Effective Atomic Weight,Effective Atomic Numbers and Effective Electron Densities of Hydride and Borohydride Metals for Fusion Reactor Shielding

The effective atomic weight, A _eff , mass attenuation coefficients, μ/ρ, half-value layer, HVL, effective atomic numbers, Z _eff and effective electron densities, N _eff of hydride and borohydirde metals, with potential shielding applications in fusion reactors have been investigated in the present work. The gamma ray interaction parameters, μ/ρ, HVL, Z _eff and N _eff were calculated for photon energy range 1 keV–100 GeV. The A _eff was calculated using fast neutron removal cross-sections (Σ _R ) for neutron energy 2–12 MeV. The effective atomic number using fast neutron Σ _R was evaluated for compound/composite materials first time. The compounds or mixture containing low as well high atomic weight elements are required for fast neutron shielding. The Mg (BH₄)₂, TiH₂ and ZrH₂ hydride and borohydride metals are found to be the superior shielding materials. This study should be useful for design of effective shielding using hydrides and borohydrides metals in fusion reactors.     

Photon interaction and energy absorption in glass: A transparent gamma ray shield

The effective atomic number, Z_eff, the effective electron density, N_e,eff, and the energy dependence, ED, have been calculated at photon energies from 1 keV to 1 GeV for CaO-SrO-B₂O₃, PbO-B₂O₃, Bi₂O₃-B₂O₃, and PbO-Bi₂O₃-B₂O₃ glasses with potential applications as gamma ray shielding materials. For medium-Z glasses, Z_eff is about constant and equal to the mean atomic number in a wide energy range, typically 0.3 < E < 4 MeV, where Compton scattering is the main photon interaction process. In contrast, for high-Z glasses there is no energy region where Compton scattering is truly dominating. Heavy-metal oxide glasses containing PbO and/or Bi₂O₃ are promising gamma ray shielding materials due to their high effective atomic number and strong absorption of gamma rays. They compare well with concrete and other standard shielding materials and have the additional advantage of being transparent to visible light. The single-valued effective atomic number calculated by XMuDat is approximately valid at low energies where photoelectric absorption is dominating.     

Scope of Pb-Sn binary alloys as gamma rays shielding material

An attempt has been made to prepare binary alloys of Pb and Sn in different compositions. The physical properties of the prepared alloys viz. dimensions and density has been measured. Further, different shielding parameters: effective atomic number (Z_eff), electron density (N_e), mean free path (mfp) were computed for the prepared Pb-Sn binary alloys in the wide energy range from 1.0 keV to 100.0 GeV. The variation of effective atomic number, electron density, mean free path for the selected alloys with incident photon energy has been analyzed. The work has been extended to compute exposure buildup factor (EBF) using five parametric geometric progression (GP) fitting method in the energy range 0.015–15.0 MeV and up to the penetration depth of 40 mfp. Further, the variation of exposure buildup factor with incident photon energy as well as penetration depth for the selected alloys has been investigated.     

Calculation of the cross-sections for fast neutrons and gamma-rays in concrete shields

This work is concerned with the theoretical calculation of both the total mass attenuation coefficients (μ/ρ) for gamma rays and the effective removal cross-sections (Σ_R) for fast neutrons. Calculations were carried out for four types of concrete of different densities namely (1) dolomite–sand ρ=2.5 g.cm⁻³, (2) barite–barite ρ=3.49 g.cm⁻³, (3) magnetite–limonite ρ=3.6 g.cm⁻³ and (4) ilmenite–ilmenite ρ=3.69 g cm⁻³. The total mass attenuation coefficients have been calculated at energies from 10 keV to 1 GeV using the XCOM (version 3.1) computer program and cross- section database for elements from Z=1 to 100. Also the effective removal cross-section have been calculated using the elemental composition of the concrete mixes. The calculated values are widely needed and used as a database for radiation shielding design of research reactors, power station and particle accelerators. The results were displayed in tables and figures. Calculated results were compared with those previously measured and a reasonable agreement was found between them.     

Effective atomic and electron numbers of some steels at different energies

The effective atomic numbers (Z_eff) and effective electron density (N_e) for three different steels have been determined via the mass attenuation coefficients (μ/ρ). The mass attenuation coefficients have been calculated at the photon energy range of 1 keV–1 GeV and measured at the photon energies of 662, 1173 and 1332 keV. The measurement has been performed using a gamma spectrometer that contains a NaI(Tl) detector connected to Multi-Channel-Analyzer (MCA). The measured results of effective atomic numbers (Z_eff) and effective electron density (N_e) were found to be in good agreement with the calculations.     

