The 1/v law for U-235 cross section

In summary, the cross section for fission of U-235 is significantly higher for slow, thermal neutrons compared to fast neutrons. This can be explained by the presence of resonances in the cross section, which arise from competing paths and contribute to the overall magnitude. These resonances, known as Fano resonances for elastic scattering and after Wigner for inelastic processes, are located above 1 eV energy. The 1/v increase in cross-section may be true for all isotopes and is related to scattering length and partial wave analysis. Heavy elements like U-235 also have threshold states, which act as resonances at energies very close to 0. Further details on this topic can be found in the script linked in
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DrDu
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TL;DR Summary
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?
 
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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 !
 
  • #5
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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1. What is the 1/v law for U-235 cross section?

The 1/v law for U-235 cross section is a mathematical relationship that describes the decrease in the cross section (a measure of the probability of a nuclear reaction occurring) as the velocity of the incident neutron decreases. It is based on the principle that slower moving neutrons are more likely to be captured by the U-235 nucleus, resulting in a decrease in the cross section.

2. How does the 1/v law affect nuclear reactions involving U-235?

The 1/v law plays a crucial role in nuclear reactions involving U-235, as it explains the decrease in the probability of a reaction occurring as the velocity of the neutron decreases. This is important in nuclear reactors, where controlling the rate of reactions is necessary for safe and efficient operation.

3. What is the significance of the 1/v law in nuclear physics?

The 1/v law is significant in nuclear physics as it helps to explain the behavior of neutrons and their interactions with nuclei. It also allows for the calculation of cross sections and reaction rates in nuclear reactions, which is essential for understanding and predicting the behavior of nuclear systems.

4. How was the 1/v law for U-235 cross section discovered?

The 1/v law for U-235 cross section was first observed by the physicist Enrico Fermi in the 1930s. He noticed that the probability of a nuclear reaction occurring decreased as the velocity of the neutron decreased, and he was able to mathematically describe this relationship, which became known as the 1/v law.

5. Are there any exceptions to the 1/v law for U-235 cross section?

While the 1/v law holds true for most nuclear reactions involving U-235, there are some exceptions. For example, at extremely low velocities, the cross section may actually increase due to the effects of resonance absorption. Additionally, at very high velocities, the cross section may also increase due to the effects of relativistic energy transfer. However, these exceptions are generally only observed in extreme conditions and do not significantly affect the overall validity of the 1/v law.

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