I want to consider the possibility of a very light particle being captured by a neutron star. (For the purpose of discussion, let us allow the neutron star mass (or radius) a tunable parameter, so that we can have the neutron star be on the verge of becoming a black hole.)
On one hand, the neutron star has a huge gravitational attraction, and should capture anything that passes near it.
On the other hand, if the de Broglie wavelength is large, I would think this should indicate that the wave is less likely to be scattered by the neutron star.
But for a very massive neutron star, I would imagine that the de Broglie wavelength should be gravitationally blue-shifted rather significantly, which would indicate a much higher likelihood of the particle being captured by the neutron star since we are back to particle-particle scattering.
If the neutron star resides in a bose-einstein condensate fluid of many particles, what would happen? Would the particles near the neutron star be lifted out of the BEC if their de Broglie wavelengths become gravitationally blueshifted?
(Would it be reasonable to expect an axions (or some other very light particle condensate) to accumulate inside neutron stars?) I realize I asked lots of questions: I'm trying to get a feel for what this interaction would look like, and wanted to mention my line of thinking on this, in case I'm thinking of something the wrong way.