Calculation of the Effects of Silver (Ag) Dopant on Radiation Shielding Efficiency of BiPbSrCaCuO Superconductor Ceramics Using EGS4 Code

Abstract

In the current study, the effects of silver (Ag) additive on the radiation shielding efficiency of BiPbSrCaCuO superconducting ceramics was calculated using the EGS4 code and discussed theoretically by comparison with XCOM data. The mass attenuation coefficients (µ/ρ) for BiPbSrCaCuO superconductor ceramics and their contents were investigated theoretically (WinXcom and EGS4) at gamma-ray energies ranging from 59.5 to 1332 keV. The theoretical values were computed in the energy range from 1 keV to 100 MeV using the WinXcom program. Then, using the mass attenuation coefficients, some shielding parameters were determined, such as the mean free path (MFP), the half value layer (HVL), the effective atomic number (Zeff), the radiation protection efficiency (RPE), the macroscopic fast neutron removal cross-sections (ΣR, cm⁻¹) and the gamma-ray kerma coefficients ($k_{\gamma }$). Theoretically, the results obtained with XCOM and EGS-4 were found to be in good agreement. The radiation shielding efficiency (RPE), neutron removal cross-section (ΣR, cm⁻¹), maximum and semi-valent layer (HVL), and mean free path (MFP) values were found to be smaller for BiPbSrCaCuO superconducting ceramics as the silver (Ag) contribution was increased. Data from this study can guide further research and development of shielding materials for gamma-ray and neutron shielding.

1. Introduction

Superconducting materials play a significant role in the development of technology. Superconductivity is a phenomenon where certain materials, when cooled below a critical temperature, exhibit zero electrical resistance. This property opens up a wide range of possibilities and applications across various fields. Ceramic superconductors, also known as high-temperature superconductors, are materials that exhibit superconductivity at higher temperatures than traditional metallic superconductors. The discovery of ceramic superconductors in 1986 opened up new possibilities for the use of superconductivity in practical applications [1].

Superconductors are used in many sciences, research fields, technological advancements, and medical applications such as magnetic levitation, MRI (magnetic resonance imaging), electrical energy transmission, particle accelerators, and energy storage. Radiation sensors and superconducting quantum interferometer devices (SQUIDs) are among the most important examples of superconducting electronics [2].

Superconductors have potential applications in high-energy physics, such as magnets for nuclear fusion reactors and particle accelerators. However, these applications can present challenges, as the superconducting materials can be sensitive to high levels of radiation, which can affect their superconducting performance and cause them to degrade over time [3]. The mass attenuation coefficient (MAC) is a parameter that describes the ability of a material to attenuate or reduce the intensity of a beam of electromagnetic radiation as it passes through the material. It is a measure of the probability that an incident photon will interact with the material through processes such as absorption, scattering, or both. It depends on the energy of the gamma rays and the properties of the material. For a given material, the mass attenuation coefficient generally decreases as the energy of the gamma rays increases, because higher-energy gamma rays are less likely to be absorbed or scattered by the atoms in the material. The MAC is a key parameter used to calculate the fraction of gamma rays that penetrate a material and the fraction that are absorbed or scattered. The MAC depends on the energy of the incident radiation and the composition of the material. Different materials have different MAC values, and the MAC can vary significantly for different types of radiation (e.g., X-rays, gamma rays) and energy ranges. The MAC is an important parameter in various fields, including radiation protection, medical imaging, industrial radiography, and material characterization. It is used to calculate the amount of radiation absorbed or transmitted through a material, which is crucial for determining radiation doses, optimizing imaging techniques, and ensuring safety in various applications. By understanding the behavior of superconductors in response to gamma-ray radiation and using different values for the MAC (µ/ρ), Z_eff, RPE, and gamma-ray kerma (kγ) coefficient, we will be more resistant to gamma-ray radiation, and better high-energy particle physics experiments on superconductors with good performance can be designed [4]. The XCOM software was developed by Berger and Hubbell as a tool for calculating the mass attenuation coefficients and photon cross-sections for elements, compounds, and mixtures over a wide range of energies, from 1 keV to 100 GeV [5]. To make the software more accessible and user-friendly, Gerward et al. developed a modified version of XCOM known as WinXCOM [6].

