is determined by the excitation energy in C* and by the law of probability.

These reactions can be considered as a two-stage processes.

• The first stage is the formation of a compound nucleus expressed by σ_a+X➝C*
• The second stage is the decay of a compound nucleus expressed by P_C*➝b+Y
• The result cross-section of certain reaction a+X➝[C*]➝b+Y is given by σ_(a,b)= σ_a+X➝C* . P_C*➝b+Y

Resonances

For the compound nucleus peaks in the cross-section are typical. Each peak is manifesting a particular compound state of nucleus. These peaks and the associated compound nuclei are usually called resonances. The behaviour of the cross-section between two resonances is usually strongly affected by the effect of nearby resonances.

Resonances (particular compound states) are mostly created in neutron nuclear reactions, but  it is by no means restricted to neutron nuclear reactions. The formation of resonances is caused by the quantum nature of nuclear forces. Each nuclear reaction is a transition between different quantum discrete states or energy levels. The discrete nature of energy transitions plays a key role. If the energy of the projectile (the sum of the Q value and the kinetic energy of the projectile) and the energy of target nucleus is equal to a compound nucleus at one of the excitation states, a resonance can be created and peak occurs in the cross section. For light nucleus, the allowable state density in this energy region is much lower and the “distance” between states is higher. For heavy nuclei, such as ²³⁸U, we can observe large resonance region in the neutron absorption cross-section.

It is obvious the compound states (resonances) are observed at low excitation energies. This is due to the fact, the energy gap between the states is large. At high excitation energy, the gap between two compound states is very small and the widths of resonances may reach the order of the distances between resonances. Therefore at high energies no resonances can be observed and the cross section in this energy region is continuous and smooth.

Region of resonances of ²³⁸U nuclei.
Source: JANIS (Java-based Nuclear Data Information Software); The ENDF/B-VII.1 Nuclear Data Library

Direct Reactions vs. Compound Nucleus Reactions

Direct Reactions

• The direct reactions are fast and involve a single-nucleon interaction.
• The interaction time must be very short (~10^-22 s).
• The direct reactions require incident particle energy larger than ∼ 5 MeV/Ap. (Ap is the atomic mass number of a projectile)
• Incident particles interact on the surface of a target nucleus rather than in the volume of a target nucleus.
• Products of the direct reactions are not distributed isotropically in angle, but they are forward focused.
• Direct reactions are of importance in measurements of nuclear structure.

Compound Nucleus Reactions

• The compound nucleus is a relatively long-lived intermediate state of particle-target composite system.
• The compound nucleus reactions involve many nucleon-nucleon interactions.
• The large number of collisions between the nucleons leads to a thermal equilibrium inside the compound nucleus.
• The time scale of compound nucleus reactions is of the order of 10^-18 s – 10^-16 s.
• The compound nucleus reactions is usually created if the projectile has low energy.
• Incident particles interact in the volume of a target nucleus.
• Products of the compound nucleus reactions are distributed near isotropically in angle (the nucleus loses memory of how it was created – the Bohr’s hypothesis of independence).
• The mode of decay of compound nucleus do not depend on the way the compound nucleus is formed.
• Resonances in the cross-section are typical for the compound nucleus reaction.

 

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Neutron Nuclear Reactions

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Cadmium is a naturally-occurring chemical element with atomic number 48 which means there are 48 protons and 48 electrons in the atomic structure. The chemical symbol for cadmium is Cd. Cadmium was first discovered in 1817 by two German chemists – Friedrich Stromeyer and Karl Samuel Leberecht Hermann.

Natural cadmium consists of eight isotopes, ¹⁰⁶Cd (1.3%),  ¹⁰⁸Cd (0.9%), ¹¹⁰Cd (12.5%), ¹¹¹Cd (12.8%), ¹¹²Cd (24.3%), ¹¹³Cd (12.2%), ¹¹⁴Cd (28.7%) and ¹¹⁶Cd (7.5%). Two of them are radioactive isotopes with very long half-life (¹¹³Cd – 7.7 x 10¹⁵ y and ¹¹⁶Cd – 2.9 x 10¹⁹ y).

