Nuclear Forces and Why Nuclei Hold Together

Two Competing Interactions Inside the Nucleus

Inside a nucleus, every proton and neutron (nucleons) experiences two key interactions that compete with each other:

• Strong nuclear force (attractive): binds nucleons together, but only when they are extremely close. It is effectively a short-range force.
• Electrostatic (Coulomb) force (repulsive between protons): pushes protons apart and acts over a long range compared with nuclear sizes.

Nuclear stability is largely a balance: the strong force must “win” at short distances to overcome proton–proton repulsion, but the Coulomb repulsion grows as more protons are packed into the same small region.

Qualitative Force–Range Diagrams: What “Short Range” and “Long Range” Mean

A useful way to reason about nuclear binding is to sketch force (or potential energy) versus separation distance between two nucleons. You do not need exact numbers; the shape and range are the key ideas.

1) Strong nuclear force: attractive only at very small separations

Qualitatively, the strong interaction between nucleons behaves like this:

• At very small separation, it is strongly attractive (binding).
• Beyond a few femtometers (a few nuclear diameters), it drops off rapidly and becomes negligible.
• At extremely tiny separations, there is often described an effective “hard core” repulsion (nucleons do not collapse into one point), but for stability arguments the main point is the short attractive range.

Strong force (qualitative) vs distance r  (not to scale)  Attraction  ^  |        ________  |       /        \  |______/          \__________  |  |----------------------------------> r        short range (falls to ~0 quickly)

This short range is crucial: a nucleon only “feels” strong attraction from a limited number of nearby neighbors.

Continue in our app.

• Listen to the audio with the screen off.
• Earn a certificate upon completion.
• Over 5000 courses for you to explore!

Or continue reading below...

Download the app

2) Coulomb repulsion: weaker per pair, but long range and cumulative

For two protons, the Coulomb force is repulsive and decreases gradually with distance, but it never truly “turns off” the way the strong force does:

Coulomb repulsion between protons vs distance r (qualitative)  Repulsion  ^  |\  | \  |  \  |   \  |    \________________________  |----------------------------------> r        long range (decreases slowly)

Even though the Coulomb interaction between any single pair of protons is not as strong as the strong nuclear attraction at very short distances, it has two advantages from the “repulsion” point of view: it acts over the whole nucleus and it adds up over many proton pairs.

Saturation: Why the Strong Force Does Not Keep Getting Stronger in Big Nuclei

A defining property of nuclear binding is saturation: each nucleon interacts strongly only with a limited number of nearby nucleons, because the strong force is short-range. This has two major consequences:

• Binding per nucleon does not grow without limit as you add more nucleons. Adding more nucleons mostly adds new “local” bonds, not global ones.
• Nuclear density stays roughly constant across many nuclei: nucleons pack to a typical spacing, and adding more nucleons mostly increases the nuclear size rather than compressing it.

By contrast, Coulomb repulsion between protons is not saturated in the same way: every proton repels every other proton, including those on the far side of the nucleus.

Local-neighbor picture (a mental model)

Imagine nucleons as people in a crowded room:

• The strong force is like a “handshake” that only works if you are close enough to touch. Each person can only shake hands with a few neighbors.
• Coulomb repulsion is like everyone with the same magnetic polarity: you feel a push from many others across the room, not just your immediate neighbors.

This is why, as nuclei get larger, the total attractive benefit per nucleon from the strong force tends to level off, while the total repulsive cost from proton–proton interactions keeps increasing.

Why Neutrons Are Essential for Stability

Neutrons play a special stabilizing role because they contribute to strong nuclear binding without adding Coulomb repulsion.

Neutrons add attraction without adding proton–proton repulsion

• Adding a neutron increases the number of strong-force “bonds” available (neutron–proton and neutron–neutron interactions contribute to binding).
• But adding a neutron does not increase Coulomb repulsion, because neutrons are electrically neutral.

So, for a nucleus with many protons, additional neutrons can help “dilute” the proton fraction and provide extra strong-force binding to counter the growing repulsion among protons.

Why stable nuclei tend to need more neutrons as Z increases

As the number of protons increases, the Coulomb repulsion grows significantly because the number of repelling proton pairs increases rapidly. To remain bound:

• The nucleus benefits from having more neutrons than protons at higher proton numbers.
• This shifts the balance toward more strong-force attraction per proton without increasing repulsion.

Qualitatively: small nuclei can be stable with roughly similar numbers of protons and neutrons, but heavier stable nuclei generally require a neutron “excess.”

