Shielding Behaviour Analysis of Double Layered Slabs. Gamma Ray Shielding


Doctoral Thesis / Dissertation, 2016

223 Pages, Grade: 9.99


Excerpt

TABLE OF CONTENTS

Preface

Table of Contents

List of Figures

List of Tables

List of Abbreviations

List of Symbols

CHAPTER 1
LITERATURE REVIEW
1.1 INTRODUCTION
1.2 TYPES OF RADIATIONS
1.3 SOURCES OF RADIATIONS
1.4 RADIOACTIVITY
1.4.1 Natural Radioactivity
1.4.2 Radiation Protection and Dose Quantities
1.4.2.1 Exposure of Radiations
1.4.2.2 Radiation Dose
1.4.2.3 Absorbed dose (Dr, Gy)
1.4.2.4 Organ absorbed dose, (Dr, Gy)
1.4.2.5 Equivalent-dose (Dr, Gy)
1.4.2.6 Effective dose (E)
1.4.2.7 Fluence (Φ, m(2 ־
1.4.2.8 ICRU-sphere.
1.4.2.9 Ambient dose equivalent, (Я.10, Sv)
1.5 RADIATION EXPOSURE RISK..
1.5.1 Effects of Ionizing Radiations on Health
1.6 APPLICATIONS OF IONIZING RADIATIONS
1.7 RADIATION PROTECTION organizations
1.8 INTERACTIONS OF GAMMA-RAYS WITH MATTER
1.8.1 Interaction Mechanisms of γ-ray with Matter
1.8.1.1 Photoelectric-absorption
1.8.1.2 Compton-scattering
1.8.1.3 Pair-production
1.8.1.4 Triplet production
1.9 RADIATION SHIELDING
1.9.1 Characterization of the Source
1.9.2 Characterization of Shielding-material
1.9.2.1 Linear Attenuation Coefficient
1.9.2.2 Total Mass Attenuation Coefficient
1.9.2.3 Total Interaction Cross-Section
1.9.2.4 Mass Energy Absorption Coefficient
1.9.2.5 Effective and Equivalent atomic-numbers
1.9.2.6 Electron Density
1.9.2.7 Mean Free Path and Optical-Thickness
1.9.2.8 Half Value Layer (HVL)
1.9.2.9 KERMA
1.9.2.10 Buildup Factor (BUF)
1.9.2.11 Double Layered Transmission Exposure Buildup Factor
1.9.3 Dose Calculations by the Point-kernel Method
1.9.3.1 Fluence-to-dose Conversion
1.9.3.2 Calculation of uncollided-radiation dose
1.9.3.3 Calculation of total dose
1.10 THE LITERATURE REVIEW
1.10.1 Mass Attenuation Coefficient (ßm)
1.10.2 Mass Energy Absorption Coefficient (/¿en/ p)
1.10.3 Atomic-Numbers (Zeq & Zeff)
1.10.4 Buildup Factor for Homogenous Shield
1.10.5 Buildup Factor for Heterogeneous Shield
1.11 Importance of the study

CHAPTER 2
EXPERIMENTAL TECHNIQUES
2.1 INTRODUCTION ľ
2.2 INSTRUMENTS AND TECHNIQUES
2.2.1 X-Ray Techniques
2.2.1.1 Wavelength Dispersive X-Ray Fluorescence (WDXRF).
2.2.1.2 X-Ray Diffractometer (XRD-R)
2.2.2 Free Swell Ratio (FSR) Test
2.2.3 Standard Radioactive Sources
2.2.4 Gamma-Ray Spectrometry
2.2.4.1 Gamma-Ray Spectrometer
2.2.4.2 Scintillation Detector
2.2.4.3 Photo Multiplier Tube (PMT)
2.2.4.4 Pre-Amplifier
2.2.4.5 Linear Amplifier
2.2.4.6 Regulated High Voltage Power Supply
2.2.4.7 Multi-Channel Analyzer (MCA)
2.2.4.8 Lead Collimators and Lead-Alloy Blocks
2.2.5 Miscellaneous Instruments
2.2.5.1 Pocket Radiation Monitor
2.2.5.2 Electronic Balance
2.2.5.3 Digital Vernier Calipers
2.2.5.4 Radiation Laboratory
2.3 SAMPLE PREPARATION
2.3.1 Sample Preparation for WDXRF
2.4.2 Sample Preparation for XRD-R
2.3.3 Sample Preparation for Gamma-Ray Spectroscopy
2.3.3.1 Procedure for making of sample-bricks
2.4 COMPUTER SOFTWARES
2.4.1 WinXCom
2.4.2 MAESTRO
2.4.3 MAUD
2.4.4 ORIGIN
2.4.5 GEANT4 Toolkit

CHAPTER 3
COMPUTER PROGRAMS (TOOLKITS)
3.1 INTRODUCTION
3.2 NEED OF TOOLKITS
3.2.1 GRIC-Toolkit
3.2.2 GRIC2-T001kit
3.2.3 BUF-Toolkit
3.2.3.1 Corrections for overestimations
3.3 FORMULATIONS OF TOOLKITS
3.3.1.1 Mass attenuation coefficient, μπι (cm g" ) Ill
3.3.1.2 Mass energy absorption coefficient, Ill
3.3.1.3 KERMA relative to air (XR)
3.3.1.4 Equivalent atomic-number (Zeq)
3.3.2 Formulation of GRIC2-toolkit
3.3.2.1 Photon interaction
3.3.2.2 Mass attenuation coefficient of a mixture
3.3.2.3 HVL and TVL
3.3.2.4 Effective atomic-number (Zeff)
3.3.2.5 Effective electron density, Ae1־eff (electrons/g)
3.3.3 Formulation of BUF-Toolkit
3.3.3.1 BUF for SLHS
3.3.3.2 EBF for DLHS
3.4 VALIDATIONS OF THE TOOLKITS
3.4.1 Validations of GRIC-toolkit
3.4.2 Validations of GRIC2-toolkit
3.4.3 Validations of BUF-toolkit
3.5 EXAMPLE: NBS-Concrete
3 6 CONCLUSIONS

