KAHIBARO
Table of Contents
What a Capture Reaction Is
A capture reaction happens when a target nucleus absorbs an incoming particle and keeps it, at least for some time. Instead of the projectile simply bouncing away, it becomes part of the nucleus. The result is a new nucleus, often in an excited state.
A simple symbolic form is
$$
a + X \rightarrow Y^*
$$
where $a$ is the incoming particle, $X$ is the target nucleus, and $Y^*$ is the excited compound or final nucleus.
Very often, the excited nucleus then releases energy by emitting radiation or another particle. In many beginner examples, the emitted radiation is a gamma ray, so one commonly sees reactions like
$$
a + X \rightarrow Y + \gamma
$$
This is often called radiative capture.
Basic Idea
The key feature of capture is that the projectile is incorporated into the nucleus. For example, a neutron can be captured by a nucleus:
$$
{}^{A}_{Z}X + n \rightarrow {}^{A+1}_{Z}X^* \rightarrow {}^{A+1}_{Z}X + \gamma
$$
Because the neutron has no electric charge, it can often enter the nucleus more easily than a charged particle. This makes neutron capture especially important in nuclear physics.
A proton can also be captured:
$$
{}^{A}_{Z}X + p \rightarrow {}^{A+1}_{Z+1}Y + \gamma
$$
In this case, the proton must overcome electrostatic repulsion from the positively charged nucleus, so proton capture is generally harder at low energy than neutron capture.
In a capture reaction, the incoming particle is absorbed by the target nucleus. The defining idea is not scattering away, but becoming part of the nucleus.
Common Types of Capture
Several kinds of particles can be captured. The table below shows common examples.
| Projectile | Typical reaction form | Example |
|---|---|---|
| Neutron | $X(n,\gamma)Y$ | ${}^{59}\mathrm{Co}(n,\gamma){}^{60}\mathrm{Co}$ |
| Proton | $X(p,\gamma)Y$ | ${}^{12}\mathrm{C}(p,\gamma){}^{13}\mathrm{N}$ |
| Alpha particle | $X(\alpha,\gamma)Y$ | ${}^{12}\mathrm{C}(\alpha,\gamma){}^{16}\mathrm{O}$ |
| Electron, in atomic context | not usually a nuclear reaction of this type | treated separately in electron capture |
The shorthand notation
$$
X(a,\gamma)Y
$$
means nucleus $X$ captures particle $a$ and emits a gamma ray, leaving nucleus $Y$.
Why Gamma Rays Are Often Emitted
After capture, the nucleus usually has excess energy. That energy can come from the kinetic energy of the incoming particle and from the binding energy gained when the particle joins the nucleus. The nucleus often releases this excess energy by emitting one or more gamma rays.
So the process often looks like this:
$$
X + a \rightarrow Y^* \rightarrow Y + \gamma
$$
Here, $Y^*$ means the nucleus is excited. The gamma ray carries away energy and sometimes angular momentum.
Radiative capture means capture followed by gamma-ray emission:
$$
X + a \rightarrow Y + \gamma
$$
This is one of the most common forms of capture reactions.
Neutron Capture
Neutron capture is especially important because neutrons are uncharged. Since there is no Coulomb repulsion between the neutron and the nucleus, even slow neutrons can often be captured.
A typical neutron capture reaction is
$$
{}^{238}\mathrm{U} + n \rightarrow {}^{239}\mathrm{U} + \gamma
$$
This process changes the mass number by 1, but the atomic number stays the same, because a neutron has no charge.
Neutron capture plays a major role in reactor physics, isotope production, and the formation of heavy elements in stars.
There are two broad ways to think about neutron capture at a simple level. Sometimes the neutron is directly absorbed and gamma rays are emitted. In other cases, the neutron first forms an excited compound nucleus, which then de-excites. The compound nucleus idea belongs more generally to reaction mechanisms, but capture reactions are often described this way.
Proton and Alpha Capture
Charged particles such as protons and alpha particles feel electric repulsion from the positively charged nucleus. This repulsion is called the Coulomb barrier. Because of this, charged-particle capture usually requires higher projectile energy than neutron capture.
For proton capture,
$$
{}^{A}_{Z}X + p \rightarrow {}^{A+1}_{Z+1}Y + \gamma
$$
the mass number increases by 1 and the atomic number also increases by 1.
