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If we consider the perspective that the neutron star is just a very large atom, then theoretically (disregarding that the smallest possible neutron star is kilometers in diameter) from the hydrogen atom to the neutron star, there'd be a continuous transition from being treated as a quantum system to one that is classical. And how do we view such a transition? Would it be possible to treat a small neutron star just like an atom?

seilgu
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    Do you mean just a very large nucleus? – G. Smith Jan 01 '20 at 12:38
  • The interior can be regarded as a Fermi gas of neutrons, but you seem to mean something else. The crust is complicated. –  Jan 01 '20 at 13:07
  • @G.Smith yes, a large nucleus. – seilgu Jan 01 '20 at 13:21
  • @Pieter I mean, if you can consider its interior as Fermi gas and surface as crust, what prevents you from considering the nucleus of Uranium as having a crust? – seilgu Jan 01 '20 at 13:22
  • I don't understand the question. Seems to me that if you're looking at scales where classical physics works (e.g. calculating the orbits of planets around a neutron star), then you use classical mechanics; if you're in the strong gravity regime, you use GR; if you're looking at the structure, you use QM. – Allure Jan 01 '20 at 14:06
  • If you’re talking about its true nature as a quantum or classical system, then it’s quantum at a fundamental level (probably) and you’ll need a quantum theory of gravity to even hope for an analytical solution to the problem. Otherwise you’re stuck with semi-classical approximation schemes. – Thatpotatoisaspy Jan 01 '20 at 14:43
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    A neutron star really isn't a giant nucleus. See, for example, https://physics.stackexchange.com/a/275716/123208 Rob Jeffries has written several other great answers about neutron star structure. – PM 2Ring Jan 01 '20 at 15:51

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The neutron star is a hybrid of classical and quantum physics. Both disciplines are required to understand its structure.

Take the simple example of hydrostatic equilibrium. In Newtonian mechanics (a classical theory) this can be written as $$\frac{dP}{dr} = - \rho g\ ,$$ where $P$ is the pressure, $\rho$ is the density and $g$ is the local gravitational acceleration; all of which depend on radial distance form the centre. In General Relativity (also a classical theory) the right hand side is modified by three multiplicative terms that take accont of the curvature of spacetime and the contribution of pressure and kinetic energy density to the mass-energy.

But to solve this equation we need to know how the pressure depends on the density and composition, and in turn how the composition might depend on the density. Both of these require quantum descriptions of the behaviour of indistinguishable fermions and the behaviour of the strong and weak nuclear forces on small scales.

ProfRob
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Nucleus of uranium is very, very complicated system, a much harder to describe accurately than neuron star. It is so, because neutron star is a gigantic quantum, composed system, which can be described with great accuracy via thermodynamics and statistical physics. It is just such big object, we may use just proper collective dynamics to describe it, and fluctuations, quantum or thermal, are nearly zero.

On the other hand, uranium nucleus, consists of few hundreds particles, and for such small system, its dynamic is dominated by quantum mechanics of many body systems ( and as you probably know, you cannot solve equations precisely even for three particles in general setting).. What is more, depending on energy regime, a lot of models of nuclear matter have to be used, and from that point of view it is whole menagerie of possible situations: it may behave like very hot fluid, it may consists of neutrons and protons, it may be described as quark soup ( because quarks are completely free when confined in barions, so in some circumstances, they may behave like one bag of quarks) etc etc.

But basically, your idea is correct: neutron stars and uranium nucleus have a lot similarity. Because of matter they're build of. From the other side you are completely wrong, because of neglecting size and energy per particle, of such big object vs small one.

Consider the thing like glass of water and very, very small droplet. It is a water. But from other point of view, it has completely different behaviour and physical properties: glass of water is just bulk matter, tiny droplet dynamics is dominated by surface tension and various properties of water steam and fluctuations. It's billion times bigger difference between uranium nucleus and neuron star.

kakaz
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