# Why is metallic hydrogen degenerate matter?

Why is metallic hydrogen considered a form of degenerate matter, akin to neutronium and electron-degenerate matter? I can understand that for the other two, degeneracy pressure is the only force countering inward gravity for very massive stars, but how does this concept also apply to super pressurised hydrogen? Furthermore, why would being supported by degeneracy pressure make the hydrogen metallic in nature?

• I do not know enough about the theory of metallic hydrogen to answer the question how close it gets to being degenerate or if there is a perfectly degenerate state similar to superconductivity in it for some parameter of pressure range. My gut feeling tells me, that degeneracy will lead to a free electron gas, which is usually the criterion for calling something a metal, so the two properties are necessarily (?) somewhat related. Once you have a free electron gas, the optical properties etc. are similar to ordinary metals, so it would make degenerate hydrogen "shiny" in some frequency range. – CuriousOne Sep 5 '14 at 19:13
• Has someone been reading Robitaille's work? If you are, please see this thread; if not, ignore me! – Kyle Kanos Oct 15 '14 at 0:40

Papers I have seen talk about a possible transition taking place at hundreds of GPa at 300K. If this were a perfect gas of hydrogen atoms, the electron number density would be $\sim 10^{31}$ m$^{-3}$, with a Fermi kinetic energy of $3\times 10^{-17}$ J (187 eV). The degeneracy parameter, $E_F/kT \sim 7000$, would represent a very degenerate gas.