It is called strong nuclear force.
The weak and strong nuclear forces are the main reasons
Between protons and neutrons exist the residual strong force (nuclear force).
The "strong force," or sometimes called the "strong nuclear force." This is the exchange of gluons between the protons and neutrons.
In a small nucleus, such as oxygen, xenon, or any of the lighter elements, the strong force generated by the protons and neutrons is stronger than the repulsion between protons, and the nucleus holds together. In a larger nucleus, such as uranium, curium, or the heavier elements, the strong force isn't strong enough to hold it together, and the electromagnetic force pulls it to pieces.
The strong atomic force holds protons (and neutrons) together in the nucleus.
Electrically the protons repel each other, right? So what keeps them united? The answer is that there is a stronger force between nucleons - protons and neutrons. This force is called the "strong force". The strong force between two protons is not strong enough to keep them together (against the electrostatic force); but if there are some neutrons present, the situation changes, because the strong force acts between protons, but also between protons and neutrons.
Yes, the strong force carried by meson exchanges between protons and/or neutrons.
It appears that you have some confusion about the particle physics inside the nucleus. Nothing "separates protons so that the strong force can hold the nucleus together", the strong force acts via the exchange of particles called mesons. The atomic nucleus contains particles called protons and neutrons. The strong force binds the protons and neutrons together via the exchange of particles called mesons between those protons and neutrons.
The residual strong force. The strong force (or color force) is what holds quarks together to form protons and neutrons. The residual strong force then holds the protons and neutrons together in the nucleus.
An atom is composed by a nucleus where protons and, in case, neutrons are joined by the so called strong force, and a number of electrons equal to the number of protons in the nucleus. Electrons are in equilibrium around the nucleus (in a stable state) due to electromagnetic attraction between their negative charges and the positively charged protons in the nucleus. In the nucleus, the strong force (that is the net result of inter-quarks forces that emerges out of protons and neutrons) is stronger with respect to electromagnetic repulsion between positively charged protons, so that the nucleus is in a stable state (protons do not repel each other) even if it is formed by all positive and neutral particles.
Two main forces act in an atom, the electromagnetic force and the strong force. The electromagnetic force pulls the nucleus apart, while the strong force holds it together. Both neutrons and protons contribute to the strong force, but only protons contribute to the electromagnetic force. If an atom has too many protons and not enough neutrons, the electromagnetic force will overpower the strong force, and the nucleus will rip apart into more stable forms.
Inside the atomic nucleus and much more strongly between the quarks inside the protons and neutrons.