CHAPTER 4
BUILDUP FACTORS FOR HOMOGENEOUS AND HETEROGENEOUS GAMMA-RAY SHIELDS
4.1 INTRODUCTION
4.2 OBJECTIVES
4.3 THEORY
4.4 GEOMETRY
4.4.1 Homogeneous Infinite Medium Spherical Shield
4.4.2 Heterogeneous Finite Media Spherical Shield
4.4.2.1 Significance of the DLEBF
4.5 MATERIAL AND METHODS
4.5.1 Samples
4.5.2 Methodology
4.5.2.1 Computations
4.6 RESULTS AND DISCUSSION
4.7 CONCLUSIONS

REFERENCES

APPENDIX-A

Comparison of Some Fitting-Functions, Used for The Computation of uildup Factors

APPENDIX В

Computed Values of EBF, DLEBF and Correction Factors for the Investigated Stratified Shields

LIST OF FIGURES

Figure 1.1: Various γ-ray shielding parameters (GSP) used to describe γ-ray shielding behaviours (GSBs) of a material

Figure 1.2: Classification of ionizing radiations

Figure 1.3: Spectrum of Electromagnetic Waves

Figure 1.4: Description of BEIR on health

Figure 1.5: Description of various types of γ-ray interactions with matter

Figure 1.6: Photoelectric-Absorption

Figure 1.7: X-ray fluorescence and Auger effect

Figure 1.8: Description of the Compton-scattering (¿?represents scattering angle and γ/represents angle of recoil).

Figure 1.9: The Pair-production

Figure 1.10: The pair and triplet production

Figure 1.11: An experimental setup recommended for the measurement of linear attenuation coefficients. The narrow-beam geometry

Figure 1.12: The relative dominance of the three major types of γ- ray interactions with matter, the Z-E graph. (Davisson and Evans, 1955)

Figure 1.13: Comparison of the two-geometries for jMmmeasurement (Davisson and Evans, 1955)

Figure 2.1: The WDXRF-analyzer

Figure 2.2: The XRD-diffractometer

Figure 2.3: Decay schemes of used sources, 55Cs and 27C (Turner, 2007)

Figure 2.4: Schematic diagram of γ-ray detection

Figure 2.5: Nal (Tl)-gamma-ray spectrometer (the dimensions in cm)

Figure 2.6: Schematic diagram of Nal (TI) spectrometer assembly

Figure 2.7: Miscellaneous apparatus used in the measurements. 93 Figure 2.8: Miscellaneous instruments used in the investigation

Figure 2.9: Steps involved in sample’s pellet making process 98 Figure 2.10: Prepared sample-bricks for gamma-ray spectroscopy

Figure 3.1: The combined flowchart of self-designed toolkits.

Figure 3.2: Input/output interface of the GRIC-toolkit

Figure 3.3: Input/output interface of the GRIC2-toolkit

Figure 3.4: Input/output interface of the BUF-Toolkit

Figure 3.5: Validation of GRIC-Toolkit for computation of total mass attenuation coefficients using standard materials (Mann et a.,2015a)

Figure 3.6: Standardization of GRIC2-toolkits for atomic cross­sections and total mass attenuation coefficients using experimental results for some building materials

Figure 3.7: Validation of GRIC2-T001kit for zeff values using measured values obtained from the literature

Figure 3.8: Validation of GRIC2-T001kit for Veieff values

Figure 3.9: Validation of BUF-toolkit for EBF for infinite medium (SLHS) using ANS-standards (ANSI/ANS-6.4.3, 1991)

Figure 3.10: Standardization of BUF-toolkit for EBF of the finite medium SLHS

Figure 3.11: Validation of BUF-toolkit for DLEBF of Water-Iron finite DLHS using the Monte Carlo-EGS4 codes

Figure 4.1: Homogeneous infinite medium spherical shield geometry, for SLHS model for infinite Water-medium (ANSI/ANS-6.4.3, 1991)

Figure 4.2: Heterogeneous finite media spherical stratified shield geometry for DLHS model for 0.5-0.5 mfp(s), Aluminium (Al) Limestone (LS)

Figure 4.3: Variations of the total and partial mass attenuation coefficients of the samples with energy of γ-rays

Figure 4.4: Variation of EBF-values with от for SLHSs of the chosen samples, at four γ-ray energies

Figure 4.5: Variations of EBFs with energies for SLHSs of the chosen samples at four от values

Figure 4.6: Description of the equivalent atomic-number (Zeq) for selected samples at the four energies

Figure 4.7: Comparative variations of BUF values with от for DLHS and SLHS made from Concrete and Limestone

Figure 4.8: Comparative variations of BUF values with от for DLHS and SLHS made from Water and Aluminium

Figure 4.9: Comparative variations of BUF values with от for DLHS and SLHS made from Concrete and Clay

Figure 4.10: Comparative variations of BUF values with от for DLHS and SLHS made from Clay and Limestone

Figure 4.11: Comparative variations of BUF values with от for DLHS and SLHS made from Water and Limestone

Figure 4.12: Comparative variations of BUF values with от for DLHS and SLHS made from Water and Clay

Figure 4.13: Comparative variations of BUF values with от for DLHS and SLHS made from Water and Concrete

Figure 4.14: Comparative variations of BUF values with от for DLHS and SLHS made from Aluminium and Limestone

Figure 4.15: Comparative variations of BUF values with от for DLHS and SLHS made from Aluminium and Clay

Figure 4.16: Comparative variations of BUF values with от for DLHS and SLHS made from Aluminium and Concrete

Figure 4.17: Variations of DLEBF-values with total от at four energies for LZFHZ-orientation (Mann et af, 2016b)

Figure 4.18: Variations of DLEBF-values with total от at four energies for HZFLZ-orientation (Mann et al., 2016b)

Figure 4.19: Variations in GSB of DLHS in two orientations, LZFHZ and HZFLZ with TOT keeping OTR, (Х!/Х2) = 1

Figure 4.20: Variation of the difference between DLEBF-values for HZFLZ and LZFHZ-orientations, with TOT

LIST OF TABLES

Table 1.1. The description of various γ-ray interaction processes with matter, and their z and E dependence (Siegbahn, 1965)

Table 1.2. The chronological description of some major advancements in BUFs

Table 2.1. FSR-values for characterization of soil for a type of clay (Prakash and Sridharan, 2004)

Table 2.2. Specifications of the γ-ray point-isotropic sources 88 Table 2.3. Specifications of the scintillation detector (Canberra, model: 802)

Table 2.4. Specifications of the Pocket Radiation Monitor

Table 3.1. The description of self-designed computer programs (toolkits)

