What is Neutron Nuclear Reaction – Definition

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.

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*.

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

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.

The ENDF/B-VII.1 Nuclear Data Library

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 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.

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.

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.