Re: Why do we expect GZK cutoff at the energies 6x10^19 eV ?

Hi Marianna,

The GZK cutoff is not due to proton pair production. It's due to the process p + photon --> p + pion, or pion photoproduction. The photons come from the cosmic microwave background (CMB), so they are encountered at similar densities all through space, even in intergalactic voids. The pion process is simply the lowest-energy inelastic process you can accomplish with p+photon. You don't calculate the GZK cutoff exactly at the threshhold, but rather at the delta (1232 MeV) resonance where the cross section is largest. The GZK cutoff is not sharp, since the cross-sections vary with energy and the CMB photons have a wide distribution. Rather, it's best stated as "a 6e19 eV proton from distance X has probability Y of undergoing a collision."

I'm not sure where you're getting 5e17 eV in either case. The threshhold for p+p-->p+p+pi is only a few GeV, but it's less important astrophysically because there are so few protons in empty space. The threshhold for p+CMB-->p+pion is indeed around 1e19 eV. Perhaps you were using starlight (optical) photons rather than microwave?

Hope this helps. A Google search turned up a worksheet at this page (pdf) that can walk you through some of the calculation.

-Ben