bei48482_FM

84 Chapter Two

0 5 10 15 20

Lead

Total

Pair production

Compton

scattering

Photoelectric effect

25

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

Linear attenuation coefficient, cm^0

-^1

Photon energy, MeV

Figure 2.29Linear attentuation coefficients for photons in lead.

Pair production becomes increasingly likely the more the photon energy exceeds

the threshold of 1.02 MeV. The greater the atomic number of the absorber, the lower

the energy at which pair production takes over as the principal mechanism of energy

loss by gamma rays. In the heaviest elements, the crossover energy is about 4 MeV, but

it is over 10 MeV for the lighter ones. Thus gamma rays in the energy range typical of

radioactive decay interact with matter largely through Compton scattering.

The intensity Iof an x- or gamma-ray beam is equal to the rate at which it trans-

ports energy per unit cross-sectional area of the beam. The fractional energy dIIlost

by the beam in passing through a thickness dxof a certain absorber is found to be pro-

portional to dx:

 dx (2.24)

The proportionality constant is called the linear attenuation coefficientand its

value depends on the energy of the photons and on the nature of the absorbing material.

Integrating Eq. (2.24) gives

Radiation intensity II 0 ex (2.25)

The intensity of the radiation decreases exponentially with absorber thickness x.

Figure 2.29 is a graph of the linear attenuation coefficient for photons in lead as a func-

tion of photon energy. The contribution to of the photoelectric effect, Compton scat-

tering, and pair production are shown.

We can use Eq. (2.25) to relate the thickness xof absorber needed to reduce the

intensity of an x- or gamma-ray beam by a given amount to the attenuation coefficient

. If the ratio of the final and initial intensities is II 0 ,

ex ex ln x

Absorber thickness x (2.26)

ln (I 0 I)





I 0



I

I 0



I

I



I 0

dI



I

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