# 7.1.4 Bremsstrahlung

Created October 19, 1995

### 7.1.4.1 Bremsstrahlung and Stopping Power

The total stopping power for electrons can be given as a combination of the collisional and radiative types of interactions:
[dT/dx] total = [dT/dx]collision + [dT/dx] radiative

(for heavy particles we only consider orbital electron interactions (an atomic process) since the probability of nuclear interaction resulting in energy loss is much smaller.)

The radiative component calculated from electromagnetic and relativistic theory is given by:

which is the basis for the approximation for the percentage of energy lost to radiation for monoenergetic electrons:

(dT/dx)r/ (dT/dx)total = EZ/1000 ;

where Z is the atomic number of the absorber and E is the charged particle energy in MeV.

For example, a stream of 100 keV electrons hits a tungsten target (Z=74). Only 0.74% of the energy lost goes to emitted x-rays.

For polyenergetic beta rays, becomes:

(dT/dx)r/(dT/dx)total = Z E(max) / 3000

since the average beta energy is 1/3 that of the maximum beta energy.

The fraction of energy lost to radiation is shown in the above equation to be inversely proportional to the charged particle's mass. Bremsstrahlung will therefore be very low for heavy charged particles (compared to electrons). Even at 100 MeV, for example, heavy particles dissipate most of their energy through the collisional process.

For mixtures of elements, one determines the "effective atomic number", Z(eff). This can be found by using the following formula

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Douglas J. Wagenaar, Ph.D., wagenaar@nucmed.bih.harvard.edu