Neutron Absorption of Lead Nuclei compared to Uranium Nuclei

[Coxy1234]

I have had a question that I cannot get an answer for. I recently had an exam for energy in the nucleus which included a question about why lead nuclei would be inadequate for use as a moderator in a reactor. When I got the answer for the question, it stated that the lead nuclei reflect neutrons on account of the nuclei being "too heavy." This didn't make sense to me because the absorption of neutrons by uranium nuclei, being a much heavier substance, absorbs neutrons, not reflects. Can anyone explain this to me? I was told to post it here.

 

[Bill_K]

You want to use a light nucleus for a moderator because it's more efficient - each collision with a neutron removes more of the momentum. Good moderators are things like lithium, beryllium, carbon.

 

[Astronuc]

It's so much reflection as simply scattering with little energy loss per scatter, and as such, a neutron is more likely to leak out of a core containing lead, unless the enrichment is sufficiently high and the lattice is sufficiently small/tight.

Moderators are general composed of light elements, e.g., light water (H₂O), heavy water (D₂O), graphite (C), or Be/BeO. One also has to consider the parasitic absorption.

Uranium, like lead, would not make a good moderator.

Pb and Pb/Bi have been proposed for fast reactors. Fast reactors normally have enrichments on the order of 20% U-235 or equivalent Pu-fissile content, as compared to 5% or less for LWRs, and even less for CANDU reactors.

 

[Coxy1234]

Ok, but a Uranium is heavier than both the lead and, say, lithium nuclei. I still don't undertand why, say, a Uranium-235 or a Plutonium-239 nuclei can absorb the neutron when it simply shouldn't upon such grounds. Does it have to do with a combined strong nuclear force between sub-particles, or is there another step I'm missing?

 

[Astronuc]

Ok, but a Uranium is heavier than both the lead and, say, lithium nuclei. I still don't undertand why, say, a Uranium-235 or a Plutonium-239 nuclei can absorb the neutron when it simply shouldn't upon such grounds. Does it have to do with a combined strong nuclear force between sub-particles, or is there another step I'm missing?

U-233, U-235 and Pu-239 have the special property of being fissile. Pu-241 and other heavier transuranics are also fissile, as well as undergoing some level of spontaneous fission.

Moderators are the lightest of elements and they are used in some nuclear systems to slow done the fast fission neutrons to energies which increase the likelihood of capture by fissile nuclides and potentially resulting in fission. There is some probability that U-235 will absorb a neutron and rather than fission, it will simply emit a gamma and become U-236, which could fission, but more likely will absorb a neutron and become U-237, and so on. U-236 will decay by alpha emission to Th-232, or otherwise rarely undergo spontaneous fission, and U-237 will eventually decay by beta emission to Np-Np-237 respectively.

http://www.nndc.bnl.gov/chart/reCenter.jsp?z=92&n=144 (select Zoom 1 if one doesn't see the details)

Candu reactors moderated with heavy water can use low enrichment from natural to slighly higher around 1-1.6%. Light water reactors (LWRs) typically use enrichements on the order of 4 to 4.95% (just shy of 5%). Fast reactors use enrichments of ~20% U-235 or equivalent. Usually the cores are large compared to the mean free path of the neutron.

The smaller the core, the higher the enrichment to maintain criticality.

For nuclear reactors, one has also to consider the parasitic absorption and activation of the structural materials, moderator, and coolant. In CANDUs and LWRs, the coolant is the moderator. In nuclear reactors, the fuel is clad in a metal that helps retain fission products. In CANDUs and LWRs, the cladding is a special zirconium alloy, while fast reactors use various types of stainless steel (SS316 is an old standard, but now low swelling ferritic-martensitics are used.)

 

[Coxy1234]

Ok ok, I see what you're saying. But I need to know why the neutron is absorbed in the first place. Like you are saying, lighter element will not absorb the neutron. So why is it that the Uranium can absorb the neutron if the variable which defines an element or isotopes ability to take the neutron is it's weight?

 

[Astronuc]

Ok ok, I see what you're saying. But I need to know why the neutron is absorbed in the first place. Like you are saying, lighter element will not absorb the neutron. So why is it that the Uranium can absorb the neutron if the variable which defines an element or isotopes ability to take the neutron is it's weight?

