# Do molecular bounded systems shield or reduce neutron cross-sections?

When talking about neutron cross-sections, literature is usually investigating isolated cases of Neutron + Atom. Here, the abundance of hydrogen is dominating neutron fluxes through material.

I wonder whether the reflection or capture propability of neutron radiation changes when the flux is penetrating a system of (organic) molecules. I can imagine two effects potentially reducing the neutron cross-section for bounded hydrogen:

1. The dense grid of organic material (folded proteins etc, imagine thick tree or a croud of humans) could be able to shield their hydrogen atoms from beeing struck by neutrons. Assuming organic material to be much denser (nuclei/volume) then other material like soil, rocks.

2. Neutrons are not able to transfer their whole energy to the hydrogen nucleus when it is electrically bounded (p is bounded to its electron, which is bounded to the electrons of the molecular system, which introduces inertia to the protons ability to move). Concluding that the capability of slowing down neutrons is reduced compared to free hydrogen.

Is this complete non-sense or could there be a measurable influence to neutron fluxes when using (a) non-organic or (b) organic material, containing the same amount of hydrogen?

• Thermalizing neutrons to make deuterium I recall we used tubs of water or paraffin and the density was all that really mattered, or amount of hydrogen per cc. – C. Towne Springer Apr 9 '14 at 4:23

Essentially no.

Being neutral the neutron interacts with electrons only magnetically and constraints on bound electrons suppress this very strongly. So, to a neutron an atom mostly looks like a nucleus sitting in space.

Likewise the neutron's electromagnetic interaction with the nucleus is strongly suppressed.

That leaves the strong nuclear interaction which has a range on order of $\approx 10^{-15}\,\mathrm{m}$.

Now, compare the size of atoms ($\approx 10^{-10}\,\mathrm{m}$) with that of nuclei ($\approx 10^{-14}\,\mathrm{m}$). Now notice that the cross-sectional area goes by the square of that ratio.

The result is that even in a very large and complicated molecule like a protein the "outer" atoms provide very, very little shielding for the "inner" ones.

• (1) Ofcourse the interaction of neutrons is only by collision with the nucleus, and not electromagnetic. I meant that the proton/nucleus might not be able to take over the neutrons momentum because it then also has to accelerate its electron shell, which is bounded to other molecules. – Martin Feb 7 '14 at 16:31
• (2) So the propability to hit a nucleus is tiny, but just as is it to hit a hydrogen nucleus. Then, a doubled material density does not make a difference in neutron flux? – Martin Feb 7 '14 at 16:40
• I'll have to wait to reformulate a proper answer, but short versions... (1) depends a lot on the energies in volved, but at most scales that is not a problem---there could be scales where it is (2) the neutron cross-section scales roughly by nuclear radius squared, so by nuclear mass to the 2/3 meaning by density to the 2/3. – dmckee --- ex-moderator kitten Feb 7 '14 at 19:49

From an energy perspective, a free neutron sees a nucleus as a three-dimensional square well with a depth of a 5--10 MeV. The presence or absence of milli-eV thermal oscillations or eV-scale molecular bonds may change the details of the shape of that potential well, but in general the change is much less important than the uncertainty in the neutron's energy or momentum.

There are a few exceptions. Neutron diffraction from a crystal is very different from neutron scattering by a gas of the same material; for the same reasons, neutron diffraction from solid hydrogen or solid oxygen would be very different from neutron diffraction by water ice. In a few systems with very low density of states (most famously, parahydrogen) very cold neutrons don't have enough energy to excite molecular transitions, and therefore have a much lower scattering cross section than higher-energy neutrons. Absorption cross sections, however, are generally (and reasonably) treated as being completely independent of the environment of the absorbing nucleus.

I suppose it's likely that a nuclear isomer (that is, a long-lived nuclear excited state) would have a different neutron capture cross section than the ground state of the same nucleus.

• Do know published work in these differences and how large they are? I am particularily interested in the difference between neutron scattering (i.e. elastic cross sections) of neutrons comparing the materials: (1) liquid water, (2) solid water (snow pack), (3) water vapor, (4) organic molecules. Assuming all materials have the same number of hydrogen in it, to what amount would the moderation lengths be different? – Martin Feb 26 '16 at 23:03
• A web search reveals a large literature; I suggest you construct a follow-up question if you can' t find what you're looking for. – rob Feb 29 '16 at 22:09

http://www.ncnr.nist.gov/resources/activation/
Running the numbers suggests composition, density, and pathlength account for real world observations
http://www.sbfisica.org.br/bjp/files/v35_850.pdf
with a foonote
http://en.wikipedia.org/wiki/Small-angle_neutron_scattering
or two, all consistent with only nuclei being important for hot neutrons.
http://www.fys.ku.dk/~willend/Neutron1_4.pdf

http://en.wikipedia.org/wiki/Atomic_form_factor#Magnetic_scattering
Neutron magnetic lattice scattering has low energies uncovering small footnotes in kind, especially atomic form factors from outer electron envelopes. If you wish to experiment, contrast C_nH_2n: high density polyethylene d = 0.97 g/cm^3 versus TPX polymethylpentene d = 0.83 g/cm^3.