## 2.2. Calculation Parameter of the compound glasses

**Radiation absorbing parameters**

Thin beam penetration through a known shield material, attenuate as what has been shown in formula 1., in this equation \({I \text{a}\text{n}\text{d} I}_{0}\) represent incident and penetrated photon intensity respectively. While \(\mu and x\) are linear attenuation coefficient (LAC) and shield thickness respectively in 1/cm and cm dimensions [5–10].

$$I={I}_{0}{e}^{-\mu x}$$

1

By the way if we have used poor thin beam (or broad beam) instead of the narrow one, the photon intensity by penetrating the gamma shield will be calculated by using a corrected formula as follows [7–16]:

$$I={B\left(E,\mu x\right) I}_{0}{e}^{-\mu x}$$

2

In this equation B is the buildup factor, which is energy dependent. This coefficient refers into two types of energy absorption buildup factors, which can demonstrate to the energy deposited in the air and in the material shield. These two factors are EBF and EABF which stands respectively for energy absorption and exposure buildup factor. The accumulated photon number inside the material shield during the photon exposure is described by EABF. In contrast, photon accumulation by the time it has been transmitted from the shield is shown by EBF.

Calculation of these two factors in various photon energies (from 0.015 to 15 MeV) and for different mean free paths can be helpful in selection of the best shielding material.

The desired shield thickness is the other important parameter that should be estimated and compared for different alloys for choosing the best one. It can be explained by using two factors named half value layer (HVL) and mean free path (MFP). MFP can be estimated by using LAC value. Also, HVL is determined in centimeter and shows the length which diminish fifty percentage of incident photon through the next equation:

$$HVL=\frac{\text{l}\text{n}2}{{\mu }}$$

3

Equivalent atomic number is an energy dependent and important factor that can describe multicomponent alloys in terms of equal components. Theoretically Zeq can be estimated by the following formula.

Where Z1 and Z2 are atomic number of compositions. R1 and R2 are the ratio of Compton partial mass attenuation coefficient and total mass attenuation coefficient of each composition

(\(R=\frac{{\left(\raisebox{1ex}{$\mu $}\!\left/ \!\raisebox{-1ex}{$\rho $}\right.\right)}_{Compton}}{{\left(\raisebox{1ex}{$\mu $}\!\left/ \!\raisebox{-1ex}{$\rho $}\right.\right)}_{Total}}\)).

$${Z}_{eq}=\frac{{Z}_{1}(\text{log}{R}_{2}-\text{log}R)+{Z}_{2}(\text{log}R-\text{log}{R}_{1})}{{\text{log}{R}_{2}-\text{log}{R}_{1}}_{}}$$

4

In this study it has been calculated by Phy-X/PSD for various energies between 0.015 up to 15 MeV. Moreover linear attenuation coefficient parameters have been calculated by Monte Carlo simulations with MCNPX2.6.0 version [7–16].

**Deterministic calculations of shielding parameter**

Recently researchers in the last few decades show more interests of calculating photon attenuation. As we know theoretical calculation of all shielding parameters for wide/various energy range are very time consuming. So that from 1995 till now many software like WinXCOM, Auto Zeff, Direct Zeff, ZXCOM, BXCOM, have been developed for all these calculations [17]. One of friendly software for these computations has been introduced from 2019 is Phy-X/PSD Many studies has shown its high precision [14], while it take much lower time in comparison of previous programs [17]. So in this manuscript this online software has been used for shield parameter calculations (LAC, EBF, EABF, HVL, MFP, Zeq, FNRCS).

Recently Monte Carlo simulation (MCS) has been developed to estimate the strength distributions of heterogeneous materials influenced by different factors. In 2018, it has been showed that MSC are very benefit method for investigating shielding parameters [2–5]. Besides using Phy/X software to investigate radiation interaction variables, here we have used high-powered beneficial Monte Carlo based tools MCNPX 2.6.0. The radiation source is located in 10cm of collimator. Five millimeters thickness glass shields attenuate parallel ionized beams. Linear attenuation coefficient (LAC), Mean Free Path (MFP) and the Half Value Layer (HVL) of this setup have been calculated and double checked by online phy-X/PSD software, for all various photon energies between 0.015MeV to 15MeV.