Table 3.2. Validation of GRIC-toolkit for computation of the total mass attenuation coefficient, μγα (cm g' ) for 80.895keV

Table 3.3. Validation of GRIC-toolkit for total mass energy absorption coefficients using ANS-standards (ANSI/ANS-6.4.3., 1991)

Table 3.4. Validation of GRIC-toolkit for total mass attenuation coefficient using ANS-standards (ANSI/ANS-6.4.3., 1991) 130 Table 3.5. The BUF-toolkit computed values of various γ-rays shielding parameters of Concrete (example)

Table 3.6. The BUF-toolkit computed values of the G-P fitting­function parameters for Concrete (example)

Table 3.7. The BUF-toolkit computed values of the Exposure Buildup Factor (EBF) for Concrete (example)

Table 3.8. The BUF-toolkit computed values of the Energy Absorption Buildup Factor (EABF) for Concrete (example) 142 Table 4.1. Description of samples and their zeq-values

Table 4.2. Elemental compositions and densities of the samples

Table 4.3. The optical-thickness ratio (OTR=X1IX2) of DLHS. 153 Table 4.4. Description of computed values of G-P fitting-function coefficients required in computations of EBF for the samples. 154 Table AT Comparisons of the maximum deviations in the computed EBF-values for H20 of от up to 40mfp, using different fitting methods (Harima et al., 1986)

Table A2. Comparison between methodologies used for the computation of BUFs

Table BE Correction factors for DLEBFs in Concrete-Limestone, DLHS

Table B2. Correction factors for DLEBFs in Water-Aluminium, DLHS

Table B3. Correction factors for DLEBFs in Concrete-Clay, DLHS

Table B4. Correction factors for DLEBFs in Clay-Limestone, DLHS

Table B5. Correction factors for DLEBFs in Water-Limestone, DLHS

Table B6. Correction factors for DLEBFs in Water-Clay, DLHS

Table B7. Correction factors for DLEBFs in Water-Concrete, DLHS

Table B8. Correction factors for DLEBFs in Aluminium­Limestone, DLHS

Table B9. Correction factors for DLEBFs in Aluminium-Clay, DLHS

Table BIO. Correction factors for DLEBFs in Aluminium- Concrete, DLHS

Table Bll. Description of the computed values of BUFs, for SLHS and DLHS made from Concrete and Limestone (LS), at four γ-ray energies

Table В12: Description of the computed values of BUFs, for SLHS and DLHS made from Water-Aluminium, at four γ-ray energies

Table В13: Description of the computed values of BUFs, for SLHS and DLHS made from Concrete-Clay, at four γ-ray energies

Table В14: Description of the computed values of BUFs, for SLHS and DLHS made from Concrete and Limestone (LS), at four γ-ray energies

Table В15: Description of the computed values of BUFs, for SLHS and DLHS made from Water-Limestone, at four γ-ray energies

Table В16: Description of the computed values of BUFs, for SLHS and DLHS made from Water-Clay, at four γ-ray energies

Table В17: Description of the computed values of BUFs, for SLHS and DLHS made from Water-Concrete, at four γ-ray energies

Table В18: Description of the computed values of BUFs, for SLHS and DLHS made from Aluminium-Limestone, at four γ-ray energies

Table В19: Description of the computed values of BUFs, for SLHS and DLHS made from Aluminium-Clay, at four γ-ray energies

Table B20: Description of the computed values of BUFs, for SLHS and DLHS made from Aluminium-Concrete, at four γ-ray energies

Table B21. Description of the computed values of the DLEBFs, for various OTR, {X\!X2) listed in table 6.3, for Concrete- Limestone DLHS

Table B22: Description of the computed values of the DLEBFs, for various OTR, {X\IX2) listed in table 6.3, for Water-Aluminium DLHS .

Table B23: Description of the computed values of the DLEBFs, for various OTR, {X\!X2) listed in table 6.3, for Concrete-Clay DLHS .

Table B24: Description of the computed values of the DLEBFs, for various OTR, {X\IX:2) listed in table 6.3, for Clay-Limestone DLHS .

Table B25: Description of the computed values of the DLEBFs, for various OTR, (X\IX■2) listed in table 6.3, for Water-Limestone DLHS .

Table B26: Description of the computed values of the DLEBFs, for various OTR, {X\!X2) listed in table 6.3, for Water-Clay DLHS .

Table B27: Description of the computed values of the DLEBFs, for various OTR, {X\!X2) listed in table 6.3, for Water-Concrete DLHS .

Table B28: Description of the computed values of the DLEBFs, for various OTR, {X\IX:2) listed in table 6.3, for Aluminium­Limestone DLHS

Table B29: Description of the computed values of the DLEBFs, for various OTR, {X\IX2) listed in table 6.3, for Aluminium-Clay DLHS .

Table C30: Description of the computed values of the DLEBFs, for various OTR, (X\iX2) listed in table 6.3, for Aluminium- Concrete DLHS

LIST OF ABBREVIATIONS

Abbildung in dieser Leseprobe nicht enthalten

LIST OF SYMBOLS

Abbildung in dieser Leseprobe nicht enthalten

ABSTRACT

The highest energy in the electromagnetic spectrum is occupied by the gamma-rays, (γ-rays). For the betterment of mankind, γ-rays have immense applications as non-destructive evaluation tool in various fields, such as radiological diagnostics, security screening and research. However, an exposure of γ-rays to living tissues has adverse health effects, especially when the exposure time is long and intensity is high. In this regard, the biggest concern for the scientific community in radiation protection is the safety of the nuclear reactors, which are always at the risk of accidental- leakage of γ-rays. Under such circumstances, there is always a need to minimize the exposure of γ-rays originated from critical sites such as nuclear establishments and nuclear-waste disposal sites. This can be achieved by using effective γ-ray shielding enclosures at these sites. The term shield refers to the radiation attenuating material placed around radioactive source to stop or minimize the leakage of ionizing-radiations to its immediate surroundings. For γ-ray shielding purpose, any material with sufficient thickness can be used to attenuate the intensity of the rays. However, the choice of an appropriate material is necessary for effective shielding. Mostly, high-Z (atomic-number) and high-density materials such as lead and its alloys have been recommended to use for shielding purpose. Besides, the high-cost, toxicity and non-availability in huge quantities has put some constraints on the excessive use of high-Z materials as γ-ray protective shields. If space is not a constraint, then in addition to high-Z materials, commonly available low-Z building-materials can be used for the cost effective shielding purpose. The low-Z building-materials are non­toxic, low cost, inexpensive and easily available in abundance.