Comparison of some lead and non-lead based glass systems, standard shielding concretes and commercial window glasses in terms of shielding parameters in the energy region of 1 keV-100 GeV: A comparative study

The effective atomic numbers, Z_eff of some glass systems with and without Pb have been calculated in the energy region of 1 keV-100 GeV including the K absorption edges of high Z elements present in the glass. Also, these glass systems have been compared with some standard shielding concretes and commercial window glasses in terms of mean free paths and total mass attenuation coefficients in the continuous energy range. Comparisons with experiments were also provided wherever possible for glasses. It has been observed that the glass systems without Pb have higher values of Z_eff than that of Pb based glasses at some high energy regions even if they have lower mean atomic numbers than Pb based glasses. When compared with some standard shielding concretes and commercial window glasses, generally it has been shown that the given glass systems have superior properties than concretes and window glasses with respect to the radiation-shielding properties, thus confirming the availability of using these glasses as substitutes for some shielding concretes and commercial window glasses to improve radiation-shielding properties in the continuous energy region.     

Gamma ray and neutron shielding properties of some concrete materials

Shielding of gamma-rays and neutrons by 12 concrete samples with and without mineral additives has been studied. The total mass attenuation and linear attenuation coefficients, half-value thicknesses, effective atomic numbers, effective electron densities and atomic cross-sections at photons energies of 59.5 and 661 keV have been measured and calculated. The measured and calculated values were compared and a reasonable agreement has been observed. Also the recorded values showed a change with energy and composition of the concrete samples. In addition, neutron shielding has been treated in terms of macroscopic removal cross-section (Σ_R, cm⁻¹) concept. The WinXCom and NXcom programs were employed to calculate the attenuation coefficients of gamma-rays and neutrons, respectively.     

Development of high-performance heavy density concrete using different aggregates for gamma-ray shielding

Primary and secondary containment structures are the major components of the nuclear power plant (NPP). The performance requirements of the concrete of containment structures are mainly radiological protection, structural integrity and durability, etc. For this purpose, high-performance heavy density concrete with special attributes can be used. The aggregate of concrete plays an essential role in modifying concrete properties and the physico-mechanical properties of the concrete affect significantly on its shielding properties. After extensive trials and errors, 15 concrete mixes were prepared by using the coarse aggregates of barite, magnetite, goethite and serpentine along with addition of 10% silica fume (SF), 20% fly ash (FA) and 30% ground granulated blast-furnace slag (GGBFS) to the total content of OPC for each mix. To achieve the high-performance concrete (HPC- grade M60), All concrete mixes had a constant water/cement ratio of 0.35, cement content of 450 kg/m³ and sand-to-total aggregate ratio of 40%. Concrete density has been measured in the case of fresh and hardened. The hardened concrete mixes were tested for compressive strength at 7, 28 and 90 days. In some concrete mixes, compressive strength was also tested up to 90 days upon replacing sand with the fine portions of magnetite, barite and goethite. The attenuation measurements were performed by using gamma spectrometer of NaI (Tl) scintillation detector. The utilized radiation sources comprised ¹³⁷Cs and ⁶⁰Co radioactive elements with photon energies of 0.662 MeV for ¹³⁷Cs and two energy levels of 1.173 and 1.333 MeV for ⁶⁰Co. Some shielding factors were measured such as half-value layer (HVL), tenth-value layer (TVL) and linear attenuation coefficients (μ). Experimental results revealed that, the concrete mixes containing magnetite coarse aggregate along with 10% SF reaches the highest compressive strength values exceeding over the M60 requirement by 14% after 28 days of curing. Whereas, the compressive strength of concrete containing barite aggregate was very close to M60 and exceeds upon continuing for 90 days. The results indicated also that, the compressive strength of the high-performance heavy density concrete incorporating magnetite as fine aggregate was significantly higher than that containing sand by 23%. Also, concrete made with magnetite fine aggregate improved the physico-mechanical properties than the corresponding concrete containing barite and goethite. Therefore, high-performance concrete incorporating magnetite as fine aggregate enhances the shielding efficiency against γ-rays.     

