Stopping power of ionizing radiation

[CloudChamber]

Hello All,
can anyone fill in the Bethe formula (-dE/dx) with
a. the information for an alpha particle?
b. the information for a beta particle?
Either one would be great!

 

[Bob S]

A good discussion of the dE/dx formula for beta particles in beta decay is given in Eq 27.3 of http://pdg.lbl.gov/2010/reviews/rpp2010-rev-passage-particles-matter.pdf. You don't mention what material you would like dE/dx for, but I suspect it is for air. A typical beta decay energy is ~ 0.5 to 1 MeV, so βγ ≈1. In Fig. 27.1, the dE/dx min at this energy is ≈1.5 MeV per gram/cm² (in copper). In the following table, http://pdg.lbl.gov/2010/reviews/rpp2010-rev-atomic-nuclear-prop.pdf the minimum dE/dx for unit charge particles in air is about 1.81 MeV per gram/cm².

For alpha particles from alpha decay, βγ << 1. so using the same plot, but multiplying by z² = 2² = 4 for alphas, dE/dx is probably 200 to 400 MeV per gram/cm².

For numbers, use the value of K/A in the dE/dx equation in Table 27.1: K/A = 0.307 MeV per gram/cm²

Note: (βγ)² = γ² - 1

 

[Bob S]

Here in attachment is calculation of dE/dx for low energy alphas in air. Note that at β γ = 3, dE/dx = 7.25 MeV per gram/cm², which is 4 times the expected 1.81 MeV per gram/cm² for singly charged particles. To get MeV per cm of air, multiply by 0.00122 grams per cm³.

 

[Bob S]

Here is the same dE/dx program with only the charge and the mass changed to calculate the electron stopping power. Of course, electron straggling is very large, and is not included. Note that the minimum ionization of 1.81 MeV per gram/cm² is at βγ = 3. A good rough dE/dx value for all beta decay betas is ≈2 MeV per gram/cm²,