Gamma-ray shielding-behaviour (GSB) of a material can be estimated from its γ-ray shielding parameters (GSP). There are numerous parameters based on various processes by which γ-ray photons interact with the matter. Total mass attenuation coefficient (/-¿m, cm g־ ) is one of the most important GSP used in the study of GSB of a material.

This book is related to the GSBs of homogeneous and heterogeneous shields using buildup factors (BUFs). BUF is one of the important parameters which accounts for scattered photons influencing the transmitted intensity of γ-rays through a shielding material. The magnitude of such influence depends on material’s BUF. A report entitled, ‘Gamma- ray Attenuation Coefficients and Buildup Factors for Engineering Materials’ serves as the American Nuclear Society (ANS)-standards for radiation analysis (ANSI/ANS-6.4.3-1991). These standards provide the BUF-values for a homogeneous infinite shielding medium in the wide range of optical-thickness, (ОТ) 0.5-40mfp and energy 15keV-15MeV. The concept of infinite homogeneous shielding appears more theoretical as compared to the finite heterogeneous shield. The information regarding BUF for a finite heterogeneous shield is missing in the ANS-standards. The literature review has suggested that some researchers have attempted to develop some analytical formulae for γ-ray shielding analysis of finite heterogeneous shields such as Kalos-formula, modified Kalos-formula and Lin and Jiang-formula using EGS4-code. The EGS4-code are based on Monte Carlo method which is a slow computational method. It has been found that Lin and Jiang-formula is most suitable to compute the double layered transmission exposure buildup factor (DLEBF), which uses the geometric progression (G-P) fitting-method and database of ANS­standards. The computer program, BUF-toolkit has been designed to compute the approximate accurate values of the BUFs for a single-layer- homogeneous-shield (SLHS) and a double-layered-heterogeneous-shield (DLHS) using the G-P fitting-formula at the desired energy and от of the shield. This toolkit has been validated with Monte Carlo EGS4-code.

It has been confirmed that for the same от value, the DLHS protects the γ- rays more effectively than the SLHS made from either one of the constituting materials. Additionally, the DLHS offers better GSB with its orientation such that starting from source γ-rays interact firstly with low-Z layer, followed by high-Z layer (LZFHZ), than the reverse orientation i.e. HZFLZ.

The ANS-standards are two and half decade old and they have neglected some γ-ray interaction phenomena (Coherent-scattering and Bremsstrahlung) during the compilation. These neglected phenomena are dominant in high-Z materials, thus for high-Z materials, ANS-standards show significant errors in experimental results. During the time interval from 1991 to 2018, more accurate values of GSP have been derived thus demanding to update the ANS-standards accordingly. A part of the present report has been compiled with a hope that designed computer program (BUF-toolkit) and computed data will be useful in the next revision of the ANS-standards particularly in the compilations of DLEBF.

CHAPTER 1 LITERATURE REVIEW

1.1 INTRODUCTION

Gamma-rays are the most energetic electromagnetic radiations which are emitted from the radioactive nuclei. Being ionizing in nature, gamma (γ) - rays have beneficial as well as adverse biological consequences. The human race was unaware of the existence of γ-rays until 1896, when Henri Becquerel demonstrated some new kind of radiations being emitted from uranium ore that could affect photographic plates. Around the turn of the 19th century, these nuclear radiations were named as alpha (a), beta (β) and gamma (γ) rays. In general the emission of γ-ray follows the a and β emissions. Alpha and beta decay of unstable parent nuclei leave the daughter nuclei in the excited states. These excited nuclei in turn make transitions to their ground states by emitting γ-ray photons.

The discovery of γ-rays had an enormous impact right from the beginning and changed the world drastically. This discovery contributed not only in the progress of nuclear physics, but also advanced medical science to new heights. Gamma-rays were soon perceived to present health hazards resulting from damage to the living cells. The discovery of nuclear fission in 1938, based on Einstein’s mass energy relation, caused the birth of an atomic bomb. In 1945, explosions of two such bombs at Hiroshima and Nagasaki in Japan had started the race between different countries in the manufacturing of nuclear weapons. The fallout of various nuclear test explosions executed by various countries created worldwide atmospheric radioactive pollution, utilization of nuclear energy for peaceful purposes had started in the mid-fifties, when some experimental nuclear fission reactors were constructed. However, the problems of handling nuclear wastes and emission of radioactivity into the environment from the nuclear- establishments diluted the general trust of the public in the beneficial role of nuclear energy. Eventually, the disaster at the nuclear power plant at Chernobyl on April 26, 1986 put an end to the rapid industrial use of radioactivity. This has been the worst nuclear accident ever to have occurred in the nuclear power industry. The nuclear-reactor was completely destroyed in the accident due to which considerable amounts of radioactive materials were released to the environment and many workers were exposed to very high doses of ionizing radiations that had fatal, health consequences. This event released 890 times137 Cs and eighty-seven times of90 Sr as much as released from the bomb that exploded in Hiroshima.

However, due to ever increasing demand for electricity and limitations of the existing conventional resources of power production, the nuclear energy gained importance again over time. Learning from the past experiences, these days, many safety and security measures are taken into account as recommended by many organizations such as International Atomic Energy Agency (IAEA), International Commission on Radiological Protection (ICRP), NCRP (National Council on Radiation Protection and Measurements) and BEIR (Biological Effects of Ionizing Radiation). Since 1952, including the recent Fukushima Daiichi nuclear-disaster, about sixty- three major nuclear accidents have occurred at various nuclear power plants. Thereby, indicating some drawbacks in the existing safety measures and the possibility of such accidents in future.

Since there is always a risk of nuclear accidents, it is indispensable to cope up with adverse consequences. The most important task after the event of a nuclear power plant accident is protection of the general public. The most effective way of mitigating acute effects is the prompt evacuation of the local population, but it requires both an early notification and expeditious movement to be successful. The alternative way is the construction of local buildings from the materials that can attenuate the exposed radiation dose well below the safe limits.

The charged particles (a and ß) emitted from fallout can be easily stopped by the building materials and ordinary clothing (Keamy and Cresson, 1986). The intensity of γ-rays can never be reduced to zero, but it can be minimized using appropriate shielding-materials. Thereby, to circumvent any risk from γ-ray exposures of the population, the choice of building materials used in making their houses should have good γ-ray shielding abilities.

