Nuclear fission reactors require the presence of a neutron moderator in order to sustain a chain reaction, as it slows down neutrons sufficiently in order for them to be absorbed by fuel (e.g. U-235) nuclei. While moderation is a consequence of interactions or ''collisions'' between neutrons and nucleons and is a process which occurs at the length scale of atomic nuclei, atoms are in most cases parts of larger molecules, which might in general have an anisotropic structure. Therefore, one would expect that when examining the problem of neutron transport on the molecular length scale, neutron transport and moderation are influenced by the molecular structure, since there exists an ''average/overall'' molecular scattering cross section. Furthermore, if all of the moderator molecules in some volume of space are aligned in a certain direction, one would expect the anisotropy to be also exhibited at macroscopic length scales.

Therefore, I'm interested by the following:

  1. Does molecular strucure and its anistropy directly influence nuclear moderation (is this statement true)?
  2. If the moderator is anisotropic on a macroscopic length scale, does this influence reactor operation (assuming a reactor architecture similar to usual BWR or PWR reactors)?
  3. Would there exist any benefits to the performance of a nuclear reactor if macroscopic moderation properties (cross section) can somehow by manipulated or tuned during operation?

I have previously come across the following articles: ''The Effect of Anisotropic Scattering Upon the Elastic Moderation of Fast Neutrons'' (https://www.tandfonline.com/doi/abs/10.13182/NSE71-A19668) and ''The Effect of Linearly Anisotropic Neutron Scattering on Disatvantage Factor Calculations'' (https://www.researchgate.net/profile/C_Siewert/publication/242048056_EFFECT_OF_LINEARLY_ANISOTROPIC_NEUTRON_SCATTERING_ON_DISADVANTAGE_FACTOR_CALCULATIONS/links/554350cd0cf24107d3949fc8.pdf), which discuss anisotropic scattering, but as far as I gathered it concerns anisotropy on the length scales of atomic nuclei, so I'm not entirely sure of the articles' relevance.

  • $\begingroup$ Seems to be a lot of effort for little gain. After the first scattering even, any anisotropy is now aligned in a direction different from the propagation of the neutron, so it doesn't do much. $\endgroup$
    – Jon Custer
    Sep 15, 2020 at 12:26
  • $\begingroup$ This is the case for liquid and gas moderators, such as water and hydrogen, but what about solids like carbon or berilium? Graphite e.g. consists of carbon atoms arranged in a lattice, so it should make sense for caron atoms to oscillate about their equilibrium positions after a scattering event, while their equilibrium positions remain static (excluding high energy neutrons knocking out carbon atoms). Do you think that if the underlying structure on which neutron moderation anisotropy depends remains unchanged during scattering, anisotropy doesn't change either? $\endgroup$
    – Eipijemin1
    Sep 16, 2020 at 8:40
  • $\begingroup$ My point was that moderation is a process involving many scattering events. After the first event the neutron trajectory is randomized with respect to any anisotropy. $\endgroup$
    – Jon Custer
    Sep 16, 2020 at 12:42

1 Answer 1


One small correction, fission reactors do not require moderation. There are a class of reactors called fast reactors that do not have any (or very little) neutron moderation. Modern Light Water Reactors (LWRs) are thermal reactors that do have moderation.

Yes, thermal cross sections can depend on molecular structure and anisotropic materials, but it is a relatively small effect. Fission neutrons start off at very high energies (MeV range) and the binding energies of molecules is much lower than the neutron energy (by many orders of magnitude), so the crystalline structure does not effect the scattering. However, as the neutrons slow down to thermal energies (less than 1 eV), the crystalline structure of the material can become more important to neutron scattering. At low energies, the neutrons will scatter off the entire molecule rather than individual atoms. In Monte Carlo codes, this effect is captured in "s(alpha,beta) tables".

The only material that I know of where material anisotropy matters is graphite.

Anisotropic neutron scattering means something else. In the references you gave, anisotropic scattering is referring to the preferential direction of neutron scatter after a collision. This is usually only important when a neutron hits a molecule with about the same mass (i.e. Hydrogen), but there is small effect for heavier nuclei, or neutrons with very high energy.


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