In nuclear industry cadmium is commonly used as a thermal neutron absorber due to very high neutron absorption cross-section of ¹¹³Cd. ¹¹³Cd has specific absorption cross-section. There is a cadmium cut-off energy (Cadmium edge) in the absorption cross-section. Only neutrons of kinetic energy below the cadmium cut-off energy (~0.5 eV) are strongly absorbed by ¹¹³Cd. Therefore cadmium is widely used to absorb thermal neutrons in a thermal neutron filters.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1 Nuclear Data Library

See also:

Glossary

¹¹³Cd has specific absorption cross-section. There is a cadmium cut-off energy (Cadmium edge) in the absorption cross-section. Only neutrons of kinetic energy below the cadmium cut-off energy (~0.5 eV) are strongly absorbed by ¹¹³Cd. Therefore cadmium is widely used to absorb thermal neutrons in a thermal neutron filters.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1 Nuclear Data Library

See also:

Cadmium

Boron is a naturally-occurring chemical element with atomic number 5 which means there are 5 protons and 5 electrons in the atomic structure. The chemical symbol for boron is B. Significant concentrations of boron occur on the Earth in compounds known as the borate minerals. There are over 100 different borate minerals, but the most common are: borax, kernite, ulexite etc.

Natural boron consists primarily of two stable isotopes, ¹¹B (80.1%) and  ¹⁰B (19.9%). In nuclear industry boron is commonly used as a neutron absorber due to the high neutron cross-section of isotope  ¹⁰B. Its (n,alpha) reaction cross-section for thermal neutrons is about 3840 barns (for 0.025 eV neutron). Isotope  ¹¹B has absorption cross-section for thermal neutrons about 0.005 barns (for 0.025 eV neutron). Most of (n,alpha) reactions of thermal neutrons are 10B(n,alpha)7Li reactions accompanied by 0.48 MeV gamma emission.

Moreover, isotope ¹⁰B has high (n,alpha) reaction cross-section along the entire neutron energy spectrum. The cross-sections of most other elements becomes very small at high energies as in the case of cadmium. The cross-section of ¹⁰B decreases monotonically with energy. For fast neutrons its cross-section is on the order of barns.

Boron as the neutron absorber has another positive property. The reaction products (after a neutron absorption), helium and lithium, are stable isotopes. Therefore there are minimal problems with decay heating of control rods or burnable absorbers used in the reactor core.

On the other hand production of helium may lead to significant increase in pressure (under rod cladding), when used as the absorbing material in control rods. Moreover ¹⁰B is the principal source of radioactive tritium in primary circuit of all PWRs (which use boric acid as a chemical shim), because reactions with neutrons can rarely lead to formation of radioactive tritium via:

 10B(n,2x alpha)3H                             threshold reaction (~1.2 MeV)

and

10B(n,alpha)7Li(n,n+alpha)3H     threshold reaction (~3 MeV).

See also: Tritium

Boron letdown curve (chemical shim) and boron 10 depletion during a 12-month fuel cycle.

At the beginning of specific fuel cycle concentration of boric acid is highest. At the end of this cycle concentration of boric acid is almost zero and a reactor must be refueled, because there is no positive reactivity that can be inserted to compensate negative reactivity of fuel burnup (increase in reactor slagging).

 

See also:

Glossary

Isotope ¹⁰B has many applications. Its (n,alpha) reaction cross-section for thermal neutrons is about 3840 barns (for 0.025 eV neutron) and therefore it is very good neutron absorber. In nuclear power mostly natural boron is used, but it is not an exception the use of enriched boron (by the isotope ¹⁰B). Boron as the neutron absorber has following applications:

• Chemical shim. By chemical shim, we mean that boric acid is dissolved in the coolant/moderator. Chemical shim is used to long term reactivity control.
• Control rods. Many control rods use isotope ¹⁰B as a neutron absorbing material.
• Safety systems. The one of three primary objectives of nuclear reactor safety systems is to shutdown the reactor and maintain it in a shutdown condition. Therefore all safety systems (which must ensure subcriticality of the reactor after the transient) use high concentrations of boric acid.
• Burnable absorbers. Isotope ¹⁰B is widely used as the integral burnable absorber. When compared to gadolinium absorber (another commonly used burnable material), ¹⁰B has an order of magnitude smaller cross-sections. Therefore ¹⁰B compensate reactivity longer, but not so heavily.
• Converter in neutron detectors. Neutrons are not directly ionizing and they have usually to be converted into charged particles before they can be detected. Most common isotope for the neutron converter material is ¹⁰B.

