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Looking at explanations of neutron stars, the neutrons towards the center of the star are stabilised by the enormous pressure, and so don't undergo nuclear decay. I am wondering if this is possible under different circumstances. Could uranium nuclei experience this sort of stability if they were put under enormous pressure?

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It is not the pressure that is responsible, it is the presence of a dense, degenerate electron gas. The pressure is incidental.

If the electron Fermi energy is high enough, then beta decay is blocked because the maximum energy of the decay electron is lower than the Fermi energy, and so there are no unoccupied states available for the decay electron.

238U undegoes alpha decay. This could not be blocked in the same manner because the alpha particle is a boson. However, the next stage in the decay chain, the beta decay of 234Th could be blocked at high densities.

However, you then have to think about just how high the electron Fermi energy is. It is going to be high enough to initiate electron capture reactions that will turn the thorium into more neutron-rich nuclei.

Similar considerations apply to the 235U decay chain. The initial alpha decay to thorium would not be blocked, but the following beta decay could be.

In neutron star crusts you ened up with an equilibrium mixture where the energy density of the material is minimised. At high densities, the peak of the binding energy per nucleon curve, which is usually shown in the low-density limit with a peak around 56Fe, is pushed to heavier, more neutron-rich materials. Whether 238U or 235U ever sit near the peak of the binding energy per nucleon curve at high densities is unlikely. A review of neutron star crust physics by Chamel & Haensel (2008) suggests that even at densities beyond $10^{16}$ kg/m$^3$, the proton number of the equilibrium nuclei does not rise above 50, whilst the neutron number can exceed 1000.

In other words, whilst you might stop the initial decay chain (ultimately eneding in lead), you would just end up creating more neutron-rich nuclei instead. You wouldn't be able to preserve the uranium.

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