Neutron Nuclear Reactions

The study of neutron nuclear reactions and nuclear reactions in general is of paramount importance in physics of nuclear reactors. Progress in the understanding of nuclear reactions generally has occurred at a faster pace compared to similar studies of  chemical reactions and generally a higher level of sophistication has been achieved.

Shortly after the neutron was discovered in 1932, it was quickly realized that neutrons might act to form a nuclear chain reaction. When nuclear fission was discovered in 1938, it became clear that, if a neutron induced fission reaction produces new free neutrons, that each of these neutrons might cause further fission reaction in a cascade known as a chain reaction. Therefore the calculations of nuclear reactors are determined by the transport of neutrons, their interaction with matter and their multiplication within a nuclear reactor.

neutron nuclear reactions

Definition

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

In order to understand the nature of neutron 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 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 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.

Basic characteristics of 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.

Basic characteristics of 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.
Nuclear reactions, that occur in a time comparable to the time of transit of an incident particle across the nucleus (~10-22 s), are called direct reactions. Interaction time is critical for defining the reaction mechanism. The very short interaction time allows for an interaction of a single nucleon only (in extreme cases). In fact, there is always some non-direct (a multiple internuclear interaction) component in all reactions, but the direct reactions have this component limited. To limit the time available for multiple internuclear interactions, the reaction have to occur at high energy.  

Direct reactions have another property which is very important. Products of a direct reaction are not distributed isotropically in angle, but they are forward focused. This reflects the fact that the projectiles makes only one, or very few, collisions with nucleons in the target nucleus and its forward momentum is not transferred to an entire compound state.

The cross-sections for direct reactions vary smoothly and slowly with energy in contrast to the compound nucleus reactions and these cross-sections are comparable to the geometrical cross-sections of target nuclei.

Types of direct reactions:

  • Elastic scattering in which a passing particle and a targes stay in their ground states.  
  • Inelastic scattering in which a passing particle changes its energy state.  For example the (p, p’) reaction.
  • Transfer reactions in which one or more nucleons are transferred to the othes nucleus. These reactions are further classified to as:
    • Stripping reaction in which one or more nucleons are transferred to a target nucleus from passing particle. For example the neutron stripping in the (d, p) reaction.
    • Pick-up reaction in which one or more nucleons are transferred from a target nucleus to a passing particle. For example the neutron pick-up in the (p, d) reaction
  • Break-up reaction in which a breakup of a projectile into two or more fragments occurs.
  • Knock-out reaction in which a single nucleon or a light cluster is removed from the projectile by a collision with the target.

Direct nuclear reaction

Example: This threshold reaction of fast neutron with an isotope 10B is one of the ways, how radioactive tritium in primary circuit of all PWRs is generated.

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 (channel) that dominates the decay of C* is determined by the excitation energy in C*.

compound nucleus reaction

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

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

Absorption reaction of fissile 235U. The uncertainty of the exit channel is caused by “loss of memory” of resonance [236U].

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.

Compound state - resonance

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.

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.

Resonance region - Compound Nucleus

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

The ENDF/B-VII.1 Nuclear Data Library

Types of neutron-nuclear reactions

Generally, a neutron scattering reaction occurs when a target nucleus emits a single neutron after a neutron-nucleus interaction. In an elastic scattering reaction between a neutron and a target nucleus, there is no energy transferred into nuclear excitation.
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. Thus while momentum is conserved in an inelastic collision, kinetic energy of the “system” is not conserved.
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 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 simply 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 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.

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 decay process is called spontaneous fission and it is very rare process.
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.
Charged particle reactions are usually associated with formation of a compound nucleus, which is excited to a high energy level, that such compound nucleus can eject a new charged particle while 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.

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Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

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