Monte Carlo simulation is a computational technique that uses random sampling to model and analyze complex systems or processes. It is particularly useful when analytical solutions are difficult or impossible to obtain. Monte Carlo simulation is an important tool used in various fields, including those previously mentioned such as nuclear physics, nuclear engineering, medical physics, radiation safety management, and reactor design. By simulating the behavior of gamma rays as they pass through materials, Monte Carlo methods were used to calculate mass attenuation coefficients and other parameters important to understanding gamma-ray interactions [7,8,9,10]. Kinetic energy released in materials (KERMA) is a term used in radiation physics to describe the amount of energy deposited in a material by ionizing radiation [11]. Kerma is generally greater than the absorbed dose because some of the energy released from the interaction of ionizing radiation with matter can be carried away by very energetic secondary particles such as electrons or photons, which can travel some distance before depositing their energy in the material. When ionizing radiation interacts with matter, it can ionize atoms and molecules in the material, creating charged particles such as electrons and ions. These charged particles can then transfer their energy to other atoms and molecules in the material through further ionization and excitation, creating a cascade of secondary particles. Some of these secondary particles can have very high energies and can travel some distance before depositing their energy in the material. This means that the energy deposited by the ionizing radiation may not be entirely absorbed in the immediate vicinity of the interaction site, resulting in a difference between the kerma and absorbed dose. These energetic particles can escape from the material of interest and interact with other materials, or simply exit the system without depositing all their energy, thereby reducing the absorbed dose in the material of interest.

Recently, there have been many studies focused on calculating gamma kerma coefficients for a wide variety of composite substances. These studies aim to better understand the behavior of ionizing radiation in these materials and to develop more effective radiation shielding and dosimetry systems [8,12,13,14,15,16]. In recent years, many studies have been carried out in this field of study [17,18,19,20].

In this study, the mass attenuation coefficients of BiPbSrCaCuO superconductor ceramics were theoretically calculated using Monte Carlo simulations based on EGS4 and WinXCOM for energies from 59.5 to 1332 keV. The computed theoretical XCOM and EGS4 mass attenuation coefficient (MAC) values were used to determine some shielding parameters such as the MFP, HVL, Zeff, RPE, and gamma kerma coefficients (kγ). At the same time, macroscopic effective removal cross-sections (ΣR, cm⁻¹) for fast neutrons have also been calculated.

2. Material and Methods

2.1. Monte Carlo Simulation

In the current study, in order to determine gamma attenuation parameters and kerma coefficients, EGS4 (Electron Gamma Showers) Nelson and Hirayama was used to perform the calculations [21]. Monte Carlo simulations with EGS4 were used to simulate the HPGe detector response. Since random number generation is of importance in MC calculations, one must use a verified random number generator. A RANLUX random number generator was used with the EGS4 code, as it was shown to produce relatively better distributions and a longer sequence [22]. For the model executed with EGS4, the efficiency was divided into 10,010 energy bins, each one having a width of 0.3 keV.

The calculated area is divided into 241 cells, and a cylindrical geometry is achieved when this shape is rotated 360° on the axis given Figure 1. It will be assumed that Figure 1 shows a series of cylindrical circular projectiles, each with a radius represented by R1, R2, …, R11 and planes represented by P1, P2, …, P20. A part of the code was created for the point radioactive source in a manner where all photons were released over the z-axis, giving a beam of collimated photons [8,10,23,24].

In the calculations, two sources of uncertainty contributed to the data obtained: statistical uncertainties and cross-section uncertainties in the Monte Carlo program used. In all calculations, the program generated 10⁸ photons, which reduces the statistical uncertainty to as low as 0.5% for all the photon energies, which are smaller than the symbols in the plots. The uncertainty in the MAC parameters used by EGS4 is generally around 2%. Mass absorption coefficients were determined by making calculations for gamma photons with energies of 59.5, 122, 383, 511, 662, 1274, and 1332 keV. The relative error of the simulated values is less than 1%. Therefore, we estimated the total uncertainty to be around 3%.