Light elements can absorb neutrons. For example, the hydrogen nucleus (proton) will absorb (actually connect with) a neutron and form a deuteron. Now that usually requires a slow enough neutron. Above a certain energy, a neutron will just scatter of a proton, which will recoil. The proton get increased momentum and energy, the neutron slows down. A proton is the most effective particle for slowing neutrons, but it will absorb (combine with neutrons). The deuteron is the next best slower of neutrons, but it is less likely to absorb or combine with a neutron, although it could and in doing so the product is a triton or tritium nucleus.

It is the nuclear force that determines whether or not a neutron is absorbed, and the strength depends on the stability of the nucleus, which interacts with a neutron.

He-4 is a very stable nucleus and basically doesn't absorb neutrons.

B-10 is a strong neutron absorber, but Be-9 and B-11 are not.

The (n,γ) cross-sections can be seen here - http://www.nndc.bnl.gov/chart/reColor.jsp?newColor=sigg (zoom 1)

 

[Bill_K]

Coxy1234, Which are you asking about, absorption or moderation? I know the title says "absorb", but then you ask "why lead nuclei would be inadequate for use as a moderator". Moderators don't absorb neutrons, they slow them down.

 

[Astronuc]

Coxy1234, Which are you asking about, absorption or moderation? I know the title says "absorb", but then you ask "why lead nuclei would be inadequate for use as a moderator". Moderators don't absorb neutrons, they slow them down.

Moderators (and structural materials) do in fact absorb neutrons, and that must be considered in the nuclear design. Protons do combine to form deuterons, Li-6 and Li-7 absorb neutrons and undergo (n,α) reactions, some carbon-12 becomes C-13. However, the fraction of absorbed neutrons may be very low (depending on the isotope), but enough to consider for criticality. Absorption by structural materials however is a much stronger factor.

There is also the matter of reactivity management, which is a different topic, but that has to do with burnable poisons/absorbers (B-10, Gd-155,157, Er-167) which deplete (or transform) along with the depletion of enrichment.

 

[Coxy1234]

@ Bill K: My question had to do with the relation of neutron absorption on account of weight. I couldn't see why weight would alter a nucleus's ability to absorb neutrons the heavier the material. I was using the question about moderators as a plot for the question. I see now that the speed of the neutron, as well as the weight of the material's nucleus, defines the nucleus's ability to absorb neutrons, and that was what I was missing for the answer to this question.
@ Astronuc: Thanks again for the help, Astro.

 

[Astronuc]

@ Bill K: My question had to do with the relation of neutron absorption on account of weight. I couldn't see why weight would alter a nucleus's ability to absorb neutrons the heavier the material. I was using the question about moderators as a plot for the question. I see now that the speed of the neutron, as well as the weight of the material's nucleus, defines the nucleus's ability to absorb neutrons, and that was what I was missing for the answer to this question.
@ Astronuc: Thanks again for the help, Astro.

With respect to weight/mass, it is really a matter of atomic density and the nuclear structure of the nuclides.

The macroscopic cross-section Ʃ for a given reaction is given by Nσ, where N is the atomic density and σ is the microscopic cross-section. Each nuclide has its own unique σ(E), that is the microscopic cross-section is a function of energy of the interacting particle, which in the context of this discussion is neutrons.

The neutron physics (neutronics) of nuclear system quickly becomes complicated because of the different materials (coolant, moderator, structural, burnable poisons (neutron absorbers) and control elements, and fuel), and with irradiation, fission products, activated corrosion products, and transmuation of fuel into heavier elements (transuranics or transplutonics) and isotopes.

Moderated systems use thermal or epithermal neutrons. Thermal neutrons are in equilibrium with their medium, but even at 0.025 ev, the neutron speed is ~2.2 km/s. Even in moderated systems, there is a population of fast neutrons, and the fast flux can be ~3 times that of the thermal flux, but fast neutrons have a lower probability of causing a fission reaction. Moderators serve to slow down fast neutrons from fission (E ~ 1-10 MeV) down to the eV range. This is accomplished by collisions of the neutrons with the moderator atoms, as well as other materials. In addition to collisions and scattering, the neutrons may be absorbed by those materials.

There are different types of scattering: elastic and inelastic. The neutron may lose energy/momentum by causing the displacement of a nucleus, but the neutron collision might also excite a higher energy state in the nucleus, or it could even knock out another neutron. The knock out part is really limited to the higher energies of fast neutrons since the binding energy of nucleons is usually several MeV for the nuclides of most elements.

Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html#c2