Perkin Elmer 1600 Fourier Transform Infrared (FTIR) using the KBr
disc technique.
2.4. Theoretical and experimental gamma-rays transmission
The mass attenuation coefficient is written as [10]
mm ¼
lnðI0=IÞ
rt
ð3Þ
where r is the density of material (g/cm3), I0 and I are the incident
and transmitted intensities, respectively, and t is the thickness of
absorber (cm).
Theoretical values of the mass attenuation coefficients of
mixture or compound have been calculated by WinXCom, based
on the mixture rule [1]:
mm ¼
X
i
wiðmmÞi ð4Þ
where wi weight fraction of each element in mixture, (mm)i is mass
attenuation coefficient for individual element in mixture.
The following mass attenuation coefficient relates half value
layer to linear attenuation coefficient (m) [11]:
HVL ¼ 0:693=m ð5Þ
The value of mass attenuation coefficients can be used to
determine the total atomic cross-section (st,a) by the following
relation [1]
st,a ¼
ðmmÞalloy
NA
Pn
i ðwi=AiÞ
ð6Þ
where NA is Avogradro’s number, Ai is atomic weight of constituent
element of mixture. Also the total electronic cross-section
(st,el) for the element is expressed by the following formula [1]:
st,el ¼
1
NA
Xn
i
fiAi
Zi
ðmmÞi ð7Þ
where fi is the number of atoms of element i relative to the total
number of atoms of all elements in alloy, Zi is the atomic number
of the ith element in mixture. Total atomic cross-section and total
electronic cross-section are related to effective atomic number
(Zeff) of the compound through the formula [12]
Zeff ¼
st,a
st,el
ð8Þ
Recently, Manohara et al. [13] have taken the theory one step
further by inserting analytical expressions for the atomic and
electronic cross sections in Eq. (8)
Zeff ¼
P
if Aiðm=rÞi P
jfjðAj=ZjÞðm=rÞj
ð9Þ
The diagram of experimental setup for mass attenuation
coefficient determination is shown in Fig. 1. The source and
absorber system were mounted on a composite of adjustable
stands. This setup can move in the transverse direction for proper
beam alignment. 137Cs radioactive source of 15 mCi (555 MBq)