# Proton-Neutron Lattice as a form of matter?

Would it be possible for a lattice of protons and neutrons (I'm picturing a plane of hexagons in my head) to exist bound by the strong nuclear force (not gravity)? I know that the strong force losses its power when an atomic nucleus gets to be too large, but in a lattice, it would only have to bond one proton to a few neutrons or one neutron to a few protons at a time. Would this work? If so, what would be the properties of such a material?

## 2 Answers

No, because the repulsive power of the protons accumulates toward infinity, blowing the structure apart. To accomplish what you have described you would need stable, negatively charged particles like antiprotons... which of course also fail in such an arrangement because they annihilate the protons!

The instability from accumulating positive charge is also why higher elements become unstable.

You can create crystalline structures that are composed mostly of neutrons with electron-neutralized protons sprinkled in, but only if you have very powerful compression to keep the neutrons stable and the whole arrangement bound together. That's the material in neutrons stars, sometimes called "neutronium" (yes, as in Star Trek), and it's very, very stiff. Breaks in the neutron crusts of such stars lead to abrupt changes in the otherwise incredibly precise timing of pulsar radio bursts.

• What do you mean that the repulsive power of the protons accumulates towards infinity? The decrease in intensity of the effect of the postive charge of the inverse square law would mean that only protons "in range" can affect a local area of the lattice, right?
– John
Apr 26, 2012 at 13:10
• the potential energy of the repulsion goes like $1/r$, but the number of protons repelling you goes like $r^2$ (surface area of the sphere.) $1/r *r^2 = r$ so the energy density blows up horribly. Apr 26, 2012 at 19:43
• Wait, neutron star matter isn't liquid? Sep 9, 2019 at 7:00
• The traditional model is that the interior of the neutron star is a superconducting fluid, but the outer crust is crystalline. Sep 9, 2019 at 11:51

A lone proton in between a crystal lattice could find itself with more negative charge then equilibrium from the neighbouring clouds of electrons. Thus there is a compressive force driven by the lattice and heat, in addition to proton repulsion of the nuclear force.

I expect over time their will be a determination that the coulomb barrier may not be static under all conditions and because it is not yet understood it's difficult to replicate working Low Energy Nuclear reactions. However the anomalous results show something is happening. That can only mean that the understanding is incomplete based on observations to date.