Hello all, i am having a few problems simulating cosmic rays with a silicon CCD detector, mainly because my knowledge on particle physics is quite poor. I am simulating primary cosmic rays, which predominantly consist of single protons and alpha particles. I am treating the protons as minimum ionizing particles, since the kinetic energy of cosmic ray protons are between 10^9 eV and 10^20 eV. I tried to use the Bethe-Bloch equation to determine the minimum ionisation energy but failed miserably. However, from some online searching, i found that minimum ionizing particles lose 1.66 MeV cm^2/g of energy when travelling through silicon. My first question, am i correct to treat the cosmic ray protons as minimum ionizing particles? Secondly, can i also treat the alpha particles as minimum ionizing particles? I have read the alpha particles do not penetrate matter very well. So confused !!! Any help is appreciated, thanks. Cheers.
Protons are minimum ionizing between 1 and 2 GeV. See http://en.wikipedia.org/wiki/Bethe_formula Also see Eq (27.3) and discussion in http://pdg.lbl.gov/2009/reviews/rpp2009-rev-passage-particles-matter.pdf Above ~ 2 GeV, the dE/dx equation for protons rises logarithmically, but this does not include radiative effects. See the Fig. 27.1 in the LBL pdf and look at the radiative correction effect at high energies.. For alpha particles, the ionization rate is z^{2} = 4 times as high as protons for the same β (see url). Alpha particles are probably minimum ionizing between 4 and 8 GeV (again same β). Bob S. [added] Here is the particle properties table from the particle data Group. http://pdg.lbl.gov/2009/reviews/rpp2009-rev-atomic-nuclear-prop.pdf Silicon minimum ionization is shown to be 1/66 MeV per g/cm^{2}
A proton of that high energy is nowhere near minimum ionizing. Also, it's losing a significant fraction of its energy through other processes, so ionization energy loss is only a tiny piece of the story. You do realize that for your CCD to detect primaries, it needs to be in space, right?
If an individual proton (a cosmic ray secondary) enters a 100-micron-thick silicon particle detector, there is less than 0.1% chance that there will be a nuclear interaction (nuclear cascade) before it exits. The nuclear interaction length is about 108 grams per cm^{2}. So the main (≈99.9% probability) signal would be the Bethe-Bloch dE/dx ionization. See http://pdg.lbl.gov/2009/reviews/rpp2009-rev-atomic-nuclear-prop.pdf Per Vanadium, a primary cosmic ray proton will develop a full nuclear cascade within ~450 grams per cm^{2} (5 interaction lengths) of the upper atmosphere, and never reach the ground. A lot of "cosmic rays" reaching the ground are actually muons from pion decay in the upper atmosphere.. Bob S
Hi, thanks very much for your replies. The simulation is for CCDs in space, so im definitely dealing with primary cosmic rays. From what i gather, i need to use the Bethe-Bloch equation to determine dE/dX at all cosmic ray energies and not use the minimum ionizing energy. I also need to include radiative losses, which are dominant at higher energies. Im assuming that radiative losses are not accounted for in the Bethe-Bloch formula and i need to use an additional formula? When i use the Bethe-Bloch formula, i seem to get a constant decay and not an increase in the curve after the minimum ionization point as the particle speed (or energy) increases. Is there anywhere online where i can get an excel spreadsheet or an applet for the Bethe-Blcoh formula, that allows me to input my parameters (e.g. 10 MeV - 1000 MeV protons through silicon) and gives me the dE/dX curve vs. particle energy? Thanks.