What is a neutron's polarizability? It is undergraduate textbook level knowledge that atoms are polarizable – that is, they become electric dipoles in electric fields due to the deformation of the electron wave function(s). Intrinsically, this is because the atom is a composite object that has a spatial extent. It is possible to produce crude formulae for the polarizability of atoms.
Neutrons and protons, being baryons, are also composite objects that have a spatial extent (radius around $1\operatorname{fm}$). Thus, they should be polarizable. What is the polarizability of these objects? Is it in line with crude models?
A quick search reveals results like this for the neutron's polarizability, that references an experimental value of $9\times 10^{-4} \operatorname{fm}^{-3}$ (in cgs units), but a more comprehensive overview, with a description of how to do the crude calculation would be appreciated.
 A: The "crude model" that you link to is, essentially, dimensional analysis. It states that the polarizability $\alpha$ should more-or-less obey
$$
\frac\alpha{4\pi\epsilon_0} \approx a^3
$$
where $a$, which must have units of length, is the only length scale available in the problem: the radius-or-diameter of the atom's charge distribution.
For hydrogen, we have the "Bohr volume" $\frac{4\pi}3 a_0^3 \approx \frac12\rm\,Å^3$ and, experimentally, $\alpha/4\pi\epsilon_0 \approx \frac23\rm\,Å^3$.
Larger atoms tend to be more polarizable than smaller atoms, as well.
If we guessed that the similarly-normalized polarizability for the neutron were comparable to the neutron's volume, we'd be in for a bit of a shock: the neutron's volume is $\frac{4\pi}3 \rm(1\,fm)^3$ but its polarizability has been measured to be about a factor of a thousand smaller, $10^{-3}\rm\,fm^3$.
But a neutron doesn't look very much like a neutral atom, either.
An atom has a pointlike positive charge at the center and most of its (central) volume has roughly uniform negative charge.
The neutron seems to have a negative core, a positive skin, and a negative halo.
Perhaps this multi-component charge distribution allows a sort of Schiff screening to reduce the apparent dipole effect?
Or perhaps, if your model for distribution of charge within the neutron is that it spends some fraction of its time as a virtual proton or delta orbited by a virtual pion, the strong interaction between those components is so "stiff" that the electric field just doesn't disturb it very much?
The reference you found in your question is a 2009 report on a lattice QCD computation which gets the neutron polarizability wrong by a factor of three.
If that was the state of the art eight years ago, it's probably fair to complain that "crude calculations" of the neutron polarizability are the best that anybody can do right now.