The gradual increased use of nuclear energy in various fields such as nuclear-reactors, diagnostics and weapons has motivated the scientific community to think about the radiation safety measures of residential- buildings. For making radiation-safe buildings (shelters), the engineering materials should be characterized by their γ-ray shielding behaviours (GSBs) in addition to other conventional physical properties. Generally, high-Z materials such as Pb, Zn, Cd, Sn, Sb and their Alloys have been used for γ-rays shielding purpose at nuclear-establishments (IS: 14688, 1999). But, due to their high cost and toxicity, these materials cannot be used in the construction of residential-buildings. Thus, some commonly accessible building materials, e.g. burnt-clay-brick, cement, soil, concrete, ceramic-tile, lime, mud, clay, pop etc. are used for the construction of houses. These materials belong to the low-Z group of materials as their effective atomic-number (Zeff) <18, (Hine, 1952) for γ-rays in the energy- range 15keV-15MeV. From the knowledge of GSB of these common building materials the radiation protection abilities of a shelter (house) can be estimated.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.1: Various γ-ray shielding parameters (GSP) used to describe γ-ray shielding behaviours (GSBs) of a material.

The GSB of a material can be characterized by comparing its various γ-ray shielding parameters (GSP). The name and symbols of GSP have been shown in Fig. 1.1. Gamma-rays interact with any material in two ways, i.e. absorption and scattering. The scattering of photons is further of two types, i.e. coherent and incoherent scattering. For transport study of γ-ray, the incoherent scattering is dominant for the energy higher than 0.6MeV. The incoherent scattering of γ-ray leads to the buildup of multiple-scattered photons inside and around the shielding-materials. White (1950) introduced the concept of γ-ray buildup factor (BUF) and Fano (1953a) confirmed its importance in attenuation studies. The BUF is a parameter dependent on energy (E), material (Z) and dimensions of the shielding-material (geometry). It corrects the sample’s attenuation calculations due to scattered photons. Thus, it is a very important parameter in the estimation of the shielded radiation dose, contributed due to scattered-radiations by various materials present around the radioactive source. The standard reference data of BUF is accessible as American Nuclear Society (ANS) standards (ANSI/ANS 6.4.3-1991). The ANS-standards provide BUF values for 23 pure elements, two mixtures viz. air and concrete and water in the energy-range 15keV-15MeV and optical-thickness (ОТ) range 0.5- 40mfp (mean free path). Considering BUF as a useful parameter for GSB analysis, its values for homogeneous and heterogeneous shields have been computed and provided in this study.

The ANS-standards are approximately 26 years old, and they have neglected some phenomena such as coherent scattering and bremsstrahlung during their compilations. These neglected phenomena are dominant in high-Z materials, thus for high-Z materials, the ANS-standards need modifications. During the last 26 years, more accurate values of GSP have been derived thus demanding to update the ANS-standards accordingly. The present report has been compiled with a hope that designed computer programs and computed data will be useful in the next revision of the ANS­standards particularly in the compilations of BUFs for stratified shields i.e. DLEBF.

1.2 TYPES OF RADIATIONS

Radiation is defined as the electromagnetic (EM) wave or subatomic particle that transports energy. Depending on its ability to ionize the interacting matter, radiation is classified into two types viz. ionizing and non-ionizing, (Knoll, 2000). Ionization means the conversion of a neutral atom or a molecule into a positively charged ion by the ejection of one or more electrons from it.

Radiation with energy less than the threshold energy for the ionization of the irradiated material is termed as non-ionizing radiation. Examples of this kind are visible light, infrared radiation, microwaves and radio waves.

Ionizing radiation carries sufficient energy to break the chemical bonds and to eject the electrons from parent atoms and molecules, thereby producing ions in the exposed material. Fig. 1.2 shows that the ionizing radiations have been classified into direct-ionizing and indirect-ionizing radiations. Directly-ionizing radiations are fast moving charged particles such as electrons, positrons, protons and a particles with energy higher than threshold energy for the irradiated material. Indirectly ionizing radiations are uncharged particles such as photons and neutrons that can initiate the nuclear transformations. Directly ionizing radiation deposits energy in the medium through direct Coulomb interactions with orbital-electrons of the atoms present in the medium. Indirectly-ionizing radiations deposit energy in the medium through a two-step process. Firstly, a charged particle is produced in the medium. Secondly, the produced charged particles deposit energy in the medium through direct Coulomb interactions with the orbital electrons of various atoms in the medium.

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Figure 1.2: Classification of ionizing radiations.

Depending upon their origin, the indirect-ionizing photons can be assigned any of the following four categories:

(i) Gamma-rays: resulting from nuclear transitions.
(ii) Characteristic X-rays: resulting from electron transitions between inner shells of an atom.
(iii) Bremsstrahlung (continuous X-rays): resulting from electron- nucleus Coulomb interactions.
(iv) Annihilation radiations: resulting from positron-electron annihilation.

Radiations having a wide range of energies of the EM spectrum as shown in Fig. 1.3. Gamma-rays are EM in nature similar to the visible light, but have much higher energy as indicated in Fig. 1.3. Both, X-rays and γ-rays are hazardous for all living-beings. These ionizing-rays can easily penetrate any protective barrier such as cloths and skin, which otherwise are capable to stop other types of radiations (visible light, a and ß particles). Gamma- rays have so much penetrating power that thick (several inches) and dense (heavy weight) material like lead (Pb) may be required to stop them. Gamma-rays can easily pass through the human body; as they pass through, ionization is produced along its path that can damage living tissues and DNA etc. and thus can cause various physiological effects related to uncontrolled mutation or cancer. Whereas the exposure to non-ionizing radiation is comparatively safe as it can heat the sample and produces some chemical changes only.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.3: Spectrum of Electromagnetic Waves.

1.3 SOURCES OF RADIATIONS

1.3.1 Natural and Man-made Sources

Human-beings are largely exposed to the natural EM radiations coming from the solar-rays, cosmic-rays and natural radioactivity. The major radioactive elements present in the Earth’s crust such as Potassium (40 K), Thorium ( Th), Uranium ( U) and decayed members of their radioactive-series emit energetic particles such as a, ß and γ-ray photons.

