Nuclear Doppler broadening of resonances

[dRic2]

Hi,
absorption cross section in resonance depends on the relative speed of neutron and nucleus in Center of Mass frame. As you can see here
https://www.nuclear-power.net/glossary/doppler-broadening/
Temperature plays a big role in determining resonance absorption cross.
I don't understand why the area under the curve remains the same. Can you give some physical insight ?

Thanks
Ric

PS: I have a "feeling" for it, I'd like a "rigorous" logical proof that does not require math. In the book I consulted it is simply stated that the curve can be expressed as a particular function and then it was left to the reader to prove that the integral is independent of temperature. I don't like this approach because the meaning of the function was not explained so I could not get the physical intuition behind it.

 

[Charles Link]

I am not sure what the nature of the source is that is getting scattered, but what I believe they are telling you is that if you have a very broadband source that has equal powers for equal energy intervals (or frequencies), that the total scattered power will be independent of temperature. You can either get a lot of scattered power in a very narrow energy (frequency) region, or a little bit of power in each energy interval that occurs over a wide range of energies (or frequencies).

 

[dRic2]

what I believe they are telling you is that if you have a very broadband source that has equal powers for equal energy intervals (or frequencies), that the total scattered power will be independent of temperature. You can either get a lot of scattered power in a very narrow energy (frequency) region, or a little bit of power in each energy interval that occurs over a wide range of energies (or frequencies).

But Why ?

I am not sure what the nature of the source is that is getting scattered

What source ? I don't understand. Sorry if I poorly stated the question here let me try to make it a little better:

I have neutrons moving inside of a medium. The "probability" of a neutron to be absorbed by the atoms of the medium has some peaks at particular energies. The kinetic energy of the neutron seen by the atom depends on the relative velocity. A temperature change implies a change of atoms' velocity so the relative velocity between the atoms and the neutrons changes. This implies a change in the "probability" (cross section) that a neutron is absorbed near the peak (resonance).

 

[Charles Link]

In the total scattering cross section, it doesn't matter how much the particles are scattered. Anything that gets scattered at all by the scatterers is counted as having been scattered. In this scenario, regardless of temperature, the number of scatterers doesn't change. Thereby the total scattering cross section doesn't change. The frequency that each scatterer selects is affected by the temperature, but not the existence of the scatterer.

 

[dRic2]

Thanks for the reply. I think I'll be back in a couple of days because I have to study a lot and my brain decided to stop working right now :D

 

[dRic2]

In the total scattering cross section

But I'm talking about absorption cross section... it's one specific reaction.

Anything that gets scattered at all by the scatterers is counted as having been scattered

Again, I'm only counting the neutron that are absorbed not every neutron that interacts with a nucleus.

In this scenario, regardless of temperature, the number of scatterers doesn't change.

Sorry, I'm not following at all...

God, I feel stupid right now :(

 

[Charles Link]

I didn't realize you were doing absorption cross section here, but the principles are very similar to scattering cross section. Try reading through this "link" which will tell you all about scattering cross sections. https://www.physicsforums.com/threa...a-rutherfords-experiment.965947/#post-6131309 .
Absorption cross sections are actually easier to do because you don't need to worry about what direction the particle goes. It simply gets swallowed up. I think by reading and studying the "link", you might get an understanding for cross sections in general=both the differential one $\frac{d \sigma}{d \Omega}$, and the total scattering cross section $\sigma_{total}$.
And don't give up. This stuff is normally not written up very well in the textbooks. It took me a long, long time to figure it out. I do think you might find the above "link" very helpful.