Do neutron stars reflect light? 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?
 A: Neutron stars are usually assumed to have intrinsic spectra that approximate  closely to black bodies - though the details are many and need a full consideration of the strong magnetic fields and electrodynamics near the surface. They have a thin layer (few cm) of non-degenerate, gaseous material at their surfaces, rich in ionised or partially ionised iron-peak elements. However, accretion from the ISM possibly means that most neutron stars have a skin of hydrogen or helium present.
Modelling of neutron star atmospheres is well established (I found this review by Potehkin (2014) extremely useful). Isolated, non-magnetic neutron stars have spectra that are close, but not identical to black bodies.There can be absorption features if there are significant densities of iron-peak elements in the atmosphere. H/He atmosphere have spectra shifted towards higher energies. Strong magnetic fields introduce more complications, including cyclotron absorption lines. In these models the neutron star is unlikely to be very reflective because by definition, something that approximates a blackbody absorbs most radiation incident upon it. Some isolated neutron stars have now been observed at X-ray wavelengths and their spectra are close to blackbodies with some evidence for broad absorption features that might be due to cyclotron lines (e.g. Haberl 2005). 
However, there is an idea that in some neutron stars, the outer atmosphere may be cool enough and/or the magnetic field strong enough to cause a phase transition to a solid state just below a very thin hydrogen atmosphere (Turolla et al. 2004). In these circumstances the surface can become (partially) reflective. Potekhin et al.(2012) considered a condensed iron surface in strong magnetic fields ($10^{12}-10^{14}\ G$) covered by a very thin atmosphere. They find certain photon energy ranges where the reflectivity can reach of order 50 percent.
Older neutron stars will have lower temperatures and probably lower magnetic fields. The ionisation state of the atmosphere will change and the effects of magnetic fields would diminish.
A: 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.
A: 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.
A: 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.
