8.3.6.3. Neutron Capture

Table of Contents

What Neutron Capture Means

Neutron capture is a process in which an atomic nucleus absorbs a neutron. Because a neutron has no electric charge, it is not repelled by the positive charge of the nucleus. This makes neutron capture especially important in nuclear physics. A neutron can come very close to a nucleus and, if conditions are right, become part of it.

If a nucleus $^A_ZX$ captures a neutron $^1_0n$, the result is usually a heavier isotope of the same element:

$$
^A_ZX + ^1_0n \rightarrow ^{A+1}_ZX^*
$$

The star indicates that the new nucleus is often formed in an excited state. This excited nucleus may later release energy, often by emitting gamma rays. That is why neutron capture is frequently connected with gamma emission.

Neutron capture changes the mass number of the nucleus by 1, but it does not change the atomic number, because a neutron has no electric charge.

The Basic Reaction

The most common simple form of neutron capture is written as an $(n,\gamma)$ reaction. This means a nucleus absorbs a neutron and then emits a gamma ray:

$$
^A_ZX + n \rightarrow ^{A+1}_ZX + \gamma
$$

Here, the neutron is captured, and the excess energy is carried away by the gamma photon. The product nucleus is a heavier isotope of the original nucleus.

For example,

$$
^{59}_{27}\mathrm{Co} + n \rightarrow ^{60}_{27}\mathrm{Co} + \gamma
$$

The element stays cobalt, because the atomic number remains 27, but the isotope changes from cobalt 59 to cobalt 60.

Why Capture Can Happen Easily

Charged particles, such as protons or alpha particles, must overcome electric repulsion from the nucleus. Neutrons do not face this Coulomb barrier. As a result, even slow neutrons can interact strongly with nuclei.

This does not mean every neutron will be captured. A neutron may also scatter from the nucleus instead of being absorbed. Whether capture happens depends on the type of nucleus and the neutron energy.

Energy and Excited Nuclei

When a neutron is captured, the final nucleus usually has extra energy. Part of this comes from the motion of the neutron, and part comes from the binding of the neutron inside the nucleus. The nucleus is therefore often left excited:

$$
^A_ZX + n \rightarrow ^{A+1}_ZX^*
$$

Then it de-excites:

$$
^{A+1}_ZX^* \rightarrow ^{A+1}_ZX + \gamma
$$

Sometimes more than one gamma ray is emitted in a sequence as the nucleus drops through several energy levels.

In neutron capture, the captured neutron becomes part of the nucleus. The resulting nucleus is often unstable at first and releases energy by gamma emission.

Radiative Capture

The name radiative capture is often used for neutron capture followed by gamma-ray emission. This is the usual meaning of neutron capture in many basic discussions.

The reaction is important because it can create radioactive isotopes. A stable nucleus can capture a neutron and become an unstable isotope that later decays by beta emission. This is one major way new isotopes are produced in reactors and in stars.

A common sequence is:

$$
^A_ZX + n \rightarrow ^{A+1}_ZX + \gamma
$$

followed later by beta decay:

$$
^{A+1}_ZX \rightarrow ^{A+1}_{Z+1}Y + e^- + \bar{\nu}_e
$$

The capture itself does not change the element, but later decay can.

Dependence on Neutron Energy

The probability of neutron capture depends strongly on neutron energy. In many nuclei, slow neutrons are more likely to be captured than fast neutrons. These slow neutrons are often called thermal neutrons.

A useful idea is the capture cross section, usually written as $\sigma$. A larger cross section means a greater probability of capture.

For many cases, especially at low energies, capture approximately follows a $1/v$ trend, where $v$ is neutron speed. This means slower neutrons can have a larger chance of being captured.

$$
\sigma \propto \frac{1}{v}
$$

This is not true in every situation, but it is a common and important pattern.

For many nuclei, neutron capture becomes more probable when the neutron is slower. Thermal neutrons are therefore often very effective for capture reactions.

Resonance Capture

For some neutron energies, the probability of capture rises sharply. These sharp increases are called resonances. They happen when the combined system of neutron plus nucleus has an allowed energy state that matches the incoming neutron energy well.

In that case, the neutron is especially likely to be absorbed. Resonance capture is very important in reactor physics and nuclear measurements.