2.2. Gamma Attenuation Parameters

In this study, according to the formula Bi_1.64−xPb_0.36Ag_xSr₂Ca₂Cu₃O_4+2n (x = 0.00, 0.04, 0.08, 0.12, 0.16), n = 3 was generalized and silver-doped superconducting ceramic samples were selected [25]. The samples were named BiPbSrCaCuO (x = 0.00), BiPbAgSrCaCuO-1 (x = 0.04), BiPbAgSrCaCuO-2 (x = 0.08), BiPbAgSrCaCuO-3 (x = 0.12), and BiPbAgSrCaCuO-4 (x = 0.16), respectively. Mass attenuation coefficient (MAC) parameters were determined as prescribed in the following:

The attenuation of gamma rays in a material can be described using the Beer–Lambert law, which states:

$$I=I_0{e}^{-\mu x}$$

(1)

where I is the intensity of the gamma-ray beam after it has passed through a thickness x of the material, I₀ is the initial intensity of the beam, and µ (cm⁻¹) is the linear attenuation coefficient of the material for the specific energy of the gamma rays being considered.

While the linear attenuation coefficient (μ) is commonly used to describe how strongly a material absorbs gamma rays, it has the disadvantage of depending on the density of the material. Therefore, it is often more useful to use the density-independent mass attenuation coefficient (μ/ρ), which is expressed in units of cm²/g.

The density-independent mass attenuation coefficient can be calculated using the following formula $\mu /\rho$ (cm²/g):

$$I=I_0{e}^{-\left(\mu /\rho \right)\rho x}=I_0{e}^{-\left(\mu /\rho \right)d}$$

(2)

According to the Beer–Lambert law equation, the thickness “d” is expressed in unit area mass of the material (g/cm²). When a superconductor sample contains more than one metal, the mass attenuation coefficient (μ/ρ) of the sample can be calculated using the mixture rule formula, which is given as:

$$\mu /\rho ={\sum }_i{w}_i{\left(\mu /\rho \right)}_i$$

(3)

where w_i is the weight fraction of the ith component in the sample and (μ/ρ)_i is the density-independent mass attenuation coefficient of the ith component [26].

The weight fraction (w_i) of a chemical component i in a mixture can be calculated using the following relation:

$$w_i=\frac{a_i{A}_i}{\sum a_i{A}_i}$$

(4)

where $a_i$ is the number of formula units, A_i is the atomic weight of the ith element, and the summation is taken over all components in the mixture.

Mass attenuation coefficients (μ/ρ) of the samples under study are computed by MC-EGS4 simulation code and compared to WinXCOM results in the energy range of 0.0595–1.332 MeV. The theoretical mass attenuation coefficients (µ/ρ) of the superconductor samples were determined using WinXCom software version 3.1 [6,8,23,27].

The effective atomic number (Zeff) is a parameter that is often used to quantify the shielding efficiency of a material against radiation. Zeff is a weighted average of the atomic numbers of the constituent atoms in a material, taking into account both the number and energy of the incident photons or particles. The concept of Zeff is particularly useful in radiation shielding applications because it provides a convenient way to compare the radiation attenuation properties of different materials. The Zeff of the samples under investigation have been computed using the formula [28]:

$$Z_{eff}=\frac{\sum f_i{A}_i{\left(\frac{\mu }{\rho }\right)}_i}{\sum \frac{f_i{A}_i}{Z_i}{\left(\frac{\mu }{\rho }\right)}_i}$$

(5)

where f_i is the weight fraction of the i-th element in the material, A_i is the atomic weight of the i-th element, and Z_i is the atomic number of the i-th element [29].

The half value layer (HVL) of the materials is the thickness that reduces the radiation entering it by half [24]: the HVL can be calculated using the following equation:

$$HVL=\frac{0.693}{\mu }$$

(6)

The mean free path (MFP) is a measure of the average distance a particle or photon can travel in a material before it interacts with the material in some way, such as absorption, scattering, or transmission. In general, the MFP is the inverse of the linear attenuation coefficient (µ) of a material, which describes how much radiation is absorbed or scattered per unit length of the material. The mean free path (MFP) was calculated using μ values, as follows [30]:

$$MFP=\frac{1}{\mu }$$

(7)

where μ is the linear attenuation coefficient, whose unit of measurement is cm⁻¹.