The ionizing radiations have been used in medical diagnostics (imaging using X-rays and computed tomography (CT), nuclear-reactors, research laboratories, radioactive-fuel synthesis plants and facilities involved in making of nuclear weapons. Some of these radiation facilities produce radioactive waste products, thereby, cause some leakage of ionizing radiations to the surroundings. Some radioactive materials have been used in certain consumer products, e.g., in smoke-detector and CT- scanners. The residuals of nuclear-tests and nuclear accidents (nuclear- fallout) along with the above discussed sources of ionizing radiations are considered as man-made radiations.

Based on the United Nations Scientific Committee on the Effects of Atomic Radiation, report (UNSCEAR, 2000) for the total public exposure of ionizing radiations, the contribution of, natural background radiation is the largest («85%), followed by medical diagnostics («14%), and then man-made sources of nuclear radiations (<1%).

1.4 RADIOACTIVITY

In the investigation of the ionizing radiations two general phenomena viz. ‘activity’ and ‘exposure’ are used. The activity measures that how much radiation is emitted from the source per unit time, in the form of elementary-particles or photons. The exposure measures, the effect of these radiations on the irradiated substance.

1.4.1 Natural Radioactivity

The spontaneous breakdown of a radioactive atom, with simultaneous emission of nuclear radiations (a, ß and γ-rays) is called radioactive decay (disintegration). The decay can be characterized by the mass, charge and energy of the outgoing particle. The time rate of disintegrations for radioactive material is called its activity. Activity is the expectation value of the number of nuclear decay occurring in a given quantity of material per unit time. The si-unit of activity is Bq and the conventional unit is curie (Ci). A curie (Ci) is defined as the 3.7xl010 dps and a Bq corresponds to one dps. These units of activity are related as, lBq=ldps=27pCi. The activity of any radioactive substance can be estimated from its mass and half-life time.

1.4.2 Radiation Protection and Dose Quantities

1.4.2.1 Exposure of Radiations. For X-rays and γ-rays, the exposure is defined in terms of the amount of ionization these rays produce in the air. The unit of exposure is termed as roentgen (R). One roentgen, exposure has been defined as the ratio, Aq/Am, where Aq is the summation of all similar charges that produced in the air when all the electrons liberated by photons in a mass Am of air are completely stopped in it (ICRU, 1962). The si-unit roentgen is defined as; 1R = 2.58 X 104 ־C/kg.

The interaction of ionizing radiations with living tissues bears a risk of biological-damage, while this risk minimizes as the exposure decreases. The risk related to natural background radiations is very small. Exposure levels as a result of a nuclear-disaster can vary widely, depending on the nature of the accident and the type of radiations involved.

For dose assessment, i.e. computing the dose of radiations received by a person following factors must be taken into account:

-The energy and type of ionizing radiation,
- The intensity of radiations,
- The biological sensitivity of the exposed area, and
- Other factors such as time, distance and nature of shielding-material used.

1.4.2.2 Radiation Dose. The ionizing radiations can cause adverse effects on biological tissues by imparting their energy to cellular substances e.g. proteins and DNA. The absorbed dose is an average energy imparted by radiation per unit mass of tissue. The si-unit of absorbed dose is (J/kg) and termed as gray (Gy). The energy deposited in the substance causes some biological and physical effects in it. As per recommendation of ICRP, depending upon the effect produced in the radiation absorbing substance the dose is classified as absorbed dose (Dr) for physical effect and an equivalent dose (HR) for a biological effect.

The radiation dose quantities can be described in three ways viz. absorbed dose, equivalent dose and effective-dose. The absorbed dose is the total amount of energy deposited by the radiations per unit mass (in kg) of the matter. Both effective dose and equivalent dose are weighted for the susceptibility to the effect on tissues by tissue weighting factor.

1.4.2.3 Absorbed dose (Dr, Gy). Absorbed dose is defined as the locally deposited energy in the matter that exposed to the ionizing radiations. Theoretically, the energy-dose can be computed from the energy of the radiation emitted by the source, its activity and taking into account of geometrical-factor.

1.4.2.4 Organ absorbed dose, (Dj, Gy). The mean absorbed dose of an organ or tissue T of mass mj is defined as:

Abbildung in dieser Leseprobe nicht enthalten

It is to be noted that the absorbed energy spread over the volume is non-uniform it is deposited around the radiation path.

1.4.2.5 Equivalent-dose (Hr, Gy). Equivalent-dose is a refinement of the absorbed dose, by using the nature of radiations. The concept of absorbed dose was found to be insufficient for different types of ionizing radiations. In 1950s it was concluded that the exposure involving absorbed-dose of lGy neutrons was approximately ten times more carcinogenic than absorbed-dose of lGy γ-ray photons. Thus, the absorbed-dose of neutrons should be multiplied by ten. Such facts introduced a new and more useful radiation quantity, termed as equivalent dose (Hr). The Hr can be computed by multiplying the Dr with weighting factor (wR) for a human body-organ. The WR is a number that depends on the severity of biological damages of the organ and the nature of interacting ionizing radiation. The equivalent dose is measured in Sievert (Sv) and lSv=100REM (Roentgen Equivalent Man).

The weighting factor (wR) has been introduced as per recommendations of ICRP and NCRP (Turner, 2007). The equivalent-dose, Ятд, in a tissue/organ T due to the radiation R, is defined as the product of the average absorbed dose, Ятд, in T from R and a dimensionless radiation weighting factor, W-R, for each radiation: Thus, Hj$=w-r.Djjl. The values of WR specified by NCRP and ICRP are approximately similar. If the radiation consists of different components with different WR values, then the equivalent dose for the tissue, T should be computed by summing various contributions:

Abbildung in dieser Leseprobe nicht enthalten

Where, I>\M is expressed in Gy, Ятд and Hj are in Sv. It expresses long­term risks (primarily cancer and leukemia) from low level chronic exposure. The recommended values of WR by ICRU (publication 60, 1991) are listed below:

Abbildung in dieser Leseprobe nicht enthalten

1.4.2.6 Effective dose (E). Effective dose determines how much risky to an individual's exposure of ionizing radiations. The effective dose considers both the nature of the interacting radiations and the sensitivity of the specific affected part of a human body. The effective dose is measured in Sievert (Sv). The objective of the effective dose is to provide a radiation dose related to the whole of the body. To achieve this objective, the NCRP and ICRP have assigned tissue weighting factors (w1׳׳׳). Therefore, the effective dose absorbed by any organ of the human body can be obtained by multiplying the equivalent dose and Wj. The summation of equivalent doses, weighted by the tissue weighting factors Wj of several organs and tissues T of the body that are considered to be the most sensitive, is called effective dose (ICRP, 103, 2007):

Abbildung in dieser Leseprobe nicht enthalten

The weight-factors (wj) should be added up to 1. The weight-factors are normalized such that when a human body received uniform γ-ray exposure, the effective-dose (Sv) is equivalent to the absorbed-dose (Gy). The equivalent dose that is used to compute the effective dose indicates the amount of energy-density deposited in an organ. If the weighting factors (и׳׳т) have been accurately computed, then some comparisons can be obtained between the absorbed-doses by various human bodies of differing dimensions and ages (i.e. child and adult).

