neutron elastic collision energy distribution

Question

I'm interested in nuclear physics and want to accurately model nuclear reactions involving neutrons. I need to be able to calculate the the probability of each possible energy after an elastic collision with a particle of known weight. For example, if a neutron with a kinetic energy of $1$MeV hits a nucleus that weighs $100$ times as much as a neutron the neutron will end up with between $\approx0.961$MeV and $1$MeV depending on how direct the collision is. The wikipedia page for neutron moderator says that the energy lost per collision is on average $\approx\frac{2}{A+1}$ where $A$ is the mass ratio. I've noticed that using the neutron moderator equation on wikipedia gives an average energy loss of ~half the maximum possible so I assume the distribution is energy distribution symmetric.

Answer 1

No, the distribution is not symmetric in any sense.

First-principle calculation of the energy loss per collision depends on calculating the probabilities of various modes of excitation of the nucleus. HEP codes such as Geant 3 and Geant 4 have functions for this built in; the data comes from years of experimental measurements.

You say you are interested in the situation for nuclei which are about 100 times the neutron mass. A further complication arises if you want scattering cross-sections for nuclei about twice that heavy, namely, that the data for those elements is classified.