A COMPREHENSIVE STUDY ON OPTICAL FEATURES, GAMMA PHOTON BUILDUP FACTORS AND NEUTRON SHIELDING CAPABILITY OF

. Linear, nonlinear optical properties, photon buildup factors, and neutron shielding capability of glasses with chemical composition (65-x)B 2 O 3 -10Sb 2 O 3 -25Li 2 O-xBi 2 O 3 , where x = 0 (BSLB0) – 20 (BSLB20) mol% with steps of 4 mol% were examined. Molar refractivity (R molar ) and molar polarizability (α molar ) were increased as Bi 2 O 3 content mol% increase in the examined BSLB-glasses. The values of metallization criterion (M criterion ) confirmed that the BSLB-glasses were non-metallic materials. The static (ε static ) and optical (ε optical ) dielectric constants having the same trend of the refractive index (n optical ). Values of optical electronegativity (χ * ) were reduced from 0.825 for BSLB0 (Bi 2 O 3 = 0 mol%) glasses to 0.758 for BSLB20 (Bi 2 O 3 = 20 mol%) glasses. The linear electric/dielectric susceptibility (χ (1) ) increased from 0.370 to 0.397. The nonlinear optical susceptibility (χ 3 ) and nonlinear refractive index n 2optical were enhanced by increasing Bi 2 O 3 content in the BSLB-glasses. The BSLB20 glasses presented the least exposure and energy absorption build-up factors (EBF and EABF) at all considered thickness. BSLB20 sample achieved the best fast neutron removal cross section ( Σ  ) shield among all glasses. The total stopping powers (TSP) follows the trend (TSP) BSLB0 < (TSP) BSLB4 < (TSP) BSLB8 < (TSP) BSLB12 < (TSP) BSLB16 < (TSP) BSLB20 . The electron absorbing and hence shielding capacity of the BSLB-glasses improves as their Bi 2 O 3 content increase.


INTRODUCTION
Many scientists are paying more attention to the linear and nonlinear optical properties of transparent materials (glasses). These characteristics aid in the selection of appropriate glasses for specific applications [1][2][3][4][5][6][7][8][9][10][11]. Boron-based glasses are one of the most interesting glasses because of their unique physical properties, which include low cost, ease of preparation, low glass transition temperature, high refractive index, good thermal stability, and higher optical transmission in the infrared region [1,2].
Borate-based glasses are inexpensive and have excellent mechanical, thermal, optical, and electrical properties, making them useful in nuclear optical and radiation protection applications [4][5][6]13]. Furthermore, adding metal oxide glass modifiers to the glass system, such as Bi2O3, Li2O, ZnO, CaO, Al2O3, and CdO, allows the produced glasses to be used in a variety of applications [2][3][4]23]. Glasses made by mixing Bi2O3 into a glass matrix have a high density, a high refractive index, a low crystallisation rate, radiation tolerance, and an increase in other properties [8]. Furthermore, because Bi2O3 glasses have a higher photon absorption coefficient than other glasses, they have a higher radiation shielding efficiency. As a result, borate glasses containing Bi2O3 could be used as X-and gamma-ray shielding materials. Abouhaswa et al. [30] studied the structural, optical, and gamma-ray shielding characteristics of antimony lithium-borate with bismuth glasses. They reported that the enhancement of Bi2O3 content in the mentioned glasses leads to decrease of the optical energy gap and increase the refractive index. In terms of radiation protection issue, the capacity of glasses as radiation shielding increased as Bi2O3 content increase in glasses.
The main goal of this research is to look into the linear and nonlinear optical properties of antimony lithium-borate glasses of composition B2O3-Sb2O3-Li2O-Bi2O3 as well as photon (exposure and energy absorption) build-up factors, and neutron shielding capability of these glasses have been examined. To this end, several of optical characteristics such as molar refractivity, molar polarizability, dielectric constants, electronegativity, nonlinear optical susceptibility, and nonlinear optical refractive index were investigated. Furthermore, gamma-ray build-up factors, the total stopping powers (TSP), and range of the continuous slowing down approximation (CSDA) of glasses were evaluated in order to investigate their uncharged and charged particles shielding efficacy.
Non-linear refractive index,

Photon buildup factors
As is well established, the Beer-Lambert expression can be used to measure the photon absorption potential of any substance by simulation and experimentation: where and reflect the transmitted and incident photon flux through the substance of mass thickness t (g/cm 2 ), respectively. The linear attenuation coefficient ( = LAC) of the absorber is defined as (cm -1 ). When the transmitted photon flux consists of both primary (un-collided) and secondary (scattered) photons, expression (14) becomes: When the transmitted beam does not contain scattered photons, the photon buildup factor (BF) of the photon flux is equal to unity. BF has been the subject of detailed reports elsewhere [35][36][37][38].
The fraction of incident photons transmitted through the attenuator is determined by the photon transmission factor (TF). If the BF is considered, theoretically, TF is expressed as: The EXABCal computer code was used to measure exposure (EBF) and energy absorption (EABF) BF in the BSLB-glasses for selected depths up to 40 MFP in this study [36].

