The 1/v law for U-235 cross section

[DrDu]

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?

 

[hutchphd]

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...

 

[DrDu]

I thought this resonances are located at higher energies?

 

[hutchphd]

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 !

 

[DrDu]

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.