KAHIBARO
Table of Contents
What changes in a charge exchange reaction
A charge exchange reaction is a nuclear reaction in which the participating nuclei change their electric charge, but the total number of nucleons is redistributed without greatly changing the overall mass number. In simple terms, a proton in a nucleus can be turned into a neutron, or a neutron can be turned into a proton, through the interaction with an incoming particle. Because protons and neutrons have different charge, the nucleus changes from one chemical element to another.
This kind of reaction is especially important because it reveals how nuclei can change their internal identity, not just bounce apart or absorb a particle. It is closely related to the weak interaction in some contexts, but in nuclear reaction language the main idea is that the nuclear charge changes during the collision.
A general symbolic form is
$$
a + X \rightarrow b + Y
$$
where the projectile $a$ becomes the outgoing particle $b$, and the target nucleus $X$ becomes the residual nucleus $Y$. In a charge exchange reaction, the charge of the projectile changes, and the target nucleus changes charge in the opposite way so that total electric charge is conserved.
In a charge exchange reaction, total electric charge is always conserved, even though the charge of each individual nucleus may change.
A basic example
One of the most common examples is the $(p,n)$ reaction. A proton enters the target nucleus and a neutron leaves:
$$
p + {}^{A}_{Z}X \rightarrow n + {}^{A}_{Z+1}Y
$$
Here the projectile changes from a proton to a neutron. Since the outgoing particle has one unit less positive charge, the target nucleus must gain one unit of positive charge. Its atomic number increases from $Z$ to $Z+1$.
Another common example is the $(n,p)$ reaction:
$$
n + {}^{A}_{Z}X \rightarrow p + {}^{A}_{Z-1}Y
$$
Now the projectile changes from a neutron to a proton, so the residual nucleus loses one unit of positive charge.
These reactions often leave the mass number $A$ of the target nucleus unchanged. What changes is the atomic number $Z$.
Why the name "charge exchange"
The phrase "charge exchange" comes from the fact that the projectile and target effectively exchange charge character. For example, in a $(p,n)$ reaction the incoming proton emerges as a neutron, while inside the nucleus a neutron effectively becomes a proton. The total effect looks like an exchange of charge between projectile and nucleus.
This does not mean that a literal electric charge packet is handed from one object to another. Instead, it means that the identities of nucleons change in a way that preserves the total charge.
Relation to nuclear structure
Charge exchange reactions are very useful tools for studying nuclear structure. They can connect one nucleus to a nearby isobar, meaning a nucleus with the same mass number but a different atomic number. Because of this, they probe transitions between closely related nuclear states.
For example, if a nucleus has a state that differs mainly by changing a neutron into a proton, then a $(p,n)$ or $(n,p)$ reaction may excite that state strongly. This gives physicists information about how protons and neutrons are arranged and how they interact inside the nucleus.
A useful way to think about this is shown below.
Common forms
Several kinds of charge exchange reactions are widely used in experiments. The table below shows some examples.
| Reaction type | Example form | Change in target nucleus |
|---|---|---|
| $(p,n)$ | $p + {}^{A}_{Z}X \rightarrow n + {}^{A}_{Z+1}Y$ | $Z \to Z+1$ |
| $(n,p)$ | $n + {}^{A}_{Z}X \rightarrow p + {}^{A}_{Z-1}Y$ | $Z \to Z-1$ |
| $({}^{3}\mathrm{He},t)$ | ${}^{3}\mathrm{He} + X \rightarrow t + Y$ | usually $Z \to Z+1$ |
| $(t,{}^{3}\mathrm{He})$ | $t + X \rightarrow {}^{3}\mathrm{He} + Y$ | usually $Z \to Z-1$ |
Here $t$ means a triton, which is the nucleus of tritium, containing one proton and two neutrons.
These reactions are chosen because the incoming and outgoing particles differ mainly by one unit of charge, making them natural probes of charge-changing transitions in nuclei.