Fast neutron macroscopic removal cross-section ( )
The neutron absorption efficacy of a material is generally described by appropriate microscopic and macroscopic cross-sections of the neutron beam. Unlike photons, neutrons are classified into energy groups such as fast, intermediate, and thermal neutrons. Microscopic and macroscopic cross-sections of neutrons differ and depend on the class/energy of neutrons of interest. For fast neutrons, the fast neutron removal cross-section ( − Σ ) is the macroscopic cross-section for fissile neutrons, while the microscopic scattering and absorption cross-section may be adopted for thermal neutron shielding parameter.
for the glasses under study were calculated via the equation [39,40]: where, , and are the mass density, weight fraction, and mass removal cross-section of the i th element of the glass, respectively. for each constituent element was calculated using their atomic numbers, Z as given in equations 18a and b.

Stopping powers (MSP) and projected range (R) of ions
The stopping power of a charged particle travelling through a substance is the average energy lost by the particle (SP). The coulomb interaction with the orbital electrons of atoms in the substance (electronic loss) or with the atomic nuclei causes the majority of the energy loss (nuclear loss). For protons, total SP includes both electronic and nuclear losses, whereas for electrons, total SP includes both electronic and radiative losses. The ESTAR software [44] was used to determine the total SP and CSDA range (R) of electrons in the selected glasses.

Linear/nonlinear optical parameters
The variation of both (R molar ) and (α molar ) with the changing of Bi2O3 content mol% in the synthesized BSLB0-BSLB20 glasses are depicted in Figure 1(a) and (b), respectively and Table  2. It was noticed that the values of (R molar ) are directly related to the values of (α molar ), and both are increasing with the increase of Bi2O3 content mol%. This variation may be due to the increase of Bi2O3 content in the glass composition, causes the breaking in the regular structure of antimony lithium-borate glasses and raising the number of non-bridging oxygens (NBO) atoms leading to a decrease in the E optical value as in Table 2.
Values of the (T optical ) and (R loss ) with the increasing of Bi2O3 content mol% in the studied BSLB0-BSLB20 glasses are collected in Table 2. It was observed that these parameters were in an inverse relationship due to the increase in the number of (NBO) atoms. The obtained values of (M criterion ), (ε static ), and (ε optical ) with Bi2O3 content mol percent in the studied BSLB0-BSLB20 glasses are listed in Table 2. The (M criterion ) ranged from 0.300 to 0.286, indicating that the samples under consideration are appropriate for nonlinear optical applications. Also, as shown in Tables 1  and 2, the values of (M criterion ) confirm that the BSLB-glasses are non-metallic materials since their (R molar ) values are less than those of (V molar ) [32]. Furthermore, as shown in Table 2, the (ε static ), (ε optical ), and refractive index (n optical ) have the same pattern.  The effect of Bi2O3 content mol percent on the M(E optical ) and M(n optical ) of the BSLB0-BSLB20 glasses depicts as values in Table 2. These two optical parameters have the same pattern, i.e., they decreased as the Bi2O3 content in the glasses increased.
The variation of the optical electronegativity (χ * ) and the linear dielectric susceptibility χ (1) with Bi2O3 content mol% in the BSLB0-BSLB20 glasses is shown in Table 2. As shown in Table  2, the value of χ * reduces from 0.825 for BSLB0 (Bi2O3 = 0 mol%) glasses to 0.758 for BSLB20 (Bi2O3 = 20 mol%) glasses, while χ (1) increases from 0.370 to 0.397. These trends attributed to the increasing number of non-bridging oxygen (NBO) atoms in the investigated BSLB0-BSLB20 glass's framework.
Finally, Figure 2 shows the variation of the nonlinear optical susceptibility, χ 3 (a) and nonlinear refractive index, n2 optical (b) for the investigated BSLB-glasses. As shown from Figure 2 and its corresponding data in Table 2, both (χ 3 ) and n2 optical were enhanced with the increase of Bi2O3 content in the investigated BSLB0-BSLB20 glasses. This enhancement may be due to the increasing number of non-bridging oxygen (NBO) atoms in the glass's framework.

Photon buildup factors
Exposure (EBF) and energy absorption (EABF) buildup factors (BF) of the investigated BSLBglasses and their variations with respect to photon energies (0.1515 MeV) and selected penetration depths up to 40 MFP are presented in Figure 3 for BSLB0 sample and Figure 4 for BSLB20 glasses, respectively. According to the figures, the changes in the BF values with energy are similar for all the glasses except with the peak values at absorption edges which is a function of the chemical composition of the glasses. The partial PA, CS, and PP interaction modes play a major role in the behavior of the build-up factors. Generally, BF values were comparatively lowest in the PA dominated energies safe for absorption edges. On the other hand, values of BF were also lower in the PP dominated energies than the CS energies. Partial CS interaction leads to photon buildup while PA and PP processes absorb the photon and lower build-ups at energies where PA and PP dominate [36]. Comparing the BF of the glasses at two energies; 0.1 MeV ( Figure 5) and 1 MeV (Figure not shown here) and different depths is performed. At both energies, both EABF and EBF increase in values as the thickness (in MFP) of the BSLB-glasses increase; an indication that photons suffer more collisions within the interacting glass medium. Hence the number of photons with lower energy compared to the incident photon energy increase (buildup). Also observed is the fact that at the photon energy of 0.1 MeV, the highest BF was found in BSLB0 glasses while the least was obtained for BSLB12 glasses. For the 1 MeV spectra, the least BF was found for BSLB20 with BSLB4 glasses having the highest. This shows that relative values of BF vary with energy; however, as energy progresses, the BSLB20 glasses presented the least BF at all considered thickness. Considering all the calculated photon interaction parameters, it is obvious that the increase in the Bi content of glasses improves their photon absorption and protection abilities.

