It=I 0 e−mx (6.4)where mis the linear attenuation coefficientof the absorber for the photons
of interest and has the unit of cm−^1. The factor e−mxrepresents the fraction
of the photons transmitted. Because attenuation is primarily due to photo-
electric, Compton, and pair production interactions, the linear attenuation
coefficient mis the sum of photoelectric coefficient (t), Compton coefficient
(s), and pair production coefficient (k). Thus,
m=t+s+k (6.5)
Linear attenuation coefficients normally decrease with the energy of the
g-ray or x-ray photons and increase with the atomic number and density of
the absorber. The relative contributions of photoelectric effect, Compton
scattering, and pair production in water (equivalent to body tissue) at
different energies are illustrated in Figure 6.8.
An important quantity,mm, called the mass attenuation coefficient, is given
by the linear attenuation coefficient divided by the density rof the absorber
(6.6)
The mass attenuation coefficient mmhas the unit of cm^2 /g or cm^2 /mg. The
mass attenuation coefficients for fat, bone, muscle, iodine, and lead are given
in Figure 6.9.
Half-Value Layer
The concept of half-value layer(HVL) of an absorbing material for g- or
x-radiations is important in the design of shielding for radiation protection.
m
m
r
m=Interaction of g-Radiations with Matter 65Fig. 6.7. Illustration of attenuation of a photon beam (I 0 ) in an absorber of thick-
ness x. Attenuation comprises a photoelectric effect (t), Compton scattering (s),
and pair production (k). Photons passing through the absorber without interaction
constitute the transmitted beam (It).