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The setup is very simple: you have a regular ($1.35$ to $2$ solar masses) evolved neutron star, and you shine plane electromagnetic waves on it with given $\lambda$. Very roughly, what shall be the total flux of absorbed/scattered EM radiation?

Shall the result change if the neutron star is young and not evolved?

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A neutron star will have a thin layer of normal matter at the surface, and of course this reflects light just like any other normal matter.

But I guess you're really asking if neutronium reflects light, and that's a very good question that a quick Google failed to answer. EM radiation generally interacts with dipoles or scatters off electrons, so I'd guess matter made of neutrons should be transparent.

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AFAIK, neutron star $\neq$ neutronium, neutronium $\implies$ " $n$ revolving around $\bar{n}$ atoms". Neutron star\implies "pure $n$ with atomic matter shell. –  Manishearth Mar 23 '12 at 12:44
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Scratch that, neutronium=pure neutrons. Wierd--the rest of the particles become particle-antiparticle pairs when appended with -onium. –  Manishearth Mar 23 '12 at 12:46
    
Thank you for your answer and for the reference, it is actually very relevant! –  Alexey Bobrick Mar 23 '12 at 12:55
    
Would the index of refraction be the same as vacuum or would it be a giant lens? This comment says the magnetic moment of the neutrons could still interact with EM? –  endolith Mar 23 '12 at 18:39
    
There would be a reasonable gravitational redshift near the surface of a star - so you would expect it to red-en the reflected light –  Martin Beckett Mar 23 '12 at 20:08
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A neutron star is mostly neutrons, but it contains protons to a certain extent allowed by the gravity, since a pure neutron state is unstable to beta decay. The protons collect on the surface due to their electrostatic repulsion, and form a fermi-gas like state there.

The fermi-gas of protons will reflect long-wavelength light very much like an ordinary metal-- the surface will, if you scrape off the ordinary matter, be shiny like a mirror.

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Neutron star remains neutral due to charge conservation, so macroscopic motion of protons due to electrostatic forces will not happen. Another point to mention is that neutron stars have to have an atmosphere, as the surface pressure contiuously drops to zero (otherwise the surface would expand until the outer pressure gets to zero). Hence close to the surface in a thin layer there will be all sorts of physical states of matter. One definite conclusion from all this and from what you say, indirectly, is that neutron stars are not transparent. –  Alexey Bobrick Sep 9 '12 at 15:30
    
@AlexeyBobrick:yes, I agree, the electron gas neutralizing the proton is also like a metal. So you have two charged fluids reflecting light, it's still shiny once you scrape the ordinary matter off. –  Ron Maimon Sep 9 '12 at 15:47
    
This is right. Though the atmosphere could make it look lika a metal in a thin hydrogen cloud, with some wierd layers in between (strong magnetic field, high gradients of species distribution, etc.) –  Alexey Bobrick Sep 10 '12 at 17:58
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Martin, the infalling light is blue-shifted, and red-shifted on reflection. No overall change, I think. However, a suitably mechanically strong light-source on the surface of the neutron star (!) will be seen to emit light that is redder than usual.

If the neutron star had its normal matter scraped off (left as an exercise for the student) then I don't see how light would interact at all with it. Hard gamma rays would be absorbed, but anything else? Nah.

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Neutrons have a dipole moment, and there is a proton gas density in neutron stars, which should reflect light like a shiny metal. –  Ron Maimon Aug 23 '12 at 6:08
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