Resonance absorbtion of neutrons

[oksuz_]

Hi,

As you may know, the following equation gives the number of neutrons absorbed per cm³/sec in a resonance region.

F_a=Φ_av∫∑_a(E) dE

So, it is said in Lamarsh, introduction to nuclear engineering, that Φ_av depends on temperature. I do not get this because I know that the flux is something we control. Or should we think just whenever we tune the flux, let's say 1 MeV, the ambient temperature affects its energy?

Thank you in advance.

 

[mathman]

Temperature of what? If neutron temperature, then neutron flux in the resonance region of the material is affected.

 

[Astronuc]

Fa=Φav∫∑a(E) dE

That's a general equation for absorption over dE.

I do not get this because I know that the flux is something we control. Or should we think just whenever we tune the flux, let's say 1 MeV, the ambient temperature affects its energy?

The flux spectrum is determined by the fissile source, lattice design and moderator type and density. In an LWR, the neutrons are moderated by the coolant (light water), and it is with water, not the fuel, with which the neutrons are more or less in thermal equilibrium. Resonance absorption occurs at energies above the thermal equilibrium of the moderator. The resonances are broadened by the vibration of the atoms, primarily U-238 and Pu-240 (Pu-240 in irradiated fuel), and the vibration is dependent on fuel temperature, which is dependent on linear power and coolant temperature.
Typical neutron energy spectrum - https://www.researchgate.net/figure/259717796_fig2_Fig-2-Neutron-source-spectrum-from-typical-LWR-reactor

Fission neutrons are born with energies in the low MeV range (0.1 to 10 MeV), with a most probable energy slightly below 1 MeV, and a mean about 2 MeV. One should be able to find a fission neutron energy spectrum in Lamarsh.

See also - https://t2.lanl.gov/nis/publications/madland1.pdf

 

[rpp]

I believe you are referring to the flux shape near a resonance, and the bounds of the integral should be above and below the resonance.
The high resonance cross section will cause the flux to "dip" and you will get a lower flux corresponding to the peak of the cross section in the resonance.
If you assume a flat flux shape in the resonance region, you will over-estimate the resonance absorption.

It is not quite true that we "control" the flux. We can control certain things, like the fuel material, moderator material, and size of the materials, but we cannot control the flux spectrum with great accuracy. (At least in a reactor.) The flux spectrum will be a result of the slowing down process. I believe you are studying slowing down process by your question.