The radiation protection efficiency (RPE) parameter of superconductors was investigated. The efficiency (RPE) in terms of incoming and transmitted photon densities is given by the equation below [31]:

$$RPE=\left(1-\frac{I}{I_0}\right)\ast 100$$

(8)

2.3. Determination of Kerma Coefficient ($k$)

Kerma, which stands for kinetic energy released per unit mass, is a measure of the amount of energy that is transferred from ionizing radiation to the material it passes through. In other words, it is the sum of the initial kinetic energies of all the charged particles liberated by the incident radiation, divided by the mass of the material. The absorbed dose is a measure of the energy deposited per unit mass in the target material, which takes into account not only the initial kinetic energy of the charged particles but also their subsequent interactions with the material.

It is defined as the sum of the initial kinetic energies of all the charged particles (electrons and positrons) that are liberated by the incident radiation as it passes through the material, divided by the mass of the material:

The kerma coefficient (Gy·cm²/photon) for uncharged particles can be calculated using the mass attenuation coefficient and partial interaction probabilities. It is given by the equation:

$$K=k\phi \left[\frac{{\mu }_{tr}}{\rho }\right]$$

(9)

where K is the uncharged radiation of energy E, $k\phi$ is the kerma coefficient, and ${\mu }_{tr}/\rho$ is the mass energy-transfer coefficient of the substance [32]:

$$k_{Ex}(E)=k_D{\displaystyle \sum _i{w}^i[{({\mu }_{tr}/\rho )}_{\tau ,Ex}^{i}E+{\overline{f}}_C{({\mu }_{tr}/\rho )}_{C,Ex}^{i}E+{({\mu }_{tr}/\rho )}_{\kappa ,Ex}^i(E-1.022)}]$$

(10)

$$k_t(E)=k_D{\displaystyle \sum _i{w}^i[{({\mu }_{tr}/\rho )}_{\tau ,t}^{i}E+{\overline{f}}_C{({\mu }_{tr}/\rho )}_{C,t}^{i}E+{({\mu }_{tr}/\rho )}_{\kappa ,t}^i(E-1.022)}]$$

(11)

Methods for finding the photon kerma coefficients of superconductors have been given in previous studies [8,14,33,34].

The fast neutron macroscopic cross-section ΣR (cm⁻¹) is a parameter used in neutron transport theory and nuclear reactor analysis. It quantifies the probability of interaction per unit length traveled by fast neutrons through a material. The ΣR value for a neutron shield is calculated as the next relationship

$${\mathsf{\Sigma }}_R/\rho ={\displaystyle \sum _{i}w{}_i({\mathsf{\Sigma }}_R/\rho )_i}$$

(12)

and

$${\mathsf{\Sigma }}_R={\displaystyle \sum _i\rho {}_i({\mathsf{\Sigma }}_R/\rho )_i}$$

(13)

where ρi (g/cm³) and ΣR/ρ (cm²/g) are the partial density and the fast neutron removal cross-section of the ith element, respectively [28,35,36,37]. The partial density of the ith element (ρi) is obtained from the following equation:

$${\rho }_i=\rho \times w_i$$

(14)

where ρ represents the density of the sample (g/cm³) and w_i denotes the weight fraction of the ith element, respectively [28].

3. Results and Discussion

The physicochemical properties of BiPbSrCaCuO superconductor ceramics are given in

Table 1. Chemical composition (weight fraction %) of Ag-dopant BiPbSrCaCuO ceramic superconducting samples.

Compound	O	Ca	Cu	Sr	Pb	Bi	Ag
Bi1.64Pb0.36Sr2Ca2Cu3O10	15.63	7.83	18.63	17.12	7.29	33.49
Bi1.6Pb0.36Ag0.04Sr2Ca2Cu3O10	15.70	7.86	18.7	17.19	7.32	32.80	0.42
Bi1.56Pb0.36Ag0.08Sr2Ca2Cu3O10	15.76	7.90	18.78	17.26	7.35	32.11	0.85
Bi1.52Pb0.36Ag0.12Sr2Ca2Cu3O10	15.82	7.93	18.85	17.33	7.38	31.41	1.28
Bi1.48Pb0.36Ag0.16Sr2Ca2Cu3O10	15.89	7.96	18.93	17.40	7.41	30.71	1.71

. The calculated EGS4 and XCOM mass attenuation coefficients µ/ρ (cm² g⁻¹) of the samples at different energies of 59.5, 122, 383, 511, 662, 1274, and 1332 keV are given in

Table 2. Calculated (EGS4) and theoretical (XCOM) values of mass attenuation coefficients μ/ρ (cm²/g).

