# Neutron Degeneracy Pressure Calculations

Today I was having a discussion with a colleague about what would happen if you took a 1 cm cube of neutron star matter and set it on the earth. He thought it would fall through and I was trying to explain why it wouldn't

But that got me thinking... You could never do this experiment as the degeneracy pressure would blow it apart. So I began to try to find calculations about how much energy this would create... John Timlin wrote a paper (http://www.physics.drexel.edu/~bob/Term_Reports/John_Timlin.pdf) where he has many calculations starting with the Fermi energy in N Space, etc. However, as I read this, it seems to rely on the particles to be at 0K degrees.. which does not make sense. ON page 5 he even says this does not make sense.

His calculations are for a meter cubed and come out to 5.24*10^33 kg/ms(^2)

I have 2 questions....

1. Is there a way to convert this to the amount of energy released with the pressure blows the neutrons apart from each other?

2. Would the neutrons be damaged from being bound so close together? You would think that this force would somehow affect them....

Ok 3rd question.... What would happen after the neutrons separated from each other? Would they decay N ---> P+e+Ve? like normal?

• I recommend pruning your question so that it complies with the Stack Exchange "one question per question" rule. – PM 2Ring Mar 9 '19 at 8:18
• As for question 2, the density in a neutron star is mostly comparable to nuclear density, so the neutrons don't experience damaging distortion. OTOH, see en.wikipedia.org/wiki/Quark_star Regarding question 3, yes the neutrons would decay. In a neutron star, beta decay is suppressed, as explained in the top 2 answers here. – PM 2Ring Mar 9 '19 at 8:29

The first part of your question is fully answered by my answer to this question What would happen to a teaspoon of neutron star material if released on Earth?

The kinetic energy of the neutrons amounts to $$\sim 10^{33}$$ J/m$$^3$$ at typical neutron star densities of a few $$10^{17}$$ kg/m$$^3$$, which is the same order as the pressure. All of this is released if the neutron star material is suddenly unconfined.

I don't really follow what you mean by the neutrons being "damaged". Neutrons at typical nuclear densities are of course perfectly stable -- as they are in normal nuclei. If the density is significantly higher then it is possible that the increased Fermi energies of the neutrons will lead to them turning into new hadronic species like kaons, pions, sigma or lambda particles. Alternatively, their quarks may achieve "asymptotic freedom" at very high densities and behave like three fermion gases (strange quarks would also be present at these energies). It is speculated that some or all of these things may happen in the cores of neutron stars at densities of $$\geq 10^{18}$$ m$$^{-3}$$, which are several times that of normal nuclear matter.

Finally, yes, free neutrons at low densities will decay on the usual ten minute timescales. Neutrons in a high density gas will not, because beta decay is blocked by degenerate electrons - see What stabilizes neutrons against beta decay in a neutron star?

This is very hypothetical, because there is no way to transport a $$cm^3$$ of neutron matter to earth (because of the large neutron degeneracy pressure, there is no suitable container).

If it could be done, it would result in a very substantial explosion. The energy density (Fermi energy) of neutron matter amounts to a few percent of the rest mass energy, similar to what you get in a nuclear weapon (but a lot more material).

The pressure would quickly accelerate the material, and the shock front quickly reaches a velocity close to the speed of light (the Fermi velocity is roughly 25$$\%$$ of $$c$$).

On this time scale both gravity (it is a lot of mass, but gravitational acceleration is independent of mass) and neutron decay (life time is 10 min) are irrelevant. Finite temperature effects are also irrelevant, the Fermi energy of neutron matter is much bigger than the temperature. Finally, the density in neutron matter is not large compared to atomic nuclei, so neutrons are not strongly modified.