### Introduction

### Materials and Methods

^{3}) and high density concrete (density: 3.6 g/cm

^{3}). These samples were heated up to 120°C to investigate the effect of heat on shielding properties. Elemental compositions of the concretes before and after the heat treatment are given in Table 1 [4]. It is to be noted that the chemical compositions of the concrete before and after heat treatment change at large extend. These variations in chemical composition lead to alteration of shielding properties.

### 1. MCNPX code

^{8}particles have been tracked as the number of particle (NPS variable). MCNPX calculations were done by using Intel

^{®}Core

^{TM}i7 CPU 2.80 GHz computer hardware. During the simulation study, the relative error rate has been observed less than 1% of the output file.

### 2. Theoretical estimation

#### 1) Mass attenuation coefficients

*I*

_{0}and

*I*are the incident and transmitted photon intensities, respectively,

*μ*(cm

^{−1}) represents linear attenuation coefficient of the material and

*t*(cm) is the thickness of the target material. Rearrangement of Equation 1 yields the following equation for the linear attenuation coefficient:

##### (2)

$$\mu =\frac{1}{t}\hspace{0.17em}\text{ln\hspace{0.17em}}\left(\begin{array}{c}Io\\ I\end{array}\right)$$*w*

*is the weight fraction, (*

_{i}*μ/*

*ρ*) is the mass attenuation coefficient of the material,

*μ*

*is mass attenuation coefficient of element. The*

_{m}*w*

*can be defined as follows:*

_{i}*A*

*is the atomic weight of the sample,*

_{i}*n*

*is a number of formula units. The mass attenuation coefficient of elements is taken from National Institute of Standards and Technology (NIST) using XCOM program.1) The XCOM program provides mass attenuation coefficient of elements for gamma energy 1 keV to 100 GeV and using these data the mass attenuation coefficients of compounds or composites have been computed.*

_{i}#### 2) Effective atomic numbers

*, were calculated using the following equation [13]:*

_{a}*, has been calculated by:*

_{e}##### (6)

$${\sigma}_{e}=\frac{1}{{N}_{A}}{\mathrm{\Sigma}}_{i}\frac{{f}_{i}{A}_{i}}{{Z}_{i}}{({\mu}_{m})}_{i}$$*f*

*indicates to the fractional abundance of the element*

_{i}*i*and

*Z*

*the atomic number of the constituent element. The effective atomic numbers (*

_{i}*Z*

*) is related to σ*

_{eff}*and σ*

_{a}*through the following equation:*

_{e}#### 3) Exposure buildup factors

*Z*

*). The computational work of these parameters is divided in three steps as;*

_{eq}Calculation of equivalent atomic number

Calculation of GP fitting parameters

Calculation of buildup factors

*Z*

*, is a parameter which describes the concretes properties in terms of equivalent elements similar to atomic number for a single element. Since interaction processes (photoelectric effect, Compton scattering and pair production) of gamma ray with matter are energy dependent, therefore*

_{eq}*Z*

*for the concretes varies according with energy and types of concrete. The photoelectric absorption and pair production are complete removal and removal and regeneration processes, therefore the buildup of photons in the concrete samples is mainly due to multiple scattering events by Compton scattering, so that*

_{eq}*Z*

*is derived from the Compton scattering interaction process to understand buildup phenomenon.*

_{eq}*Z*

*, for each concrete sample is estimated by the ratio of*

_{eq}*(μ/*

*ρ*

*)*

_{Compton}*/(μ/*

*ρ*

*)*

*, at a specific energy. Thus first the Compton partial mass attenuation coefficient,*

_{Total}*(μ/*

*ρ*

*)*

*and the total mass attenuation coefficients,*

_{Compton}*(μ/*

*ρ*

*)*

*are for the concrete samples in the energy region 0.015 to 15 MeV using XCOM [13]. The logarithmic interpolation of*

_{Total}*Z*

*is employed by formula [14]*

_{eq}##### (8)

$${Z}_{eq}=\frac{{Z}_{1}(log\hspace{0.17em}{R}_{2}-log\hspace{0.17em}R)+{Z}_{2}(log\hspace{0.17em}R-log\hspace{0.17em}{R}_{1})}{log\hspace{0.17em}{R}_{2}-log\hspace{0.17em}{R}_{1}}$$*Z*