Elements and Compounds	μ/ρ (cm2/g)
	59.54 keV		122 keV		383 keV		511 keV		662 keV		1274 keV		1332 keV
	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM
8O	0.195	0.192	0.148	0.145	0.102	0.097	0.087	0.086	0.075	0.077	0.056	0.056	0.058	0.055
20Ca	0.679	0.670	0.201	0.202	0.106	0.100	0.086	0.088	0.080	0.078	0.056	0.056	0.054	0.055
29Cu	1.602	1.626	0.315	0.310	0.092	0.096	0.080	0.083	0.071	0.073	0.058	0.052	0.051	0.051
38Sr	3.177	3.282	0.522	0.522	0.098	0.101	0.087	0.083	0.075	0.072	0.053	0.050	0.049	0.049
47Ag	5.649	5.888	0.879	0.887	0.115	0.118	0.088	0.092	0.074	0.076	0.056	0.052	0.049	0.050
82Pb	5.115	5.120	3.262	3.366	0.254	0.251	0.160	0.156	0.115	0.110	0.064	0.058	0.057	0.056
56Bi	5.312	5.337	3.446	3.482	0.244	0.259	0.164	0.160	0.113	0.113	0.062	0.059	0.056	0.057
Bi1.64Pb0.36Sr2Ca2Cu3O10	3.122	3.108	1.555	1.597	0.155	0.163	0.113	0.115	0.085	0.090	0.058	0.055	0.052	0.054
Bi1.6Pb0.36Ag0.04Sr2Ca2Cu3O10	3.110	3.101	1.542	1.579	0.165	0.162	0.116	0.115	0.090	0.089	0.063	0.055	0.054	0.054
Bi1.56Pb0.36Ag0.08Sr2Ca2Cu3O10	3.087	3.095	1.539	1.560	0.155	0.161	0.120	0.114	0.091	0.089	0.060	0.055	0.055	0.054
Bi1.52Pb0.36Ag0.12Sr2Ca2Cu3O10	3.077	3.088	1.530	1.541	0.158	0.160	0.116	0.114	0.087	0.089	0.057	0.055	0.053	0.054
Bi1.48Pb0.36Ag0.16Sr2Ca2Cu3O10	3.073	3.082	1.503	1.522	0.153	0.159	0.105	0.113	0.089	0.089	0.059	0.055	0.053	0.054

. Theoretically, for each sample investigated, using WinXcom and EGS4 code, the mass absorption coefficient values obtained at all energies were found to be close to each other. The values of the half value layer (HVL), mean free path (MFP), effective atomic number (Zeff), and radiation protection efficiency (RPE) of the BiPbSrCaCuO superconductor ceramics are given in

Table 3. Calculated (EGS4) and theoretical (XCOM) values of half value layer (HVL).

Samples	Half Value Layer (HVL)
	59.54 keV		122 keV		383 keV		511 keV		662 keV		1274 keV		1332 keV
	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM
Bi1.64Pb0.36Sr2Ca2Cu3O10	0.042	0.042	0.085	0.082	0.850	0.807	1.166	1.145	1.550	1.469	2.272	2.372	2.534	2.438
Bi1.6Pb0.36Ag0.04Sr2Ca2Cu3O10	0.042	0.042	0.085	0.083	0.798	0.812	1.136	1.149	1.464	1.473	2.091	2.374	2.440	2.440
Bi1.56Pb0.36Ag0.08Sr2Ca2Cu3O10	0.043	0.042	0.086	0.084	0.850	0.817	1.098	1.154	1.448	1.477	2.196	2.376	2.395	2.442
Bi1.52Pb0.36Ag0.12Sr2Ca2Cu3O10	0.043	0.043	0.086	0.085	0.834	0.822	1.136	1.159	1.514	1.481	2.311	2.378	2.486	2.443
Bi1.48Pb0.36Ag0.16Sr2Ca2Cu3O10	0.043	0.043	0.088	0.087	0.861	0.827	1.255	1.164	1.480	1.486	2.233	2.379	2.486	2.445

,

Table 4. Calculated (EGS4) and theoretical (XCOM) values of mean free path (MFP).