Radiation shielding of concretes containing different lime/silica ratios

The shielding of γ-rays and fast neutrons by concrete has been studied for concretes containing different lime/silica ratios. Calculations were carried out for six different concrete samples. The total mass attenuation coefficients (μ/ρ, cm² g⁻¹) have been computed at photon energies of 1 keV to 100 GeV using the personal computer software package WinXCom. Also the macroscopic effective fast neutron removal cross-sections (Σ_R, cm⁻¹) have been calculated using MERCSF-N program and the removal cross-section database for all required elements. The obtained results showed that the lime/silica ratio of concrete has significant and insignificant effects on μ/ρ and Σ_R values, respectively.     

Mass attenuation coefficients,effective atomic numbers and electron densities of undoped and differently doped GaAs and InP crystals

The total mass attenuation coefficients (μ/ρ), for GaAs, GaAs (semi-insulating; S-I) GaAs:Si (N⁺), GaAs:Zn, InP:Fe, InP:Fe–As, InP:S and InP:Zn crystals were measured at 22.1, 25.0, 59.5 and 88.0 keV photon energies. The samples were irradiated with ¹⁰⁹Cd and ²⁴¹Am radioactive point sources using transmission arrangement. The X- and γ-rays were counted by a Si (Li) detector with resolution of 160 eV at 5.9 keV. Total atomic and electronic cross-sections (σ_t and σ_e), effective atomic numbers (Z_eff) and electron densities (N_el) were determined using the obtained μ/ρ values for the investigated crystals.     

Calculation of fast neutron removal cross-sections for some compounds and materials

Shielding materials usually contain some well-known compounds or substances. Thus, construction of a database for the effective fast neutrons mass removal cross-sections, Σ_R/ρ (cm² g⁻¹), for these compounds and materials will facilitate the shielding design problem. In this work, building of such database for different compounds and materials which have been widely used in shielding media has been suggested. Furthermore, a short version of this database was given. It includes the calculated values of Σ_R/ρ (cm² g^–1) and Σ_R (cm⁻¹) for some common compounds found in concrete, Portland cement clinker, iron ores and polymers. By using this database, a quick short hand calculation method for rough estimation of macroscopic removal cross-section Σ_R for these materials can be developed. It is interesting to note that considerable removal cross-section values for PVC, PP, PA6, PA6/6, PA6/10, PA11 and PPS polymers were noticed.     

Neutron dose transmission measurements for several new concrete samples including colemanite

We have prepared four baryte and four concrete samples having respectively 0%, 5%, 10% and 15% colemanite concentrations. Neutron dose transmission measurements have been done by using a source of mono-energetic neutrons (E_eff = 4.5 MeV–²⁴¹Am–Be). It has been shown that when colemanite percentages of the samples increase, neutron dose transmission values for the samples decrease. It is thus possible to enhance the neutron shielding property of baryte and ordinary concrete by adding different proportions of colemanite.     

Investigations of multiple backscattering and albedos of 1.12 MeV gamma photons in elements and alloys

The energy and intensity distributions of multiple backscattering of 1.12 MeV gamma photons emerging from targets of elements and alloys are observed as a function of thickness and atomic number (Z) of the target. The numbers of these multiply backscattered events show an increase with increase in target thickness, and then saturate for a particular thickness of the target called saturation thickness (depth). The saturation thickness decreases with increasing atomic number and varies as e^−Z. The multiple backscattering, an interfering background noise in Compton profile, has been successfully used to assign the ‘‘effective atomic number’’ to alloys. Monte Carlo calculations also support the present experimental results. The number, energy and dose albedos are also found to be saturating for the same thickness where the numbers of multiply backscattered events saturate.     

Determination of mass attenuation coefficients, effective atomic and electron numbers, mean free paths and kermas for PbO, barite and some boron ores

The total mass attenuation coefficients, μ_m, for PbO, barite, colemanite, tincal and ulexite were determined at 80.1, 302.9, 356.0, 661.7 and 1250.0 keV photon energies by using NaI (Tl) scintillation detector. Effective atomic number, Z_eff, effective electron number, N_eff, total atomic cross-section, σ_t, total electronic cross-section, σ_e, mean free path, mfp, and kerma relative to air were determined experimentally and theoretically. The theoretical mass attenuation coefficients were estimated using mixture rule. The calculated values were compared with the experimental values for all samples.     