Most of (n,alpha) reactions of thermal neutrons are 10B(n,alpha)7Li reactions accompanied by 0.48 MeV gamma emission.

See also:

Boron 10

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Boric Acid – Chemical Shim

By chemical shim, we mean that boric acid is dissolved in the coolant/moderator. Boric acid (molecular formula: H3BO3), is a white powder that is soluble in water. In pressurized water reactors, chemical shim (boric acid) is used to compensate an excess of reactivity of reactor core along the fuel burnup (long term reactivity control). At the beginning of specific fuel cycle concentration of boric acid is highest (see picture). At the end of this cycle concentration of boric acid is almost zero and a reactor must be refueled.

In certain cases also fine power changes can be controlled by chemical shim. If it is desired to increase power, then the boric acid concentration must be diluted, removing ¹⁰B from the reactor core and decreasing its poisoning effect. When compared with burnable absorbers (long term reactivity control) or with control rods (rapid reactivity control) the boric acid avoids the unevenness of neutron-flux density in the reactor core, because it is dissolved homogeneously in the coolant in entire reactor core. On the other hand high concentrations of boric acid may lead to positive moderator temperature coefficient and that is undesirable. In this case more burnable absorbers must be used.

Moreover this method is slow in controlling reactivity. Normally, it takes several minutes to change the concentration (dilute or borate) of the boric acid in the primary loop. For rapid changes of reactivity control rods must be used.

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Applications of Boron in Nuclear Power

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Boron 10

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Boron 10 Depletion

Natural boron consists primarily of two stable isotopes, ¹¹B (80.1%) and  ¹⁰B (19.9%). In nuclear industry boron is commonly used as a neutron absorber due to the high neutron cross-section of isotope  ¹⁰B. Its (n,alpha) reaction cross-section for thermal neutrons is about 3840 barns (for 0.025 eV neutron). Isotope  ¹¹B has absorption cross-section for thermal neutrons about 0.005 barns (for 0.025 eV neutron). Most of (n,alpha) reactions of thermal neutrons are 10B(n,alpha)7Li reactions accompanied by 0.48 MeV gamma emission.

Since the isotope ¹⁰B has a significantly higher neutron cross-section, the ¹⁰B depletes much more faster than ¹¹B. Without the addition of fresh boron (19,9% of ¹⁰B) into the primary coolant system the enrichment of ¹⁰B in boric acid continuously decreases. In the result the enrichment of ¹⁰B at the end of the fuel cycle can be for example below 18% of ¹⁰B. This phenomenon must be considered in all the criticality calculations (e.g. shutdown margin calculations, estimated critical conditions or general core depletion calculations).

See also:

Boric Acid – Chemical Shim

See also:

Boron 10

See also:

H3BO3 Converter

Gadolinium is a naturally-occurring chemical element with atomic number 64 which means there are 64 protons and 64 electrons in the atomic structure. The chemical symbol for gadolinium is Gd. Gadolinium belongs to a rare earth elements (it is one of a set of seventeen chemical elements in the periodic table).

Gadolinium was first discovered in 1880 by Jean Charles Galissard de Marignac. It is named for mineral (gadolinite), which is named for Finnish chemist Johan Gadolin.

Natural gadolinium consists of six stable isotopes, ¹⁵⁴Gd (2.18%), ¹⁵⁵Gd (14.8%), ¹⁵⁶Gd (20.5%), ¹⁵⁷Gd (15.7%), ¹⁵⁸Gd (24.8%) and ¹⁶⁰Gd (21.9%) and one radioisotope ¹⁵²Gd (0.2%) with half-life of 1.1 x 10¹⁴ y.

In nuclear industry gadolinium is commonly used as a neutron absorber due to very high neutron absorbtion cross-section of two isotopes ¹⁵⁵Gd and ¹⁵⁷Gd. In fact their absorption cross-sections are the highest among all stable isotopes. ¹⁵⁵Gd has 61 000 barns for thermal neutrons (for 0.025 eV neutron) and ¹⁵⁷Gd has even 254 000 barns. For this reason gadolinium is widely used as a burnable absorber, which is commonly used in fresh fuel to compensate an excess of reactivity of reactor core. In comparison with another burnable absorbers gadolinium behaves like a completely black material. Therefore gadolinium is very effective in compensation of the excess of reactivity, but on the other hand an improper distribution of Gd-burnable absorbers may lead to unevenness of neutron-flux density in the reactor core.

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Glossary