Samples	Half Value Layer (HVL)
	59.54 keV		122 keV		383 keV		511 keV		662 keV		1274 keV		1332 keV
	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM
Bi1.64Pb0.36Sr2Ca2Cu3O10	0.061	0.061	0.122	0.119	1.226	1.164	1.686	1.651	2.236	2.120	3.277	3.422	3.655	3.517
Bi1.6Pb0.36Ag0.04Sr2Ca2Cu3O10	0.061	0.061	0.123	0.120	1.152	1.171	1.639	1.658	2.112	2.126	3.018	3.425	3.521	3.520
Bi1.56Pb0.36Ag0.08Sr2Ca2Cu3O10	0.062	0.061	0.124	0.122	1.226	1.179	1.584	1.665	2.089	2.131	3.168	3.427	3.456	3.522
Bi1.52Pb0.36Ag0.12Sr2Ca2Cu3O10	0.062	0.061	0.124	0.123	1.203	1.186	1.639	1.672	2.185	2.137	3.335	3.430	3.586	3.525
Bi1.48Pb0.36Ag0.16Sr2Ca2Cu3O10	0.062	0.062	0.126	0.125	1.242	1.193	1.810	1.679	2.136	2.143	3.222	3.433	3.586	3.528

,

Table 5. Calculated (EGS4) and theoretical (XCOM) values of effective atomic number (Z_eff).

Samples	Effective Atomic Number (Zeff)
	59.54 keV		122 keV		383 keV		511 keV		662 keV		1274 keV		1332 keV
	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM
Bi1.64Pb0.36Sr2Ca2Cu3O10	54.12	53.91	62.15	63.98	33.44	35.52	30.33	31.18	26.91	28.69	26.69	25.77	24.50	25.70
Bi1.6Pb0.36Ag0.04Sr2Ca2Cu3O10	53.70	53.55	62.04	63.52	35.57	34.98	31.08	30.71	28.42	28.26	28.89	25.40	25.36	25.34
Bi1.56Pb0.36Ag0.08Sr2Ca2Cu3O10	53.08	53.52	62.34	63.19	33.39	34.74	32.08	30.52	28.66	28.11	27.42	25.30	25.74	25.23
Bi1.52Pb0.36Ag0.12Sr2Ca2Cu3O10	52.70	52.90	62.39	62.86	34.01	34.50	30.95	30.34	27.33	27.96	25.95	25.19	24.72	25.13
Bi1.48Pb0.36Ag0.16Sr2Ca2Cu3O10	52.41	52.57	61.72	62.52	32.91	34.26	27.96	30.15	27.88	27.81	26.77	25.08	24.63	25.02

and

Table 6. Values of the theoretical (XCOM) and calculated (EGS4) radiation protection efficiency (%) for superconductors.

Samples	Radiation Protection Efficiency (%)
	59.54 keV		122 keV		383 keV		511 keV		662 keV		1274 keV		1332 keV
	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM
Bi1.64Pb0.36Sr2Ca2Cu3O10	99.99	100	99.99	100	68.11	69.94	56.57	57.15	46.54	48.30	34.77	33.57	31.76	32.83
Bi1.6Pb0.36Ag0.04Sr2Ca2Cu3O10	100	100	100	100	70.34	69.73	57.49	57.01	48.24	48.39	33.55	37.14	32.81	32.94
Bi1.56Pb0.36Ag0.08Sr2Ca2Cu3O10	100	100	100	100	67.98	69.51	58.65	56.86	48.83	48.14	35.69	33.53	33.29	32.79
Bi1.52Pb0.36Ag0.12Sr2Ca2Cu3O10	100	100	100	100	68.73	69.28	57.49	56.71	47.24	48.05	34.25	33.51	32.12	32.77
Bi1.48Pb0.36Ag0.16Sr2Ca2Cu3O10	100	100	100	100	67.59	69.06	53.70	56.55	48.21	47.95	35.31	33.49	32.12	32.75

, respectively. The change graphs of the BiPbSrCaCuO superconductor samples’ HVL and MFP values versus photon energy, variation in energy with half value layer (HVL), and mean free path (MFP) for given the superconductors were plotted in the 1 keV–100 MeV energy range and shown in Figure 2 and Figure 3, respectively. From these figures, it is seen that both the half value layer (HVL) and the mean free path (MFP) values for the superconductors examined increase with the increasing photon energy.

