There are two problems when forming a neutron star -- you have to get something with roughly the mass of a few suns, and you have to compact it into a 10-mile or so radius. The only way to support the mass at that size is via neutron pressure. Electron degeneracy won't do it (hence the collapse from white dwarf to neutron star).
Current thinking is that the core is iron/nickel, with a few other radioactive decaying things in there to generate heat (along with the gravitational "squishing").
A neutron star is the remnant of a star that was once several times more massive than the Sun. When their nuclear fuel is depleted, they explode as a supernova. The remaining dense core is slightly more massive than the Sun but has a diameter typically no more than 12 miles (20 kilometers).
The remaining dense core is what I was referring to.
Also it seems that that core would be more DENSE than the sun, not more MASSIVE. IIRC, MASS is a factor of DENSITY and SIZE, or am I losing it?