Why does the nuclear volume scale (roughly) linearly with number of nucleons?

Question

As far as I know, it is the fermi repulsion that gives a collection of protons or neutrons its finite size. But this only acts on indistinguishable fermions. If the protons and neutrons do not repel each other by any other means, there would be no reason why adding neutrons to a nucleus would increase the volume of the collection of the protons.

What I'm asking, I think, is how protons and neutrons repel each other in the nucleus. Is it because of a repulsive term in the strong/weak force? Or is it fermi repulsion resulting from neutrons and protons continuously changing into each other through $W^{+/-}$ and $\pi^{+/-}$ exchange?

Answer 1

It's Fermi repulsion between the quarks in the nucleons, not between protons and neutrons, that prevents the overlap.

You wouldn't claim that a hydrogen and helium atom should overlap because they are distinguishable - obviously you need to consider the repulsion between the electrons they are made of. The same argument applies to nucleons.