Which place use both, explain briefly. Is there any connection with compact stars?
Yes, if you take the liquid-drop model to describe nuclear matter and look at the terms, then for the infinite nuclear matter you can cross out the surface term. But the density will also be different for infinite nuclear matter. The connection with compact stars is that you cannot really expect nuclear matter to be the same in a very compact star, so you must try to extrapolate from what we can study on earth to stellar conditions.
Full agreement with the explanations of Elvira and the further precisions by Gry Merete.
Nuclear matter is a hypothetical substance consisting of huge number of nucleons ( protons and neutrons) interacting through nuclear forces only - no Coulomb forces. In an infinite nuclear matter volume and number of interacting nucleons are infinite, but the ratio of the two is finite. Infinite volume implies translational invariance which means absolute positions don't matter only difference in positions matter. Infinite volume also implies that there are no surface effects.
For compact stars such as neutron stars, the composition is not only neutrons( about 80%) and protons( about 10%) but also include electrons(10%) and does not exhibit translational invariance and is not necessarily charge neutral. Unlike nuclear matter, Neutron star's matter is therefore different type of matter called 'stellar matter' or 'neutron star matter'.
For finite regions and finite nuclei one would need a model that include surface effects and Coulomb interactions. The liquid drop model mentioned earlier by Gry is one such model.
Although most neutron stars are supposed to be made of neutrons, protons, electrons and muons, these particles are present in very different phases: the outermost past of the star is made of atomic nuclei arranged in a crystal lattice. At densities exceeding about ten thousand times that of ordinary matter, atoms are fully ionised by the pressure and become progressively more neutron rich with increasing depth. At some point, neutrons "drip out" of nuclei. The inner region of the crust therefore consists of neutron-proton clusters coexisting with free neutrons and electrons. As the density attains about half that found in heavy nuclei, the crust dissolves into a uniform mixture of nucleons and electrons. Muons appear at higher densities. Other particles may also be present in the core of the most massive neutron stars.
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