8.5.1.1. Reaction Notation

Table of Contents

Reading nuclear reaction symbols

In nuclear physics, a reaction is written in a compact symbolic form that tells you what particle hits a target, what products come out, and what nucleus is left behind. This shorthand is called reaction notation.

A general nuclear reaction can be written as

$$
a + A \rightarrow b + B
$$

Here, $a$ is the incoming particle, often called the projectile. $A$ is the target nucleus. After the interaction, $b$ is an outgoing particle, and $B$ is the residual nucleus, meaning the nucleus that remains after the reaction.

This notation is useful because it summarizes the essential event in one line.

Standard form of a nuclear reaction

A more complete way to write nuclei includes both the mass number and the atomic number:

$$
{}^{A}_{Z}X
$$

where $X$ is the chemical symbol, $A$ is the mass number, and $Z$ is the atomic number.

So a full reaction may look like

$$
{}^{14}_{7}\mathrm{N} + {}^{4}_{2}\mathrm{He} \rightarrow {}^{17}_{8}\mathrm{O} + {}^{1}_{1}\mathrm{H}
$$

This means that a nitrogen 14 nucleus is struck by an alpha particle, and the products are oxygen 17 and a proton.

In any correctly written nuclear reaction, the total mass number and the total atomic number must balance on both sides of the equation.

Compact reaction notation

Very often, nuclear reactions are written in an even shorter form:

$$
A(a,b)B
$$

This means

$$
a + A \rightarrow b + B
$$

For example,

$$
{}^{14}\mathrm{N}(\alpha,p){}^{17}\mathrm{O}
$$

means that an alpha particle $\alpha$ strikes nitrogen 14, a proton $p$ comes out, and oxygen 17 is left behind.

In this notation, the target is written first, then in parentheses the incoming particle and outgoing particle, then the residual nucleus.

Common particle symbols

Nuclear reaction notation uses short symbols for frequently occurring particles. Some of the most common are shown below.

Symbol	Meaning	Nuclear form
$p$	proton	${}^{1}_{1}\mathrm{H}$
$n$	neutron	${}^{1}_{0}\mathrm{n}$
$d$	deuteron	${}^{2}_{1}\mathrm{H}$
$t$	triton	${}^{3}_{1}\mathrm{H}$
$\alpha$	alpha particle	${}^{4}_{2}\mathrm{He}$
$\gamma$	gamma ray photon	${}^{0}_{0}\gamma$

A gamma ray has no mass number and no charge in the balancing sense, so it is written with zero values in formal notation.

How to interpret a reaction

Consider the reaction

$$
{}^{27}_{13}\mathrm{Al}(p,\alpha){}^{24}_{12}\mathrm{Mg}
$$

This should be read as follows. A proton hits aluminum 27. An alpha particle is emitted. The remaining nucleus is magnesium 24.

You can check it by balancing the numbers.

For mass number:

$$
27 + 1 = 24 + 4 = 28
$$

For atomic number:

$$
13 + 1 = 12 + 2 = 14
$$

So the notation is consistent.

Special notations for different reaction types

Some reactions involve capture of a particle and emission of radiation. For example,

$$
{}^{1}_{1}\mathrm{H}(n,\gamma){}^{2}_{1}\mathrm{H}
$$

This means a proton captures a neutron and emits a gamma ray, producing deuterium.

Another common case is when the incoming particle is absorbed and no massive particle comes out except the new nucleus and perhaps radiation. The notation still follows the same pattern.

For example,

$$
A(n,\gamma)B
$$

means neutron capture with gamma emission.

Natural language reading of notation

It is helpful to learn how to say reactions aloud. Here are some examples.

Notation	How to read it
${}^{59}\mathrm{Co}(n,\gamma){}^{60}\mathrm{Co}$	Cobalt 59 captures a neutron and emits a gamma ray, becoming cobalt 60
${}^{10}\mathrm{B}(n,\alpha){}^{7}\mathrm{Li}$	Boron 10 absorbs a neutron and emits an alpha particle, leaving lithium 7
${}^{235}\mathrm{U}(n,f)$	Uranium 235 absorbs a neutron and undergoes fission

In the last example, $f$ is often used informally to indicate fission, because the exact fragments are not written in the short form.

Excited nuclei in notation

Sometimes the residual nucleus is produced in an excited state. This is often shown with an asterisk:

$$
{}^{12}\mathrm{C}(p,p'){}^{12}\mathrm{C}^{*}
$$

The star means the nucleus is excited. The symbol $p'$ means the outgoing proton is not the same state as the incoming one, it is simply a proton leaving after the interaction. This notation is common in scattering and excitation reactions.

Gamma emission may follow later when the excited nucleus returns to a lower energy state.

An asterisk, $^*$, indicates an excited nuclear state. It does not mean a different element, only a higher energy state of the same nucleus.

Elastic and inelastic style notation

In some reactions, the same kind of particle goes in and comes out. For example,

$$
A(n,n)A
$$

This indicates neutron scattering from the nucleus. If the nucleus remains in the same state, this is often elastic scattering. If the nucleus is left excited, one may write

$$
A(n,n')A^{*}
$$

The prime symbol indicates that the outgoing particle is of the same type but may have different energy after the interaction.

Reaction notation and missing information

Reaction notation is compact, but it does not always show everything. It usually tells you the participants, but not the energies, angles, or probabilities. Those topics belong to reaction energetics and cross sections.

Still, the notation gives the basic identity of the process, which is the first thing physicists need.

Visual layout of a reaction

The flow of a nuclear reaction can be pictured simply.

Rendering scientific sketch…

Basic structure of a nuclear reaction

This picture shows the projectile $a$ approaching the target $A$, followed by emission of particle $b$ and formation of residual nucleus $B$.

A quick method for checking notation

When you see a nuclear reaction, verify two things. First, count total mass number on both sides. Second, count total atomic number on both sides. If either one fails, the notation is incorrect.

For example, in

$$
{}^{6}_{3}\mathrm{Li} + {}^{1}_{0}\mathrm{n} \rightarrow {}^{4}_{2}\mathrm{He} + {}^{3}_{1}\mathrm{H}
$$

mass numbers give

$$
6 + 1 = 4 + 3 = 7
$$

atomic numbers give

$$
3 + 0 = 2 + 1 = 3
$$

So the reaction notation is balanced.

Always check nuclear notation by conserving mass number $A$ and atomic number $Z$:
$$
\sum A_{\text{left}} = \sum A_{\text{right}}, \qquad \sum Z_{\text{left}} = \sum Z_{\text{right}}
$$

Why this notation matters

Reaction notation is the language used to describe nuclear processes in textbooks, laboratories, reactors, and particle beams. Once you can read forms like $A(a,b)B$, you can quickly recognize what enters the reaction, what leaves, and what new nucleus is created.

That makes reaction notation the starting point for understanding all later questions about nuclear reactions.

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