The 1/v law for U-235 cross section

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Discussion Overview

The discussion revolves around the behavior of the cross section for fission of U-235, particularly focusing on the empirical observation that it decreases like 1/v with respect to the velocity of thermal neutrons. Participants explore qualitative explanations for this phenomenon, including the role of resonances and scattering processes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that the cross section for fission of U-235 is significantly higher for slow, thermal neutrons compared to fast neutrons, which are more similar to geometric area.
  • One participant suggests that the presence of resonances in the cross section is a qualitative reason for the 1/v behavior, mentioning competing paths and the sum of these processes.
  • Another participant questions whether resonances are primarily located at higher energies, indicating a potential misunderstanding or differing perspective on resonance behavior.
  • It is proposed that the 1/v increase in cross-section might apply to all isotopes, with a suggestion that partial wave analysis could provide insight, although the participant expresses uncertainty about the underlying physics.
  • A later reply introduces the concept of threshold states in heavy elements, suggesting that these states near zero energy could also be considered a form of resonance.

Areas of Agreement / Disagreement

Participants express differing views on the nature and implications of resonances in the context of the 1/v law, indicating that multiple competing perspectives remain without a clear consensus.

Contextual Notes

Some limitations include the potential dependence on definitions of resonances and the unresolved nature of the relationship between scattering processes and the observed cross-section behavior.

DrDu
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TL;DR
How to explain the higher cross section of U-235 for thermal neutrons
The cross section for fission of U-235 is much higher for slow, thermal neutrons than for fast neutrons, for which it is similar to the geometric area.
The cross section for slow neutrons seems to decrease empirically like 1/v where v is the velocity of the neutron. What is the qualitative explanation of this fact?
 
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The qualitative reason is the presence of resonances in cross section. These arise from their being an amplitude for several different competing paths and the x-section is magnitude of the sum of these processes.
For elastic scattering I know these as Fano resonances. For inelastic
processes in nuclei they may be called after Wigner? This exhausts my knowledge of things nuclear...
 
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I thought this resonances are located at higher energies?
 
Yeah one would think... this one clearly shows the "resonance region" above 1 eV. The link above seems to indicate detail of resonances are important but I don't have access to the paper itself.
I think the 1/v increase in cross-section may be true for all isotopes (doesn't that come out of partial wave analysis?...the physics escapes me right now) Clearly something makes the fission channel the preponderant route for ##U_{235}## and maybe the other isotopes just happily scatter the neutron (but still have a large total x-section going like 1/v).
Long winded way to say I don't know !
 
Yes, scattering length and partial wave analysis turned out to be the right keywords:
I found this script:
http://www.damtp.cam.ac.uk/user/tong/aqm/aqmten.pdf
Apparently, these heavy elements have threshold states, i.e. states just bound in the effective potential for energies very near to 0. Of course this is also a kind of resonance as you suspected.
 
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