Comparison with Scattering

A neutron entering matter does not always get captured. It may instead bounce off nuclei. This is scattering. Capture and scattering are different outcomes of neutron interaction.

The table below shows the difference.

Interaction	What happens	Nucleus changes?	Common result
Elastic scattering	Neutron collides and continues	No	Neutron changes direction and energy
Inelastic scattering	Neutron excites nucleus, then continues	No permanent isotope change	Gamma emission may follow
Neutron capture	Neutron is absorbed	Yes, isotope becomes heavier	Often gamma emission

Thermal Neutron Capture

Thermal neutrons are neutrons whose energies are similar to the random thermal motion of atoms in matter. They are especially important because many nuclei capture them efficiently.

Materials with large thermal neutron capture cross sections are used in control rods, shielding, and neutron detectors. Examples include boron, cadmium, and gadolinium.

Some examples of capture reactions are:

$$
^{10}\mathrm{B} + n \rightarrow ^7\mathrm{Li} + \alpha
$$

and

$$
^{113}\mathrm{Cd} + n \rightarrow ^{114}\mathrm{Cd} + \gamma
$$

The boron example is a neutron absorption reaction that produces charged particles rather than only gamma rays. It is still a form of neutron capture in the broad sense because the neutron is absorbed by the nucleus.

Importance in Nuclear Reactors

Neutron capture plays a major role in reactors. Some captures are useful, and some reduce reactor efficiency.

If a fuel nucleus captures a neutron and then fissions, that helps sustain the chain reaction. But if a neutron is captured by a material without causing fission, that neutron is removed from the chain reaction. This is sometimes called parasitic capture.

For example, uranium 238 can capture a neutron:

$$
^{238}\mathrm{U} + n \rightarrow ^{239}\mathrm{U} + \gamma
$$

Then a series of beta decays can occur, eventually producing plutonium 239. This is an important path for breeding new fuel.

Control rods work by strong neutron capture. They absorb neutrons and reduce the number of neutrons available to continue fission.

Importance in Element Formation

Neutron capture is also one of the main ways heavy nuclei are formed in astrophysics. In stars and explosive stellar events, nuclei can capture neutrons and gradually build heavier isotopes.

If captures happen slowly compared with beta decay, the process is called the slow neutron capture process, or s process. If captures happen very rapidly, it is called the rapid neutron capture process, or r process. These broader astrophysical topics belong elsewhere, but they show how fundamental neutron capture is in nature.

Reaction Rate Idea

A simple way to think about capture rate is that it depends on how many target nuclei are present, how many neutrons pass through, and how likely each neutron is to be captured.

A common expression is

$$
R = \phi N \sigma
$$

where $R$ is the reaction rate, $\phi$ is neutron flux, $N$ is the number of target nuclei, and $\sigma$ is the capture cross section.

This relation is widely used in activation analysis and reactor calculations.

A useful formula for neutron capture rate is
$$
R = \phi N \sigma
$$
A larger neutron flux, more target nuclei, or a larger capture cross section all increase the reaction rate.

A Simple Visual Picture

The figure below shows the basic idea of a neutron approaching a nucleus and being absorbed, followed by gamma emission.

Rendering scientific sketch…

Neutron capture and gamma emission

Key Features of Neutron Capture

Neutron capture has several important features that make it different from many other nuclear interactions.

Feature	Neutron capture
Incoming particle charge	Neutral
Coulomb repulsion	Absent
Change in atomic number at capture	No
Change in mass number at capture	Increases by 1
Common follow-up emission	Gamma rays
Strong dependence on neutron energy	Yes

Final Understanding

Neutron capture is the absorption of a neutron by a nucleus. It usually creates a heavier isotope, often in an excited state, and this state commonly releases gamma rays. Because neutrons are uncharged, they can be captured even when moving slowly, and in many cases slow neutrons are especially effective. This process is central in reactors, isotope production, neutron detection, and the formation of heavy elements in the universe.

Core idea:
$$
^A_ZX + n \rightarrow ^{A+1}_ZX^* \rightarrow ^{A+1}_ZX + \gamma
$$
Neutron capture makes a nucleus heavier by one mass unit and often produces gamma radiation.

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