As has been mentioned, you cannot view a neutron star like a regular star. You may or may not know that a neutron on its own is not stable; it will decay in ~11 minutes (off the top of my head). Yet, neutron stars apparently do not decay, at least according to our limited understanding of them. This can draw parallels between a neutron star and an atomic nucleus- which is where most neutrons exist and where they can remain stable.
So, basically, you need quantum mechanics to be able to understand such a system. This doesn't look so good, because even something like the neucleus of say a uranium atom is rather complicated. And instead having a few tens of particles, a neutron star would have... yikes, something like 10^57 neutrons***!? Thats a fair amount. Treating a neutron star like one incredibly massive atomic neucleus is a very appealing idea to me, although I doubt this works beyond being an analogy.
*** calculation
Wiki says neutron stars are 1.3-2.1 solar masses, so on the same order of magnitude as our sun which has a mass of 2x10^30 kg. A neutron has a mass of 1.6x10^-27 kg. 57 orders of magnitude of difference. Assuming that all or at least the vast majority of a neutron star is in fact neutrons.