Determination of the effective atomic numbers and electron densities for YBaCuO superconductor in the range 59.5-136 keV

The effective atomic numbers and electron densities of YBa₂Cu₃O_7−δ superconductor at 59.5, 65.2, 77.1, 94.6, 122 and 136 keV were calculated by using the measured mass attenuation coefficients. Measurements were made by performing transmission experiments in a well-collimated narrow beam geometry set-up by employing Si(Li) detector with a resolution of 0.16 keV at 5.9 keV. These values are found to be in good agreement with theoretical values calculated based on XCOM data. The observed crystal structure of YBa₂Cu₃O_7−δ superconductor is close to the theoretical structure. Z_eff and N_el experimental values showed good agreement with the theoretical values for calcined and sintered YBa₂Cu₃O_7−δ.     

Effective atomic numbers for photon energy absorption of essential amino acids in the energy range 1 keV to 20 MeV

Effective atomic numbers for photon energy-absorption (Z_PEAeff) of essential amino acids histidine, leucine, lysine, methionine, phenylalanine, threonine, tryptophan and valine have been calculated by a direct method in the energy region of 1 keV to 20 MeV. The Z_PEAeff values have been found to change with energy and composition of the amino acids. The variations of mass energy-absorption coefficient, effective atomic number for photon interaction (Z_PIeff) and Z_PEAeff with energy are shown graphically. Significant differences exist between Z_PIeff and the Z_PEAeff in the energy region of 8-100 keV for histidine and threonine; 6-100 keV for leucine, lysine, tryptophan, phenylalanine and valine; 15-400 keV for methionine. The effect of absorption edge on effective atomic numbers and the possibility of defining two set values of these parameters at the K-absorption edge of high-Z element present in the amino acids are discussed. The reasons for using Z_PEAeff rather than the commonly used Z_PIeff in medical radiation dosimetry for the calculation of absorbed dose in radiation therapy are also discussed.     

Photon energy absorption parameters for some polymers

Some photon energy absorption parameters viz. mass energy absorption coefficient (μ/ρ)_en, photon energy absorption effective atomic number (Z_PEA), electron density (N_e) and KERMA relative to air has been computed in the energy range from 1 keV to 20 MeV for some polymers such as nylon, poly-acrylo-nitrile, poly-methyl-acrylate, poly-vinyl-chloride, poly-styrene, synthetic rubber and poly-tetra-fluro-ethylene. The dependence of different parameters on incident photon energy and chemical composition of the selected polymers has been studied .     

Evaluation of gamma ray buildup factor data in water with MCNP4C code

The exposure buildup factors for gamma and X-ray photons in water are computed using the MCNP4C code. The results are obtained for the energy range 0.04–6 MeV and penetration depths up to 10 mfp. The results are compared with the published buildup factor data during 1960–2010. Both agreements and discrepancies are observed between our results and the data appearing in the literature. It is concluded that at higher energies and deep penetration the existing data for photon buildup factor in water are still inadequate.     

A comprehensive study on energy absorption and exposure buildup factors for some essential amino acids, fatty acids and carbohydrates in the energy range 0.015-15 MeV up to 40 mean free path

The gamma ray energy absorption (EABF) and exposure buildup factors (EBF) have been calculated for some essential amino acids, fatty acids and carbohydrates in the energy region 0.015-15 MeV up to a penetration depth of 40 mfp (mean free path). The five parameter geometric progression (G-P) fitting approximation has been used to calculate both EABF and EBF. Variations of EABF and EBF with incident photon energy, penetration depth and weight fraction of elements have been studied. While the significant variations in EABF and EBF for amino acids and fatty acids have been observed at the intermediate energy region where Compton scattering is the main photon interaction process, the values of EABF and EBF appear to be almost the same for all carbohydrates in the continuous energy region. It has been observed that the fatty acids have the largest EABF and EBF at 0.08 and 0.1 MeV, respectively, whereas the maximum values of EABF and EBF have been observed for aminoacids and carbohydrates at 0.1 MeV. At the fixed energy of 1.5 MeV, the variation of EABF with penetration depth appears to be independent of the variations in chemical composition of the amino acids, fatty acids and carbohydrates. Significant variations were also observed between EABF and EBF which may be due to the variations in chemical composition of the given materials.