Nucleons (protons and neutrons) are held together by the residual strong force — the leftover of the color force between quarks, carried between nucleons mainly by pion exchange (Yukawa, 1935). Its potential falls off exponentially, unlike gravity or electromagnetism:
V_strong(r) = -g · (r₀/r) · e^(-r/r₀) for r > r_core
V_strong(r) = +core repulsion for r < r_core (Pauli/quark repulsion)
V_Coulomb(r) = k·q₁q₂ / r (protons only)
Every simulated nucleon pair contributes both terms; the engine integrates F = -∇V for every pair each frame (a real N-body relaxation), so the cluster you see settles into whatever configuration balances attraction, the short-range repulsive core, and Coulomb repulsion.
- Protons Z / Neutrons N — set the nucleus composition. More protons means more mutual Coulomb repulsion, but neutrons add strong-force "glue" without adding charge — which is why stable nuclei need extra neutrons as Z grows.
- Strong-force strength g — scales the residual strong-force coupling. Turn it down and you can watch Coulomb repulsion win — the same competition that limits how large a nucleus can be and drives fission and alpha decay in real heavy elements.
- Coulomb toggle — switch off electromagnetic repulsion entirely to see the strong force acting alone: nucleons pack into a dense, roughly incompressible sphere, matching the real nuclear "liquid drop" picture where density stays constant regardless of size.
- Binding energy — the (negative) sum of all pairwise potential energies. A more negative number means a more tightly bound, more stable nucleus, mirroring real binding-energy-per-nucleon curves that peak around iron-56.
Because the strong force has such short range, each nucleon only really "feels" its nearest neighbors — it saturates. Coulomb repulsion, in contrast, adds up between every pair of protons (∝ Z²) with no such cutoff. That mismatch is the real reason no stable nucleus exists forever as protons are added — eventually Coulomb wins, exactly as this simulation lets you demonstrate directly.