The range of these doses varies between small fractions of mSv to a few Sv. An effective dose of lSv is termed as the stronger dose. It can lead to harmful deterministic effects in the human body. For the lower values of dose, effects may not appear immediately. The probability of the occurrence of the effects is a function of quantity of the dose received. For an individual human body, the effective dose is the mean of all the equivalent doses absorbed by the individual. As per recommendation of NCRP (report no. 116, 1993) and ICRP (publication 60, 1991) the average annual effective dose for a human body should be < lmSv and annual average equivalent dose for skin, hands and feet should be < 50mSv.

The basic introduction of some additional physical quantities related to the radiation dose have been provided in the following section.

1.4.2.7 Fluence (Ф, m" ). It is the ratio of AN to Δα, where ΔΝ is the number of photon incident upon a small sphere of the area (cross-section) Aa, Φ=ΑΝ/ Aa. In dosimetric computations, the fluence has frequently been expressed in terms of the lengths of photon trajectories. It can be proved that the fluence, Ф=АИ AV, where Al is the sum of the photon trajectory lengths in the volume AN.

1.4.2.8 ICRU-sphere. It is a sphere geometric phantom (tissue equivalent material) of 30 cm diameter made from a material with unit density (lg cm'3 ), comprised of tissue approximation composition (by weight fraction) 0.762 oxygen, 0.111 carbon, 0.101 hydrogen, and 0.026 nitrogen (ICRP, 2013).

1.4.2.9 Ambient dose equivalent, (H. 10, Sv). It is the dose equivalent at a point in a radiation field that would be produced by the corresponding expanded and aligned field at a depth 10mm in the ICRU-sphere, on the radius vector opposing the direction of the aligned field (ICRP, 2013). The ambient dose equivalent is the useful quantity in the area of radiation monitoring.

1.5 RADIATION EXPOSURE RISK

While evaluating the external radiation exposure, neutral radiations (X- rays, γ-rays and neutrons) place on the top priority. The first aftereffect of acute radiation exposure (-100 rads) to a human body decreases in the value of RBC (red blood cell) count. For humans, the lethal-dose, LD50 -5 OOrads for the whole body of which half of the population may die out from just one-time radiation exposure without getting any medical help.

The protection from the exposure of these hazardous ionizing radiations can be achieved by any of the following ways:

- by reducing the time spent in the region of high radiation intensity,
- by increasing the distance between the source of radiations and working place,
- by placing a suitable shielding-materials between the worker (human) and the source, and
- by using a limited quantity of radioactive materials.

1.5.1 EFFECTS OF IONIZING RADIATIONS ON HEAFTH

Severity of the health effect of the radiation exposure on a person depends on the received dose and time spent in the radiation environment. The health effects of low levels of radiation exposures are negligible and may not be detected soon. The living body can repair the damaged cells caused by the ionizing radiations. Fig. 1.4 explains the probabilistic health effects caused by the exposure of ionizing radiations to human body.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.4: Description of BEIR on health.

1.6 APPLICATIONS OF IONIZING RADIATIONS

The ionizing radiations have been used for the diagnosis and treatment of various abnormalities in a human body. These radiations are used in radiological imaging techniques such as X-ray image of bones and γ-ray CT-scan of head, Non-destructive analysis (NDA) of chemical composition for sample, crystallography, processing of fuel for a nuclear-reactor, security checking of baggages without opening them at airports and railway stations etc. Additionally, ionizing radiations have been used in the scientific-research such as agricultural-research, computing the age of rocks and skeletons, nuclear-reactors and nuclear weapons.

1.7 RADIATION PROTECTION ORGANIZATIONS

The Department of Atomic Energy (DAE), established in 1954 and the Atomic Energy Regulatory Board (AERB) established in 1983 are actively working for establishing protection and safety standards for ionizing radiations. DAE is working for radiation monitoring and environmental surveillance, whereas AERB ensures and check the use of the recommended safety standards at nuclear-establishments. These organizations have many branches for the monitoring of the recommended radiation safety standards.

1.8 INTERACTIONS OF GAMMA-RAYS WITH MATTER

The matter is comprised of atoms, compounds, and empty spaces. Thus, when γ-ray photons traverse through a shielding-material, the majority of them pass through the empty spaces, but some may have a possibility to encounter with the electric field of its microscopic constituents such as electrons and the nucleus. Since the interactions of γ-ray with atomic particles are based on the chance, thus a photon has a finite probability of passing through a portion of the material without any interaction. This probability depends on a number of factors such as the photon energy, the medium composition, compaction (density) and thickness. For a high density shielding-material the chances of photon interaction with its constituents are high. Also, the higher the number of subatomic particles in the material (high-Z), higher will be the chances of the photon interactions. Thus, γ-ray interaction probability is higher for the high-Z materials than low-Z materials. Similarly, the thickness of the shielding-material is related to the probability of interaction.

There are various processes by which γ-ray can interact with matter. Fig. 1.5 explains various types of the interaction processes of γ-rays with matter. While traversing through shielding-material, a γ-photon can interact by following phenomena: it can penetrate the given portion of the material without any interaction, it can interact with the material and gets completely absorbed by depositing the whole of its energy and it can interact and then scatter by depositing a part of its energy in the material. A brief summary of the possible γ-ray interaction processes suggested by Fano (1953b) are as follows:

Abbildung in dieser Leseprobe nicht enthalten

Theoretically, there are 12 possible processes (combining both columns) by which γ-ray can interact with matter (Fano, 1953b). A summary and brief description of γ-rays interaction processes has been listed in Table 1.1 (Siegbahn, 1965).

