Radiation Shielding Protocol and Attenuation Analysis

Radiation shielding is based on the principle of attenuation, which is the ability to reduce radiation intensity through photoemission and scattering by a barrier material. When a gamma ray passes through an absorber material of thickness x, an exponential attenuation is observed in the intensity of the gamma radiation depending on the chemical content of this material according to Beer–Lambert’s law [20 (link)]: $$I=I_0{e}^{-\mu x},$$
where I is the transmitted intensity, I_o is the incident intensity, x is the thickness of the absorbent (cm), and μ (cm⁻¹) is the linear attenuation coefficient (LAC).
The half-value layer (HVL) and tenth-value layer (TVL) are defined as the thicknesses required to attenuate the incident photon intensity by factors of 1/2 and 1/10, respectively [21 (link)]: $$\mathrm{HVL} =\frac{\mathrm{Ln}2}{\mathrm{LAC}},$$
$$\mathrm{TVL}=\frac{\mathrm{Ln}10}{\mathrm{LAC}}.$$
The mean free path (MFP) (cm) is the reciprocal of linear attenuation coefficient and denotes the average distance that a photon travels inside the sample without any interactions [1 (link)]. Moreover, MAC denotes the mass attenuation coefficient, which is measured by dividing LAC by the density (ρ) [22 (link)]: $$\mathrm{MAC} =\frac{LAC}{\mathsf{\rho }}.$$
Other important shielding parameters can be derived from the mass attenuation coefficient, such as the effective atomic number (Z_eff) and effective electron density (N_eff). The Z_eff and N_eff parameters are fundamental in the field of nuclear radiation protection. Z_eff depends on the incident photon energy and is used to characterize the shielding properties of composites in terms of pure elements [23 (link)]. N_eff is the number of electrons per unit mass of the composite material measured in electrons/g. Z_eff and N_eff can be calculated from the following relationships [24 (link)]: $$Z_{eff}=\frac{{{\displaystyle \sum }}_i{f}_i{A}_i{\left(\frac{\mu }{\rho }\right)}_i}{{{\displaystyle \sum }}_{j }{f}_{i }\frac{A_j}{Z_j}{\left(\frac{\mu }{\rho }\right)}_j},$$
$$N_{eff}=\frac{N_A{Z}_{eff}}{A},$$
where f_i, A_i, and Z_i are the fractional abundance, the mass number, and the atomic number of the i-th constituent element in the composite material. $\langle A\rangle ={{\displaystyle \sum }}_i{f}_i{A}_i$ is the average atomic mass of the composite material, and N_A is Avogadro’s number.
The exposure buildup factor (EBF) is essential for radiation scattering studies and assessing shielding material performance. It is defined as the photon buildup factor in the air after penetration through a shielding material with high-energy photons. The EBFs for mortars were computed using G–P fitting parameters as mentioned in previously published studies, and this was achieved using the equivalent atomic number (Z_eq), which is an energy-dependent parameter describing the properties of the investigated mortars in terms of their equivalent elements. Z_eq is defined by the following equation [25 (link)]: $$Z_{eq}=\frac{Z_1\left(\log R_2-\log R\right)+Z_2\left(\log R-\log R_1\right)}{\log R_2-\log R_1},$$
where R₁ and R₂ are the ratios (μ/ρ) _Compton/(μ/ρ) _total, which were obtained for mortar at a specified energy using the WinXCom program, corresponding to elements with atomic numbers Z₁ and Z₂, respectively. R is the ratio for the mortar at the specific energy, which lies between ratios R₁ and R₂.
The G–P fitting parameters such as (b, a, X_k, d, and c) were then interpolated using the obtained Z_eq values at a specific photon energy according to the interpolation formula [26 ]: $$C=\frac{C_1\left(\log Z_2-\log Z_{eq}\right)+C_2\left(\log Z_{eq}-\log Z_1\right)}{\log Z_2-\log Z_1},$$
where C₁ and C₂ indicate the G–P fitting parameters obtained from ANSI/ANS-6.4.3, the standard database, for Z₁ and Z₂, respectively.
The EBF values for the selected mortar samples were calculated in the energy range between 0.015 MeV to 15 MeV assisted by G–P fitting parameters using the following equations [27 (link)]: $$B\left(E,x\right)=1+\frac{b-1}{K-1} \left(K^x-1\right) , K\ne 1,$$
$$B\left(E,x\right)=1+\left(b-1\right)x , K=1.$$
In these equations,
$$K\left(E,x\right)=c{x}^a+d\frac{\tanh \left(x/X_K-2\right)-\tanh \left(-2\right)}{1-\tanh \left(-2\right)} \mathrm{for} x\le 40 \mathrm{mfp},$$
where E is incident photon energy, and x is the mfp.