Neutrinos incident on target - interaction with nucleons or nuclei?

[Naz93]

I came across a worked example question in a particle physics book this morning that had a beam of neutrinos of energy 2.3MeV incident on a lead target. The point of the question was calculating the thickness of lead needed to reduce the beam intensity by a certain fraction - and the solution requires one to calculate the number density of "targets" in the lead.

The solution given took the targets to be the nucleons within the lead nuclei, rather than the whole nuclei (the difference mathematically giving a factor of lead's atomic number 207). The reason given for this choice was at energy 2.3MeV, the neutrinos would be interacting with the nucleons.

My question is: how can one tell what energy the interaction switches to be predominantly with the nucleons rather than the nuclei? To what energy must the incident neutrino energy be compared?

 

[mfb]

To the binding energy of nucleons in a nucleus. 2.3 MeV is in the same range, I would expect both effects to be relevant.

 

[ChrisVer]

I guess you will always have to check the compton wavelength corresponding to your energy for something like that...
For example if the wavelength corresponding to 2.3MeV is smaller than the radius of the nucleus, you will have to take in consideration interactions with the nucleons...why? because the neutrinos could see what's inside the nuclei...

 

[Naz93]

Hmm, I tried the Compton wavelength, and using E = \hbarc/λ, seems to give the Compton wavelength as about 86fm - bigger than the diameter of a lead nucleus...