For alpha capture,
$$
{}^{A}_{Z}X + \alpha \rightarrow {}^{A+4}_{Z+2}Y + \gamma
$$
the mass number increases by 4 and the atomic number increases by 2.
These reactions are very important in astrophysics, where nuclei in hot stellar interiors can capture protons or alpha particles and build heavier elements.
Conservation in Capture Reactions
As in all nuclear reactions, certain quantities must be conserved. For capture reactions, the most visible changes are in mass number and charge.
| Quantity | Rule in capture reaction |
|---|---|
| Mass number | Final total equals initial total |
| Electric charge | Final total equals initial total |
| Energy | Conserved |
| Momentum | Conserved |
| Angular momentum | Conserved |
For example, in neutron capture,
$$
{}^{A}_{Z}X + {}^{1}_{0}n \rightarrow {}^{A+1}_{Z}Y + \gamma
$$
mass number gives
$$
A + 1 = A+1
$$
and charge gives
$$
Z + 0 = Z
$$
For proton capture,
$$
{}^{A}_{Z}X + {}^{1}_{1}p \rightarrow {}^{A+1}_{Z+1}Y + \gamma
$$
charge gives
$$
Z + 1 = Z+1
$$
Always check conservation of mass number and electric charge when writing a capture reaction.
Energy Release and Q Value
Capture reactions often release energy. If the final nucleus is more tightly bound than the initial system, the reaction has a positive $Q$ value.
For a general capture reaction,
$$
X + a \rightarrow Y + \gamma
$$
the $Q$ value is
$$
Q = \left(m_X + m_a - m_Y\right)c^2
$$
if the gamma ray is treated as carrying the released energy and the masses are rest masses of the nuclei involved.
A positive $Q$ means energy is released. That energy usually appears as gamma-ray energy, kinetic energy of the products, or both.
Because this chapter is about capture reactions specifically, the main point is that capture often leaves the nucleus excited, and the released binding energy is commonly emitted as gamma radiation.
A Visual Picture
The picture below shows the basic idea of a neutron capture event.
The incoming neutron is absorbed by the nucleus $X$, producing an excited nucleus $Y^*$. Then the nucleus emits a gamma ray and settles into a lower-energy state $Y$.
Importance of Capture Reactions
Capture reactions are important for several reasons. They create new isotopes, they help build heavier nuclei, and they are central in many practical and natural processes.
In nuclear reactors, neutron capture can produce useful isotopes or remove neutrons from the chain reaction. In astrophysics, capture reactions help explain how elements are formed inside stars. In laboratories, capture reactions are used to study nuclear structure and to create radioactive nuclei for medicine and research.
Capture Versus Other Reaction Types
It is useful to distinguish capture from other reaction types at a basic level.
| Reaction type | What happens |
|---|---|
| Elastic scattering | Projectile bounces off, no change in internal nuclear state required |
| Inelastic scattering | Projectile leaves, nucleus is excited |
| Capture reaction | Projectile is absorbed by the nucleus |
| Transfer reaction | One or more nucleons are exchanged between projectile and target |
In capture, the projectile does not emerge as a separate outgoing particle in the simplest description. Instead, it becomes part of the final nucleus.
A capture reaction is different from scattering. In scattering, the projectile remains separate after the interaction. In capture, it is absorbed into the nucleus.
Simple Examples
Consider these examples:
$$
{}^{14}\mathrm{N} + n \rightarrow {}^{15}\mathrm{N} + \gamma
$$
The nitrogen nucleus captures a neutron and becomes a heavier nitrogen isotope.
$$
{}^{27}\mathrm{Al} + p \rightarrow {}^{28}\mathrm{Si} + \gamma
$$
The aluminum nucleus captures a proton and becomes silicon.
$$
{}^{12}\mathrm{C} + \alpha \rightarrow {}^{16}\mathrm{O} + \gamma
$$
The carbon nucleus captures an alpha particle and becomes oxygen.
These examples show the pattern clearly. The captured particle changes the identity or isotope of the target nucleus, and gamma emission often follows.
Final Perspective
Capture reactions are nuclear reactions in which the target nucleus absorbs the incoming particle. The most common beginner examples are radiative capture reactions, where the new nucleus emits a gamma ray to lose excess energy. Neutron capture is especially important because neutrons face no Coulomb barrier, while proton and alpha capture require enough energy to overcome electrostatic repulsion. Capture reactions are fundamental in reactors, isotope production, and stellar nucleosynthesis.