In addition, when the HVL and MFP values of the examined superconductors were compared from the figures, it was seen that the BiPbSrCaCuO superconductor samples had lower HVL and MFP values as the contribution of silver increased. Therefore, it has been observed that the superconductor samples have better attenuation properties when the silver doping is increased. The relationship between HVL/MFP and photon energy can be explained by the fact that higher-energy photons are less likely to be absorbed or scattered by the material. Therefore, as photon energy increases, HVL and MFP values increase, indicating that the material becomes more transparent to higher-energy photons. In superconducting samples, lower HVL and MFP values correspond to higher photon shielding properties [24]. The variation in Z_eff with photon energy in all superconductors samples is shown in Figure 4. Ag-doped BiPbSrCaCuO superconducting ceramic samples differ in their Zeff values depending on their chemical composition. Figure 5 shows the changes in RPE with photon energy for the investigated superconductors samples. In Figure 5, it is seen that the RPE values decrease as the photon energy increases. In addition, the effective removal cross-sections (ΣR) for the different alloys were calculated and are plotted in Figure 6. It can be seen from Figure 6 that the highest ΣR (cm⁻¹) value was recorded for Bi_1.48Pb_0.36Ag_0.16Sr₂Ca₂Cu₃O₁₀ and the lowest one was noticed for Bi_1.64Pb_0.36Sr₂Ca₂Cu₃O₁₀.

The theoretical (K_T) and simulation (K_EGS4) kerma coefficients values for the samples and the seven elements are given in

Table 7. Values of the theoretical (XCOM) and calculated (EGS4) kerma coefficients k (in pGy·cm²/photon) for superconductors and several elements.

Samples	k (in pGy·cm2/photon)
	59.54 keV		122 keV		383 keV		511 keV		662 keV		1274 keV		1332 keV
	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM	EGS4	XCOM
8O	0.31	0.31	0.47	0.46	1.89	1.81	2.45	2.43	3.03	3.12	5.40	5.45	5.92	5.63
20Ca	4.52	4.46	1.35	1.36	2.00	1.88	2.43	2.48	3.23	3.15	5.40	5.46	5.51	5.64
29Cu	13.14	13.34	3.50	3.44	1.87	1.96	2.33	2.41	2.91	2.97	5.60	5.04	5.21	5.21
38Sr	27.81	28.77	7.43	7.43	2.27	2.35	2.71	2.59	3.18	3.03	5.15	4.89	5.03	5.05
47Ag	50.84	53.05	14.08	14.21	3.14	3.23	3.03	3.16	3.33	3.43	5.52	5.10	5.10	5.26
82Pb	43.23	43.31	59.34	61.23	11.20	11.07	8.51	8.30	7.34	7.03	7.26	6.62	6.78	6.69
56Bi	45.01	45.27	62.76	63.42	10.84	11.49	8.80	8.60	7.28	7.25	7.10	6.75	6.70	6.81
Bi1.64Pb0.36Sr2Ca2Cu3O10	26.22	26.13	27.06	27.79	5.56	5.85	4.86	4.95	4.50	4.75	6.05	5.78	5.70	5.92
Bi1.6Pb0.36Ag0.04Sr2Ca2Cu3O10	26.13	26.09	26.81	27.44	5.89	5.79	4.97	4.91	4.75	4.72	6.57	5.79	5.91	5.92
Bi1.56Pb0.36Ag0.08Sr2Ca2Cu3O10	25.95	26.04	26.73	27.09	5.51	5.74	5.13	4.88	4.79	4.70	6.25	5.78	6.02	5.91
Bi1.52Pb0.36Ag0.12Sr2Ca2Cu3O10	25.87	26.00	26.54	26.74	5.60	5.68	4.94	4.84	4.57	4.67	5.93	5.76	5.79	5.90
Bi1.48Pb0.36Ag0.16Sr2Ca2Cu3O10	25.85	25.95	26.04	26.38	5.40	5.62	4.45	4.80	4.66	4.64	6.13	5.75	5.79	5.88

