Has a free neutron ever been shown to absorb/emit/interact with a photon? Protons only 'interact with' very high-energy photons, whether inside a nucleus or free, right?  I'm assuming the same about neutrons....
Neutrons have a small magnetic moment and a slight electric 'moment' (dipole?), correct?  They are sometimes considered to consist of a negative charge surrounding a positive charge?
I would assume that neutrons, in a nucleus or free, interact with photons even less often than protons, and that the gamma photon has to have an even higher energy than one interacting with a proton....
Lastly, I have read about 'photodisintegration', in which a nucleon is kicked out of a nucleus by a gamma ray.  It seems to happen to neutrons sometimes...
But, I am mostly curious about experimental evidence of free neutrons interacting with photons, how often it happens compared to free protons, and whether the interacting photon's energy has to be extremely high, higher even than a photon interacting with a proton...
 A: Low-energy photons can scatter just fine off both protons and neutrons.
When a photon scatters off a proton, the low-energy cross section in natural units is a numerical factor times $\alpha^2/M^2$, where $\alpha$ is the fine-structure constant and $M$ is the proton mass.
(Source: https://en.wikipedia.org/wiki/Thomson_scattering)
When a photon scatters off a neutron, the low-energy cross section in natural units is a numerical factor times $\alpha^2 E^2/M^4$, where $E$ is the photon energy in the frame of the neutron. (Here $M$ is now the neutron mass, but this is close to the proton mass so we don’t need to distinguish them.)
(Source: http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?bibcode=1993ApJ...417...12G&db_key=AST&page_ind=0&plate_select=NO&data_type=GIF&type=SCREEN_GIF&classic=YES)
Thus low-energy photon scattering off a neutron is less likely than the scattering off a proton by a numerical factor times $E^2/M^2$.
It is less likely because photon-neutron scattering involves the magnetic dipole moment of the neutron while photon-proton scattering involves the electric monopole moment (i.e., charge) of the proton.
I will let someone else discuss the experimental evidence. I will trust QED, which we know works extremely well.