Why Very Large Nuclei Become Harder to Bind

Two qualitative trends make very large nuclei increasingly difficult to keep stable:

1) Coulomb repulsion grows faster than strong-force benefit

Because Coulomb repulsion is long-range, each added proton repels many existing protons. Meanwhile, due to saturation, the added nucleon only gains strong-force attraction from nearby neighbors. This mismatch means:

• Attraction per nucleon tends to saturate (levels off).
• Repulsion associated with protons keeps accumulating as the nucleus grows.

Eventually, the nucleus can be bound but only marginally, and it becomes more prone to processes that reduce Coulomb stress (for example, splitting into two fragments or emitting a helium nucleus), because those processes reduce the number of protons in a single charged object.

2) Geometry: surface versus interior nucleons

In a finite nucleus, nucleons near the surface have fewer close neighbors than nucleons in the interior, so they experience less strong-force binding. As nuclei grow, the fraction of nucleons on the surface decreases, but surface effects still matter for how binding changes with size. The key qualitative point for stability is:

• Strong binding depends on having neighbors within the short range.
• Coulomb repulsion does not care whether a proton is at the surface or interior; it still contributes to the overall repulsive energy of the charged nucleus.

Practical Step-by-Step: Using Force-Range Ideas to Predict Relative Stability

The goal here is not to compute exact binding energies, but to make qualitative predictions about which nuclei are more likely to be stable based on size and proton fraction.

Step 1: Identify what changes when you add a proton versus a neutron

• Add a neutron: increases strong-force attraction with nearby nucleons; adds essentially no Coulomb repulsion.
• Add a proton: increases strong-force attraction with nearby nucleons and increases Coulomb repulsion with all other protons.

So, at higher proton counts, adding neutrons is often a more “efficient” way to increase binding than adding protons.

Step 2: Use the range argument (local vs global)

Ask: is the change mostly local or global?

• Strong force: local (short range) → benefit from an added nucleon is limited to nearby neighbors.
• Coulomb: global (long range) → cost from an added proton is spread across interactions with many protons.

This is why large proton-rich nuclei are disfavored: the global repulsion grows while the local attraction saturates.

Step 3: Apply the saturation idea to “big nucleus” intuition

For small nuclei, adding nucleons can significantly increase binding because each new nucleon can find neighbors and form strong-force bonds. For large nuclei:

• Each nucleon still only bonds strongly with nearby nucleons (saturation).
• But each additional proton increases the total Coulomb repulsion noticeably.

Therefore, stability becomes more delicate as nuclei get heavier, especially if the proton fraction is high.

Step 4: Compare two nuclei by proton fraction (qualitative)

If two nuclei have similar size (similar total nucleons) but one has more protons:

• The more proton-rich nucleus has more Coulomb repulsion.
• Unless it also has enough neutrons to provide extra strong binding, it is more likely to be unstable.

If two nuclei have similar proton number but one has more neutrons:

• Adding some neutrons can increase binding (more strong-force neighbors) without increasing Coulomb repulsion.
• But too many neutrons can also lead to instability (the nucleus may prefer to convert a neutron to a proton through beta processes), so there is a “preferred band” of neutron-to-proton ratios for stability.

Guided Prediction Questions (Size and Proton Fraction)

Use the short-range vs long-range and saturation ideas to answer these. Write your reasoning in terms of: (1) local strong attraction, (2) global Coulomb repulsion, (3) neutron role.

Questions about adding nucleons

• If you start from a nucleus and add one neutron, what changes in the balance of forces? What if you add one proton instead?
• For a nucleus with many protons, which addition is more likely to improve stability: adding a neutron or adding a proton? Why?

Questions about proton fraction

• Consider two nuclei with the same total number of nucleons, but nucleus A has a higher fraction of protons than nucleus B. Which is more likely to be stable? Explain using Coulomb repulsion and saturation.
• Why does the “need” for extra neutrons generally increase as nuclei get larger?

Questions about very large nuclei

• As nuclei become very large, which effect grows more problematic: the short-range nature of the strong force or the long-range nature of Coulomb repulsion? Explain.
• Why does saturation imply that adding more nucleons does not indefinitely increase binding per nucleon?

Ranking exercises (qualitative)

For each set, rank from more likely stable to less likely stable, and justify:

• Set 1: a medium-size nucleus with balanced protons/neutrons; a similar-size nucleus that is more proton-rich.
• Set 2: a heavy nucleus with many protons and relatively few neutrons; a heavy nucleus with many protons and more neutrons.
• Set 3: a small nucleus with a modest proton number; a very large nucleus with a high proton number.