KAHIBARO
Table of Contents
What This Force Is
Inside the nucleus, protons and neutrons stay packed together in a very tiny region. This is surprising at first, because protons are positively charged and electrically repel each other. There must therefore be another force, much stronger at short distances, that holds the nucleus together. This force is called the strong nuclear force, often just the nuclear force in introductory nuclear physics.
At the level of nuclei, the strong nuclear force acts mainly between nucleons, meaning protons and neutrons. It is the force responsible for nuclear binding. Without it, nuclei could not exist except perhaps a single proton by itself.
The strong nuclear force in nuclear structure is the force that binds protons and neutrons together inside the nucleus, overcoming the electric repulsion between protons at very short distances.
Why It Is Needed
If only the electric force acted inside a nucleus, then the protons would push one another apart. Yet many nuclei are stable. This tells us that the attractive force between nucleons must be stronger than the electric repulsion over nuclear distances.
A simple comparison helps. The typical size of a nucleus is about
$$
10^{-15}\ \text{m}
$$
which is called a femtometer, or fm. At such tiny separations, the strong nuclear force becomes dominant. At much larger distances, it quickly becomes negligible, unlike gravity and electromagnetism, which extend over long ranges.
Main Features of the Strong Nuclear Force
The strong nuclear force between nucleons has several important characteristics.
It is very strong, but only over a short range. It is attractive at typical distances between nucleons in the nucleus, which allows binding. At extremely small separations, it becomes strongly repulsive, preventing nucleons from collapsing into the same point. This short distance repulsion is important for the structure and stability of nuclei.
It also acts nearly the same between proton-proton, neutron-neutron, and proton-neutron pairs, if we ignore electric effects. This approximate independence from charge is one reason protons and neutrons can be treated as very similar particles in many nuclear models.
The table below summarizes the basic picture.
| Property | Description |
|---|---|
| Strength | Very strong at nuclear distances |
| Range | Very short, about a few fm |
| Effect at medium nuclear distance | Attractive |
| Effect at extremely small distance | Repulsive |
| Depends strongly on electric charge | No, approximately charge independent |
A key idea is that the strong nuclear force is not simply attractive at all distances. It is attractive over the range needed for binding, but becomes repulsive at very short distances.
Range of the Force
The strong nuclear force does not reach far beyond the nucleus. Its effective range is roughly a few femtometers. Because of this, each nucleon mainly interacts with nearby nucleons, not with every nucleon in a large nucleus equally strongly.
This short range explains why nuclear density is nearly constant across many nuclei. Adding more nucleons mostly increases the size of the nucleus rather than packing everything much more tightly.
A rough sketch of the force behavior as distance changes is useful. At intermediate nuclear distances, the interaction is attractive. At very small distance, it turns repulsive. At larger distance, it falls rapidly toward zero.
Strong Nuclear Force and Binding
A nucleus is bound when the total effect of the attractive nuclear interactions is enough to keep the nucleons together. In a stable nucleus, the strong nuclear force wins over the electric repulsion, at least within the nuclear size.
For light nuclei, this is often easier because there are fewer proton-proton repulsions. For heavier nuclei, more neutrons are needed to provide extra nuclear attraction without adding extra electric repulsion. This is one reason heavy stable nuclei tend to contain more neutrons than protons.
Relation to the Fundamental Strong Interaction
At a deeper level, protons and neutrons are made of quarks, and quarks interact through the fundamental strong interaction. That more basic interaction is described by quantum chromodynamics. Inside nuclei, however, we usually do not work directly with quarks and gluons. Instead, we describe the effective force between nucleons.
So, in nuclear structure, the strong nuclear force is best thought of as a residual effect of the more fundamental strong interaction. It is somewhat similar in spirit to how neutral molecules can still attract each other even though their internal electric charges are balanced.
The force between nucleons in a nucleus is not the full fundamental quark level strong interaction. It is a residual strong interaction acting between protons and neutrons.
Meson Exchange Picture
A useful historical and conceptual model is that nucleons interact by exchanging mesons. In particular, pion exchange helps explain why the nuclear force has a short range. A particle with mass does not mediate a long range force as effectively as a massless particle does.
This idea gives a rough reason for the limited range of the nuclear force. By contrast, the electromagnetic force is carried by photons, which are massless, so it has infinite range.
We do not need the full mathematical theory here, but the qualitative conclusion is important. The short range of the strong nuclear force is connected to the fact that the effective carriers in the nucleon picture are massive.
Comparison With Other Forces
It is helpful to compare the strong nuclear force with gravity and electromagnetism.
| Force | Relative strength in nucleus | Range | Acts on |
|---|---|---|---|
| Strong nuclear force | Dominant at very short distance | Short | Nucleons |
| Electromagnetic force | Important between protons, repulsive | Long | Electric charge |
| Gravity | Negligible in nuclei | Long | Mass |
Gravity is far too weak to matter in ordinary nuclear structure. Electromagnetism matters because protons repel one another. The strong nuclear force is what makes nuclei possible.
A Simple Physical Picture
You can imagine nucleons as particles that prefer to stay close, but not too close. If they are at a suitable separation, the force attracts them and forms a bound nucleus. If they are pushed extremely close together, the repulsive core prevents collapse. If they are too far apart, the force becomes too weak to hold them.
Summary
The strong nuclear force is the short range force that binds protons and neutrons in the nucleus. It is much stronger than electric repulsion at nuclear distances, attractive over the distances needed for binding, and repulsive at extremely short separations. It acts approximately the same between different kinds of nucleon pairs and is understood as a residual effect of the deeper strong interaction between quarks.
Essential facts to remember:
$$
\text{Strong nuclear force} \Rightarrow \text{binds nucleons in the nucleus}
$$
$$
\text{Range} \sim \text{a few fm}
$$
It is attractive at typical nuclear separations, repulsive at very short distances, and strong enough to overcome proton-proton electric repulsion inside nuclei.