Bethe-Bloch Formula: Charge and Energy Deposited by Particles

[PBurke1985]

Hello all,

i am using the Beth-Bloch equation to determine the energy deposited by charged particles in matter (namely protons, pions and muons). In the formula, is the number for incident particle charge in relative charge units (i.e. -1 for electron and +1 for a proton), as opposed to in Coulombs (1.6E-19 C)? I seem to get the correct answer when using relative units. Secondly, the only parameter in the Bethe-Bloch formula (the one i’m using anyway) for the incident particle, is its charge. If the charge is in relative units (+/- 1) the equation does not change for a proton, pion or muon, since they all have a squared charge of +1. Does this mean that these three particles deposit the same amount of energy inside matter through ionization? I am interested in very high energies (10 MeV - 10^10 MeV).

Thanks.

 

[Bob S]

If the charge is in relative units (+/- 1) the equation does not change for a proton, pion or muon, since they all have a squared charge of +1. Does this mean that these three particles deposit the same amount of energy inside matter through ionization? I am interested in very high energies (10 MeV - 10^10 MeV).

Exactly. The Bethe Bloch dE/dx ionization equation depends only on the incident particle velocity and charge, not mass. There is a very small dependence (fraction of 1%) on the sign of the charge, which was observed on comparing positive and negative pions and muons in emulsions in the 1950's. As pointed out in another thread, there are other effects besides dE/dx due to nuclear interactions at extremely high energies. (The Bethe-Bloch ionization is an interaction of the incident particle with atomic electrons).

Bob S