Neutron data is found in the Evaluated Nuclear Data Files (ENDFs).
All that is needed for reactor calculations is supposed to be there: cross sections, anisotropy, collision parameters, energy-angle distribution of outgoing neutrons, etc. Values of cross sections are usually given for energies of the incoming neutron comprised between 1.e-5 eV and 20 MeV. The upper limit is chosen because no neutron with higher energy exist in a reactor (but they do exist in accelerators and in the upper atmosphere!).
Several families of evaluations exist in the world: ENDF/B (USA), JEFF (Europe), JENDL (Japan), CENDL (China), BROND (Russia). They are regularly updated every few years. Sometimes they agree, other times not so much. When they don't agree, it is hard to known which is right 🙁; when they do agree, it is hard to know if they haven't just copied each other 🙁.
Nuclear data found in ENDF files is not suitable for utilization in Monte-Carlo (or even deterministic) codes. They need to be processed by the Data Processing codes.
In the Resolved Resonance Range (RRR) the cross sections are frequently described by their resonance parameters. This description need to be transformed into a simple point-wise representation adapted to linear interpolation between energy points (point-wise reconstruction in the free-gas region).
In the Unresolved Resonance Range (URR), where only average resonance parameters are known, this knowledge need to be transposed into a probability tables representation.
Cross sections are given at 0 Kelvin. They need to be brought at the application temperature by performing a Doppler broadening.
Anisotropies are usually given in a Legendre polynomials representation, which needs to be converted into a (mu, P(mu)) probability distribution function.
The product of the processing code need to be stored in a file to be used by the Monte-Carlo code. A popular format nowadays is the ACE format, originally agreed between NJOY (the processing code of Los Alamos) and MCNP (the Monte-Carlo code of Los Alamos). Others codes may use other formats.