We think that they are made of free particles and the cores may be composed of neutron degenerate matter. But we don't know for sure and it's fairly complicated. You can look up neutron stars on...
As the name suggests, neutron stars are actually composed of neutrons. When there is a sufficiently strong gravitational field, atoms (or superheated plasma consisting of fragments of atoms)...
It's pretty complicated, and we really don't know what the core is actually like... some astrophysicists think it's mostly neutrons (hence the name "neutron star"), while others think it might be...