*and*

_{1}*Z*

*are the atomic numbers corresponding to the ratios*

_{2}*R*

*and*

_{1}*R*

*respectively.2) R is the ratio,*

_{2}*(μ/ρ)*

_{Compton}*/(μ/ρ)*

*at specific energy and the ratio*

_{Total}*(μ/ρ)*

_{Compton}*/(μ/ρ)*

*for*

_{Total}*Z*

*lies between two successive ratios.*

_{eq}*Z*

*. The GP fitting parameters for the elements were taken from the ANS, 1991 standard reference database.3)*

_{eq}*b, c, a, X*

_{k}*,*and

*d*) in the photon energy range of 0.015 to 15 MeV up to a 40 mfp by equations [15, 16] as

##### (11)

$$\begin{array}{c}K(E,x)=C{x}^{a}+d\frac{\text{tan\hspace{0.17em}}h\hspace{0.17em}\left({{}^{x}X}_{K}-2\right)-\text{tan\hspace{0.17em}}h\hspace{0.17em}(-2)}{1-\text{tan\hspace{0.17em}}(-2)}\\ \text{for\hspace{0.17em}penetration\hspace{0.17em}depth\hspace{0.17em}}(x)\le 40\hspace{0.17em}\text{mfp}\end{array}$$*X*is the source-detector distance in terms of mfp and b is the value of the EBF at 1 mfp,

*K*(

*E, x*) is the dose multiplicative factor, and

*b, c, a, X*

_{K}*,*and

*d*are computed GP fitting parameters which depends on the attenuating medium and source energy. The

*Z*

*of the concretes is given in Table 3.*

_{eq}#### 4) Macroscopic effective neutron removal cross-section

*∑*

*(=*

_{R}*∑*

_{i}*ρ*

*×(*

_{i}*∑*

*/*

_{R}*ρ*)

*) in unit of cm*

_{i}^{−1}where

*ρ*

*is partial density of the element of the concrete sample. The values obtained for*

_{i}*∑*

_{R}*/ρ*by above equation are accurate within 10% of the experimental values investigated for aluminum, beryllium, graphite, hydrogen, iron, lead, oxygen, boron carbide etc.5) The

*∑*

_{R}*/ρ*values of elements have been taken from Kaplan and Chilton.6,7)

### Results and Discussion

### 1. Mass attenuation coefficients

*μ/ρ*) values of the concrete samples are shown for photon energy rage 1 keV to 100 GeV. The large variation of

*μ/ρ*values of the concrete samples is to be observed and it is divided in three parts as low (E<100 keV), medium (100 keV<E<3 MeV) and high-energy (E>3 MeV) regions. The ordinary concrete sample are showing lesser

*μ/ρ*values than high density concrete sample because ordinary concrete contains lesser composition of high atomic number elements. The variation in low energy region is very sharp increase and decrease of the coefficients with increase in energy. The variation in explained by photo electric effect where interaction cross-section is dependent upon photon energy and atomic number as

*Z*

^{4–5}*/E*

*. The variation in medium energy region is explained by Compton scattering where interaction cross-section is approximately independent upon photon energy and depend upon atomic number only. In high energy range, the variation of*

^{7/2}*μ/ρ*values is due to dependency of interaction cross-section as

*Z*

*. The*

^{2}*μ/ρ*values for few selected energies were computed using MCNPX, compared with XCOM and given in Table 2. It can be noted that the

*μ/ρ*values using MCNPX are comparable with NIST using XCOM program. Here it is concluded that the MCNPX is capable of simulation for radiation interaction in presence of external interfering agent.

*μ/ρ*values for the ordinary and high density concretes are lesser before heat treatment and increases after the heat treatment. It can be concluded that the heat treatment marginally increases shielding effectiveness.

### 2. Effective atomic numbers

*Z*

*) of the concrete samples is shown for photon energy rage 1 keV to 100 GeV. The variation of*

_{eff}*Z*

*with photon energy is similar to the*

_{eff}*μ/ρ*values, therefore it can be explained by photoelectric effect, Compton scattering and pair production interaction processes.

*Z*

*for the ordinary and high density concretes are lesser before heat treatment and increases after the heat treatment. Therefore, it concluded that the heat treatment marginally increases shielding effectiveness for the concrete samples.*

_{eff}### 3. Macroscopic effective neutron removal cross-section

*∑*

*value for ordinary concrete sample. At same time the variation in chemical compositions of heavy concrete samples are insignificant, which results in unnoticed change of*

_{R}*∑*

*value.*

_{R}