For Reactor physics and particle transport calculations, weather the neutron is considered as quantum or classical particle? why?
It depends on the scale/process you are looking at. When looking at the neutron-induced nuclear reactions there are quantum effects, e.g. in the anisotropy of the scattered neutrons. However, when looking at the statistical behavior of (billions of) neutrons in a reactor, the classical laws of thermodynamics (Boltzmann equation) apply and quantum effects are embedded in nuclear data libraries. So this is decoupled in fact.
For most cases the movement of the neutrons described as classical, but the cross-sections of interaction with nuclei are essentially quantum e.g.
https://en.wikipedia.org/wiki/Neutron_cross_section#Microscopic_versus_macroscopic_cross_section
http://web.ihep.su/dbserv/compas/src/breit36/eng.pdf
Whether to treat it as a particle or a wave depends on the computer's performance at the moment rather than which is physically more correct.
When an atom scatters a neutron, it can be in all directions. If we treat it as a particle, we can use Monte Carlo simulations to determine the single direction in which it will be scattered by drawing a "lottery" weighted by the probability of being scattered. By repeating the simulation many times, we can cover a large number of scattering patterns to understand the system. The probability distribution of scattering used for the simulation is given by experimental data or quantum mechanical calculations.
On the other hand, if we treat the scattering as a wave, then the scattering is a superposition of waves scattered in all directions. In a transport code, one has to keep track of thousands of times of scatterings per neutron. Even if there were only two times, we would first have to write down all the waves resulting from the first scattering and then superimpose all the waves from the second scattering, which could occur in any direction.
It is actually a very good question. It is discussed in Appendix III of "The slowing down and thermalization of neutrons" by Mike Williams. And, yes, the conclusion is that the classical Boltzmann equation with quantum mechanical scattering laws is accurate for reactor physics and transport applications.
The argument goes that you are usually in the classical limit of Uehling-Uhlenbeck equation -the quantum Boltzmann equation-, and the density is low enough that you do not need to consider Fermi-Dirac statistics. I definitely recommend you to read MMRW's book.
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