Neutron Capture Cross Section Dependence on Target Material Temperature

[jbirch]

So I have been reading about the cross section of neutron capture and have been reading about how the cross section for neutrons in a given material depends on neutron energy, the most important factor obviously. But I have not seen as much information on how, for a neutron of a given thermal or lower energy, the capture cross section changes with the tempetature of the target material.

So let's say we have a set of neutrons of 1 mev, obviously a very low energy and is either thermal or cold depending on your definition. And they are being launched into a slab of Aluminum. So the energy of the neutron is fixed at 1 mev for all neutrons being launched into the Aluminum each time they are launched into the Aluminum but the tempetature of the Aluminum changes. So if the neutrons are always at 1 mev, or another arbitrarily chosen low energy, and the size of the Aluminum slab is kept the same and the temperature of the Aluminum changes, with everything else in the experiment kept the same, then how do we determine how the neutron capture cross section changes in according to temperature of the target Aluminum ? How would the neutron capture cross section change as the Aluminum temperature is changed from 300 K to 250 K to 200 K to 150 K and then down to 20 K ? I know that for some target materials like Uranium there is a significant difference in neutron capture cross section but would changing the temperature fo Aluminum change the cross section at all ?

Any information on the theory behind the effect of the target temperature on the capture cross section or links to data tables, results and papers and publications that show what happens would be greatly appreciated.

Thank you for any help you can provide,

jbirch

 

[brian_palmer]

If you look at graphs of the energy dependence of neutron cross sections you will notice a couple of recurring trends. First, many materials have "1/v" behavior...this means the likelihood of interactions is inversely proportional to the speed (or directly proportional to the time nearby). A second recurring theme you would notice is that many material exhibit an abundance of resonances or large spikes in their various cross section.
Now to your question. The primary effect of increased temperature is to lower the peak and broaden the resonances. It is referred to "Doppler Broadening" and is quite well documented and understood.

I hope this helps.

 

[JohnX]

Thanks for the reference to "Doppler Broadening" !

 

[Astronuc]

http://www.nndc.bnl.gov/sigma/index.jsp?as=27&lib=endfb7.1&nsub=10

http://www.nndc.bnl.gov/sigma/getPlot.jsp?evalid=14982&mf=3&mt=102&nsub=10

In the thermal energy range, the relative velocities of the neutron and target atoms become important. For Al, the 1/v or 1/E effect is not too strong.

The resonances are well beyond the thermal region in the keV range.

The temperature also affects density or lattice spacing which has a small effect on the macroscopic cross section.

 

[JohnX]

So, the effect of doppler broadening is only significant for thermal energy neutrons irradiation?
I was trying to look for some information on the cross section variation for 14 MeV neutrons, but I just couldn't find any.

 

[Astronuc]

So, the effect of doppler broadening is only significant for thermal energy neutrons irradiation?
I was trying to look for some information on the cross section variation for 14 MeV neutrons, but I just couldn't find any.

In a moderated nuclear reactor, e.g., LWR or CANDU, as fuel temperature increases, "the nuclei move at higher speeds, increasing the probability of resonance capture of epithermal neutrons (Doppler effect, Doppler broadening, Resonance broadening)," so it is the resonances in the epithermal region that are important.
Ref: http://www.nuceng.ca/ep6p3/class/Module3C_Temp&VoidJun21.pdf

See (n,γ) of U-235 and U-238:

http://www.nndc.bnl.gov/sigma/getPlot.jsp?evalid=15321&mf=3&mt=102&nsub=10
http://www.nndc.bnl.gov/sigma/getPlot.jsp?evalid=15324&mf=3&mt=102&nsub=10

The doppler effect would not apply to fast neutrons in a CANDU or LWR reactor.

 

[JohnX]

Thank you!
Another question I wanted to ask is,
Would the doppler broadening affect the cross sections of interaction of neutrons with the structural materials in a nuclear fusion reactor (D-T) ?