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In ENDF there are cross-sections given for different types of nuclear interactions. For example, this file gives the cross-sections for different neutron energies. However, it is not clear, which temperature of the medium itself (not the neutron gas) is implied.

Is there a way to know, for which temperature are those cross-sections given. Or maybe to know the cross-section values for different temperatures of the medium.

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The graphs are most likely a composite of data from many different experiments, since the neutron energies span 12 orders of magnitude. Since room temperature corresponds to an energy of about $10^{-8}$ MeV per d.f., the temperature of the uranium target wouldn't matter except at the extreme low energies. The linked pdf just looks like someone's powerpoint slides, but if you look for the actual source of the data on the ENDF web site, they should give references to scientific papers. –  Ben Crowell Aug 6 at 18:46
    
Minor comment to the post (v2): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. –  Qmechanic Aug 6 at 19:49

3 Answers 3

For those of you are perhaps a little behind on the background, these cross section libraries need to be processed before they can be applied to a realistic material. This would be appropriate for situations like a simple source term with the neutron tracks propagating throughout the material. You know the temperature, and you have the library specific to your materials. Thus, you'll be adding up the elements in the material as well as applying the nuclear Doppler broadening.

What temperature is ENDF referenced to? I don't believe this approach would be very general if the cross sections were specific to a certain temperature. You certainly couldn't go any lower, since the information is irrevocably lost. Some quick searching gives me a good quote to use here:

https://moodle.polymtl.ca/pluginfile.php/44472/mod_resource/content/3/week5.pdf

Cross section values are measured and reported in reference tables for a frozen nuclide situation where the material absolute temperature is set at 0K

Now I think that this statement applies to ENDF. I had always assumed that, just because it seemed like the most straightforward approach. I could be wrong, and I would welcome correction. However, I had always thought that the processing of cross sections came down to convolution of the 0K cross sections with the thermal distribution of the material's atoms. Transitioning from one non-zero reference temperature to a different temperature would be a very different and more complicated process.

In fact, the graphs in your linked presentation go down to $10^{-11} MeV$, which corresponds to a temperature much lower than a typical lab environment. Consider that if the cross sections were at room temperature, the graph would be level off at energies higher than that, because the atomic lattice is vibrating faster than the neutron is moving. So we can conclude that it's either at a very low reference temperature, or it's the natural 0K reference. I can't say conclusively, but the latter seems to be much more likely.

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For the most part, the temperature of the medium doesn't matter. Thermal energies are typically around $kT=25\,\mathrm{meV}$, while nuclear reactions typically have energies of a few MeV. A factor of a billion in energy is a big difference. A skim of the explanatory text in the datafile corresponding to your plots reveals no mention of temperature.

If you're interested in scattering of thermal neutrons, temperature does matter: the phonons in the material have roughly the same energy as the neutrons, and the relationship between energy and scattering amplitude can become complicated. That's more of a materials science phenomenon than a nuclear physics phenomenon, though, and you need a different set of libraries. The folks I know in that business use MCNP and its $S(\alpha,\beta)$ libraries; I see the ENDF also contains thermal data which do reference material temperatures.

I observe that the first page of your linked PDF shows a factor of ten difference in cross section between each of the total, absorption, and gamma production cross sections for neutrons on uranium — with the "total" cross section being uniformly lower than the "gamma production" cross section. I don't know how the LANL NIS has generated those plots, but they goofed on that one. (If you were feeling generous you might contact them and let them know; probably other figures are also affected.) At the NNDC there is a much more sophisticated interface to the ENDF.

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According to the Section 1.1 of the ENDF-6 Formats Manual, each header of the raw ENDF/B-VII.1 Incident-Neutron Data file available in the LANL Data area has the following format:

  ZA,  AWR,  LRP,   LFI,  NLIB, NMOD
ELIS,  STA,  LIS,  LISO,     0, NFOR
 AWI, EMAX, LREL,     0,  NSUB, NVER
TEMP,  0.0, LDRV,     0,   NWD, NXC

where the TEMP field denotes the temperature in Kelvins. So, the initial ENDF/B-VII.1 files seem to always give the cross-sections for zero temperature, unless the Doppler broadening with the SIGMA1 procedure from the PREPRO codes collection is applied.

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I hope you'll accept your own authoritative and correct answer :-) –  rob Aug 7 at 1:04
    
@rob : Yes, it is a bit strange situation indeed. And each time when it happens, I am not sure what to do. :) Now it may seem that I knew the answer from the very beginning, but I did not. I spent several hours searching for the relevant documentation, and you people gave me the useful hints for that. So, I voted for yours and AlanSE's answers only. :) –  v_2e Aug 7 at 6:33
    
It's totally within the guidelines. –  rob Aug 7 at 12:05

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