for energies from 59.5 to 1332 keV. The gamma kerma coefficients (gy·cm²/photon) of the seven elements that make up the superconductors in the wide energy range between 1 keV and 100 MeV are given in Figure 7 as a function of photon energy. It is seen in Figure 7 that the kerma coefficients of the elements increase as the atomic number and photon energy increase. The dominance of different processes of gamma ray interaction also plays a role in determining the kerma coefficients. At low energies, where the photoelectric effect is dominant, the kerma coefficients increase with increasing atomic number because electrons acquire almost no kinetic energy in the interaction. Compton scattering is almost elastic at low photon energies, which contributes to the increase in kerma coefficients. At higher energies, the scattering and pair production processes dominate, leading to higher values of the kerma coefficient. In summary, the Z-dependence of the mass attenuation coefficient, as well as the dominance of different interaction processes, contribute to the alterations in the kerma coefficients with respect to energy. The graph of the changes in gamma kerma coefficients for the BiPbSrCaCuO superconducting ceramic samples is shown in Figure 8. It is clear that the kerma coefficients of the BiPbSrCaCuO superconductors are almost the same for all energies. The behavior of the kerma coefficient curves with respect to gamma-ray energy is determined by the relative contributions of various partial photon interaction processes such as the photoelectric effect, Compton scattering, and pair production. The contribution of each process depends on the photon energy and the atomic number of the absorber material. In the intermediate energy region, as the photon energy increases, the contribution of Compton scattering and pair production increases relative to the photoelectric effect, resulting in a decrease in the kerma coefficient.

4. Conclusions

In this study, radiation protection parameters of silver-doped BiPbSrCaCuO superconductor samples were investigated at gamma energies of 59.5 to 1332 keV. The theoretical values of mass attenuation coefficients have been calculated in the energy range from 1 keV to 100 MeV by means of the WinXCom software. It was used to determine some shielding parameters such as HVL, MFP, Zeff, RPE, and kerma ($k_{\gamma }$) by using mass attenuation coefficient values. In addition, the effective removal cross-sections (Σ_R) for the different alloys were calculated. Mass attenuation coefficients (MAC), HVL, MFP, Zeff, RPE and gamma-ray kerma coefficients ($k_{\gamma }$) were evaluated at 59.5, 122, 383, 511, 662, 1274, and 1332 keV gamma energies for BiPbSrCaCuO superconductors and seven elements using the EGS4 Monte Carlo simulation package. The variation in the radiation shielding parameters for superconductors was computed in the in the energy range from 1 keV to 100 MeV utilizing the WinXCom program, and these were plotted. The values of the MAC (µ/ρ), Zeff, RPE, and gamma-ray kerma ($k_{\gamma }$) coefficient are all dependent on the incident photon energy and the elemental composition of the material through which the gamma rays are passing.

One potential application of superconductivity in particle physics is in the construction of superconducting magnets, which are used to bend and focus charged particle beams in particle accelerators. These magnets must be able to operate in high-radiation environments, where gamma rays can be produced as a result of the interaction between particles and materials. The mass attenuation coefficients of the materials used in the magnets are therefore important parameters to consider in the design and optimization of these magnets.

As the silver (Ag) contribution increases for BiPbSrCaCuO superconducting ceramics, there is a serious decrease in the mass attenuation coefficients up to the first 500 keV. At higher energies, the mass attenuation coefficients drop less. The radiation shielding efficiency (RPE), the neutron removal cross-section (ΣR, cm⁻¹), the maximum and semi-valent layer (HVL), and the mean free path (MFP) values were found to be small for BiPbSrCaCuO superconducting ceramics as the silver (Ag) contribution was increased. Data from this study can guide further research and development of shielding materials for gamma ray and neutron shielding. This work will be useful in designing applications of superconductivity for use in high-energy particle physics experiments, where gamma rays can be produced as a result of the interaction between particles and materials.