The linear attenuation coefficient (
μ) is a key factor for evaluating the effect of gamma radiation of appropriate energy with the studied material and can be deduced from Beer-Lambert Law [14 (
link)] as follows in Equation (1):
The initial and transmitted intensities are
I0 and
I respectively, across a target material of thickness
x.
I0 and
I were determined by evaluating the area under the photopeak in without the polymer absorber
Areawithout and with the polymer sample
Areawith respectively.
The ability of the considered polymers to be checked as radiation protecting materials by calculating the mass attenuation coefficient (
μ/
ρ) by dividing the calculated linear attenuation coefficient (
μ) of a particular polymer by its density (
ρ). Theoretically, (
μ/
ρ) can be evaluated using Equation (2) [15 (
link)]:
where
wi and (
μ/
ρ)
i was the weight fraction and the mass attenuation coefficient of the
ith constituent element in the polymer material, respectively.
The half, tenth value layers or
HVL and
TVL are two important parameters in designing a suitable radiation shielding material. These parameters are defined as the attenuator thicknesses needed to decrease the γ-ray intensity to 50% and 10% of its initial value and estimated using Equations (3) and (4), respectively [16 (
link)]:
Due to the interaction of gamma rays with the polymer sample, the mean-free path (MFP) is known as the medium distance traveled by a photon between two successive reactions is defined as and described in Equation (5) [17 (
link),18 (
link)]:
The
MFP is also, practically, the attenuator distance which decreases the initial photon intensity of 36.8% when passing across the polymer absorber. The (
Zeff) is another useful radiation interaction factor used to discuss the attenuating properties of the mixtures or compounds in terms of pure elements and depends on the incoming photon energy.
Zeff values for the studied polymers can be obtained using Equation (6) [18 (
link)]:
where
fi,
Zi and
Ai, refer to the molar fraction, atomic number and atomic weight of the
ith constituent element in the selected polymer, respectively.
The effective electron density (
Neff), measured in electrons/g, defined as the number of electrons per unit mass of the polymer material and is derived using the calculated
Zeff according to Equation (7) [19 ]:
where
represents the mean atomic mass of the polymer, and
NA is Avogadro’s number.
When choosing a shielding material, the exposure buildup factor (EBF) must be considered to edit the absorption calculations resulting from buildup of secondary photons resulting from Compton scattering [20 (
link)]. To determine the EBF for the selected polymers, the Geometric-Progression fitting method (GP) was employed, and the computations were determined according to the three following steps [7 (
link)]:
The (
Zeq), which is an energy-dependent parameter describing the properties of the investigated polymers in terms of their equivalent elements, was first calculated using the next formula [21 (
link),22 (
link)]:
where
R1 and
R2 are the (
μComp/
μtotal) ratios corresponding to the elements with atomic numbers
Z1 and
Z2, respectively, and
R is the (
μComp/
μtotal) ratio for the selected polymer at a specific energy, which lies between the ratios
R1 and
R2.
The computed
Zeq values of the investigated polymers were then used to interpolate the GP fitting EBFs (
b,
c,
a,
XK,
d) in the range of energy 0.015–15 MeV using the interpolation formula [22 (
link)] (9):
where
C1 and
C2 are GP fitting parameters, taken from the ANSI/ANS-6.4.3 standard database [23 (
link)], corresponding to
Z1 and
Z2 between which
Zeq of the selected polymer lies. As an example, the GP fitting parameters and the
Zeq for PMP (C
6H
12) in the energy range 0.015–15 MeV are listed in
Table 1.
Finally, the EBF for the selected polymers were then estimated with the help of the obtained GP fitting parameters, using the following relations [24 (
link),25 (
link)]:
and
where
where
E is incident γ-ray energy and
x is the penetration depth in terms of mfp.
Alabsy M.T., Alzahrani J.S., Sayyed M.I., Abbas M.I., Tishkevich D.I., El-Khatib A.M, & Elsafi M. (2021). Gamma-Ray Attenuation and Exposure Buildup Factor of Novel Polymers in Shielding Using Geant4 Simulation. Materials, 14(17), 5051.