Muon Attenuation: Is Heavy Metal Significant?

[stakhanov]

I am looking at muons being lost as they travel through a concrete bunker (with various things inside). The minimum energy (mean) for a muon to go through the walls is about 1.82GeV, and for the stuff inside (flakes of magnesium) it is 2.7GeV. For a piece of heavy metal it is 0.13GeV (it's only a small piece). The mean muon energy in the spectrum is ~6GeV.

I want to know whether the attentuation due to the heavy metal is going to be noticeable or if it will be lost amongst the attenuation due to the concrete and magnesium (I have a feeling it won't but I need to prove it).

Can you just add the energies and say that for a muon to pass through them all it must have above 4.65GeV? If so then if the heavy metal is not there (reducing the energy needed to 4.52) there probably isn't going to be a significant difference in flux.

Is there a better way of going about this?

 

[Astronuc]

See if this helps.

http://mightylib.mit.edu/Course%20Materials/22.01/Fall%202001/heavy%20charged%20particles.pdf

One needs to find the equivalent data for different Z materials as shown in figure 1 for water.

 

[stakhanov]

Thanks for the reply. I do have the equivalent data for the various materials I'm looking at. I have worked out stopping power. I have radiative loss data (enough to work out the linear approximation for energies above the muon critical energy) for all the materials. I have range as a function of energy for all the materials (from which I have the minimum energy needed to pass through a material of a particular thickness).

What I really need to know is whether I can just add these minimum energies (for a series of different media in a line) and say that the sum of the minimum energies is the energy a muon must have in order to get through them all.

 

[Astronuc]

I seem to remember that the treatment would be essentially a set of sequential problems, that is, one has 3 regions with different LET's. One simply solves for slowing down in the first region to get the particle (muon in this case) energy at the interface between regions 1 and 2, then solve for the slowing down through the second region and use the energy at the interface of regions 2 and 3, and then solve for the slowing down in the third region.

Is that what one is asking?

 

[stakhanov]

Yeah that's what I am after pretty much.

The number of muons at a specific energy is described by a spectrum (which is dependednt on what angle they arrive from the zenith). I figured that because the dE/dX is pretty flat between 1-100GeV (it's about 2MeV/g cm^2), then as muons lose energy through the medium, the spectrum (between 1-100GeV) will just shift down to a lower energy but keep the same form roughly. So muons with energy E1 are attenuated out and muons of energy E2 (where E2>E1) lose energy to become the new E1 muons and so on. If this is true then I think it must be ok to add the minimum energies for all the materials.

Thanks for your replies.