Fast neutron macroscopic removal cross-section ( )
The calculated values of Σ for BSLB-glasses varied from 0.1265-0.1584 cm -1 as the Bi2O3 of the glass system increased from 0-20 wt%. This shows consistent growth in the fast neutron removal capacity of the glasses. This is attributed to the growth in partial densities of B and Li in the glasses. These two elements have comparatively higher fast neutron removal cross-sections than other elements present in the glass systems. Based on the Σ results, the best fast neutron shield among the glasses is BSLB20. A comparison of the Σ of water, OC [45] and recently studied glasses (80TeO2.20BaO (TB), 80TeO2.20ZnO (TZ), TVB25 and TVM60) [25,[46][47][48] and BSLB20 is depicted in Figure 6. This shows that the value of Σ for BSLB20 higher than these others and a preferred fast neutron shield compared with these materials.    Total stopping powers (TSP) and CSDA-Range of electrons in the glass system The total stopping powers (TSP) and range of the continuous slowing down approximation (CSDA) of the BSLB-glasses were evaluated in order to investigate their charged particle shielding efficacy. Figure 7 and Figure 8 show the variance of the glasses' TSP and CSDA ranges as a function of electron kinetic energy up to 15 MeV, respectively. In general, as the electron's kinetic energy increases, the TSP of the electron in the glasses decreases at first, then increases slightly. Changes in partial stopping powers caused by electron collision and radiation are thought to be the cause of this action. The collision stopping power (CSP) dominated the TSP of the electron in the glasses below 1 MeV, while the radiative stopping power (RSP) dominated above this energy. With increasing electron kinetic energy, CSP typically decreases while RSP increases, resulting in the observed behavior of the TSP spectra of the glasses. The TSP fits the pattern (TSP)BSLB0 < (TSP)BSLB4 < (TSP)BSLB8 < (TSP)BSLB12 < (TSP)BSLB16 < (TSP)BSLB20 across the entire kinetic energy continuum. The electron's TSP is usually directly proportional to the electron density (Na) of the interacting medium [49]: The Na (Figure 7b) is arranged in the same order as TSP (Figure 7a). This helps to understand why the electron's TSP was highest in the BSLB20 glass study. In addition, Figure 8 shows that the CSDA range of all glasses increases as the electron's kinetic energy increases. Higher-energy particles have a faster velocity and can therefore travel further than lower-energy particles; this explains the observed range trend. The distribution follows the opposite pattern as TSP, so the highest electron range was found in BSLB0 glasses and the lowest in BSLB20 glasses. Since the electron loses more energy in the BSLB20 sample than in the rest glasses, it comes to rest at a lower depth inside the bottle, as shown. As the Bi2O3 content of the BSLB-glasses increases, so does their electron absorption and thus shielding ability.

CONCLUSION
The present study aimed to investigate the linear, nonlinear optical properties, the photon buildup factors, and neutron shielding capability of antimony lithium-borate reinforced with Bi2O3 with chemical composition (65-x)B2O3-10Sb2O3-25Li2O-xBi2O3, where x = 0-20 mol% with steps of 4 mol%. Results revealed that: Values of (R molar ) are in direct relation with the values of (α molar ) and both were increasing with the increase of Bi2O3 content mol% in the examined BSLB-glasses. The (T optical ) and (R loss ) were in an inverse relationship due to the increase in the number of (NBOs) atoms in glass's framework. The values of (M criterion ) confirm that the BSLB-glasses are nonmetallic materials and the (ε static ) and (ε optical ) having the same trend of the refractive index (n optical ). Value of χ * reduces from 0.825 for BSLB0 (Bi2O3 = 0 mol%) glasses to 0.758 for BSLB20 (Bi2O3 = 20 mol%) glasses, while χ (1) increases from 0.370 to 0.397. Both χ 3 and n2 optical were enhanced with the increase of Bi2O3 content in the investigated BSLB0-BSLB20 glasses. The BSLB20 glasses presented the least BF (EBF and EABF) at all considered thicknessBased on the Σ results, the best fast neutron shield among the glasses is the BSLB20 sample. Throughout the entire kinetic energy spectrum, the TSP follows the trend (TSP)BSLB0 < (TSP)BSLB4 < (TSP)BSLB8 <