Conservation laws in charge exchange
Like all nuclear reactions, charge exchange reactions must satisfy the usual conservation laws. The most important ones here are charge conservation, nucleon number conservation, energy conservation, and momentum conservation.
For a typical $(p,n)$ reaction,
$$
p + {}^{A}_{Z}X \rightarrow n + {}^{A}_{Z+1}Y
$$
the total charge before the reaction is
$$
(+1) + Z = Z+1
$$
and after the reaction it is
$$
0 + (Z+1) = Z+1
$$
so charge is conserved.
The total number of nucleons is also conserved. The incoming proton contributes one nucleon, and the outgoing neutron is also one nucleon.
For charge exchange reactions, the key bookkeeping rule is that the atomic number $Z$ of the nucleus changes, while the mass number $A$ often stays the same.
Energy considerations
A charge exchange reaction can occur only if the energy conditions allow it. The reaction energy is described by the $Q$ value,
$$
Q = \left(m_{\text{initial}} - m_{\text{final}}\right)c^2
$$
If $Q > 0$, the reaction releases energy. If $Q < 0$, energy must be supplied by the projectile. Many charge exchange reactions have threshold energies because the final particles and nucleus may have slightly larger total mass than the initial system.
In practice, even when the reaction is allowed, the outgoing particle energy also depends on whether the final nucleus is left in its ground state or in an excited state.
Physical interpretation inside the nucleus
Inside the target, a charge exchange reaction can often be pictured as one nucleon changing type. In a $(p,n)$ reaction, the net nuclear effect is
$$
n \rightarrow p
$$
inside the target nucleus. In a $(n,p)$ reaction, the net nuclear effect is
$$
p \rightarrow n
$$
This makes charge exchange reactions very sensitive to the proton-neutron degree of freedom in nuclei. They are therefore powerful tools for studying transitions that involve changes in isospin.
A full treatment of isospin belongs to more advanced nuclear physics, but at a beginner level it is enough to know that protons and neutrons are closely related nuclear particles, and charge exchange reactions probe that relationship directly.
Experimental importance
Charge exchange reactions are often used to investigate nuclear transitions that are difficult to study in other ways. By measuring the energy and angle of the outgoing particle, physicists can infer which state of the final nucleus was produced.
Such reactions are important in the study of beta-like nuclear transitions. Even though beta decay and charge exchange reactions are not the same process, they can connect similar nuclear states. Because of this, charge exchange measurements can provide valuable information about weak transition strengths in nuclei.
A simple comparison with other reaction types
It helps to contrast charge exchange reactions with a few other nuclear reaction types.
| Reaction type | Main feature |
|---|---|
| Elastic scattering | Particles separate with no change in internal identity |
| Inelastic scattering | Nucleus is excited, but particle identities usually stay the same |
| Capture reaction | Projectile is absorbed |
| Transfer reaction | One or more nucleons are transferred between nuclei |
| Charge exchange reaction | Nuclear charge changes, often with the same mass number |
The unique feature of a charge exchange reaction is not merely that something enters and something exits, but that the proton-neutron balance changes.
Example of reaction bookkeeping
Consider
$$
{}^{14}\mathrm{N}(p,n){}^{14}\mathrm{O}
$$
Written fully, this means
$$
p + {}^{14}_{7}\mathrm{N} \rightarrow n + {}^{14}_{8}\mathrm{O}
$$
Check the conservation laws.
Before the reaction, total mass number is
$$
1 + 14 = 15
$$
After the reaction, total mass number is
$$
1 + 14 = 15
$$
Before the reaction, total charge is
$$
1 + 7 = 8
$$
After the reaction, total charge is
$$
0 + 8 = 8
$$
So both are conserved, while the target nucleus changes from nitrogen to oxygen.
Key idea to remember
Charge exchange reactions are nuclear reactions in which the charge state of the nucleus changes because a proton is effectively converted to a neutron or a neutron is effectively converted to a proton during the interaction. They are especially valuable for connecting nuclei with the same mass number and different atomic number.
A charge exchange reaction changes the element, because the atomic number changes. It often does not change the mass number of the nucleus.