1.8.1 Interaction Mechanisms ofy-ray with Matter

The total mass attenuation coefficient of a shielding-material has major contributions from photoelectric-absorption, Compton-scattering, pair- production and triplet- production processes. The basic information regarding the major γ-ray interaction processes has been provided in the following section.

1.8.1.1 Photoelectric-absorption (γ; e~). Photoelectric-absorption is a process in which the incident γ-ray photon interacts with a tightly bound orbital electron (core electrons) of an atom of the material. If the energy of the incident photon is greater than the B.E. of the electron, then the photon is completely absorbed. This results in the removal of that electron from the atom. The removed electron is known as a photo-electron and an ion results when it leaves the atom. Fig. 1.6 illustrates the photoelectric-absorption process. It follows from the principle of conservation of energy that, the resulting photo-electron has KE:

Abbildung in dieser Leseprobe nicht enthalten

where, E is the energy of the incident photon, Её represents KE of the photo-electron and Ев represents binding-energy (B.E.) of the electron.

Table 1.1. The description of various γ-ray interaction processes with matter, and their z and E dependence (Siegbahn, 1965).

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.5: Description of various types of γ-ray interactions with matter.

Note: The types of interaction are in rectangles, photons of various sorts are in pentagons and electron/positron are in circles.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.6: Photoelectric-Absorption.

It further causes two subsequent processes. Firstly, the photo-electron can produce secondary ionization events with its surrounding atoms. The photo-electron rapidly transfers its energy and moves only a short distance in the material. Secondly, the vacancy created in one of the orbits of the atom gets quickly filled by an outer orbital electron. Such a transition causes an emission of characteristic X-ray, often called a fluorescent X-ray. The energy of the emitted photon is equal to the difference in energies of the orbits of the transferred electron. Some of these photons get reabsorbed by the electrons of less tightly bound orbits, which results in the emission of the Auger electrons. Fig. 1.7 shows the basic processes involved in a photoelectric-absorption (Gerward, 2001), where Δ’κ, EL, EM represent binding-energies of the respective shells. The electron jumping from the L shell to the vacancy produced in X-shell will result in the emission of a fluorescent X-ray photon, called the Ka photon, with energy

Ea=EK-EL (1.4)

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.7: X-ray fluorescence and Auger effect.

Fig. 1.7 illustrates the emission of the Auger electron with energy, Еae a.S!

Abbildung in dieser Leseprobe nicht enthalten

The probability of this process is high for high-Z materials. A plot of the photoelectric-absorption cross-section versus energy for medium and high- z elements, shows discontinuities at several characteristic energies (Gerward, 2001). The discontinuities in the absorption curve (absorption- edges) appear at those photon energies which match to the B.E. of the electrons in the various shells of the absorbing atom. Thus, the absorption- edge lying highest in energy corresponds to the B.E. Δ’κ for the E-shell electrons. For photons having energies slightly above the E-edge are just sufficient to undergo a photoelectric-absorption in which a E-electron is ejected from the atom. For photons having energies slightly below the K- edge, this process is no longer possible, and therefore the interaction probability drops rapidly. Similar absorption-edges occur at lower energies for another electron shells of the atom, i.e. L, M etc. For energies above the E-edge and between the edges (for energies less than 0.2 MeV), the photoelectric-absorption cross-section is a continuous function which is approximately proportional to E and for higher energy i.e. lí > 0.5 MeV it is proportional to E1. The absorption-edge energy, Εκ, corresponds to an absorption-edge wavelength Лк is given by cf. Eq. (1.5)

Abbildung in dieser Leseprobe nicht enthalten

The photoelectric-absorption cross-section greatly depends on the atomic-number, (Z) of the shielding-material. It is proportional to z" where n varies between 4 and 5 depending on the energy of γ-ray. This cross­section decreases with the increase in energy. So, the photoelectric- absorption will give the major contribution to the total attenuation coefficients for γ-rays in high-Z materials and lower energy photons (£<0.2MeV).

The cause behind such increase in the photoelectric-absorption cross­section with the increase in atomic-number is that, as the atomic-number increases the B.E. becomes closer to the photon energy. The probability of ejection is greater for more tightly bound electrons. Therefore K-shell electrons are most affected; about 80% of the photoelectric-absorption takes place in the if-shell, provided that γ-ray energy exceeds the B.E. of ^-electron.

1.8.1.2 Compton-scattering (jr,e~). A γ-ray photon interacts with a free or weakly bound electron, loses some of its energy and is deflected from its original direction of travel. In this process, a part of the incident photon energy is imparted to the recoiled electron hence it is called inelastic scattering. In this case there is no phase relationship between the photons scattered by the different electrons of the same atom and hence it is also said to be incoherent. Fig. 1.8 explains the Compton-scattering1 (Gerward, 2001). This interaction looks like a collision between the photon and a free electron. By the conservation of momentum and energy, the electron must recoil in a specific direction with a specific energy. The recoiling electron rapidly loses its energy and moves a short distance in the shielding- material. The scattered photon deflects off in a different direction with a lower energy. The direction of the Compton photon (a secondary photon) is not along the same trajectory as the initial incoming photon. The deflected or scattered photon may escape from the material or undergo further Compton-scattering or can be absorbed through the photoelectric- absorption within the material.

The relationship between photon deflection and energy loss can be determined by the conservation-law of linear-momentum and energy for the photon and recoiling electron. Let, E and E' represent the energy of the incident and the scattered photon, respectively, and Её represents the energy of the recoiling electron.

Abbildung in dieser Leseprobe nicht enthalten

Figure 1.8: Description of the Compton-scattering. (Θ represents scattering angle and (¿r represents angle of recoil)

By applying the law of conservation of linear-momentum the expression for a Compton-shift (ΔΑ) can be derived:

Abbildung in dieser Leseprobe nicht enthalten

This relation was first derived by A.H. Compton in 1923. The quantity h/nioC has the dimensions of length and is called Compton-wavelength of the electron. The KE of the scattered photon, E'=hv'=hc/Å', is then given by solving Eq. (1.7),

Abbildung in dieser Leseprobe nicht enthalten

Where, E=hv represents the energy of the incident photon, and m0c (~51 IkeV) represents the rest mass energy of the electron. The KE the recoiling electron is equal to the difference in the energy lost by the photon and the electron B.E. (Ев). For Compton-scattering to occur, the photon energy should be much higher than the electron B.E. (E » Ев). So the KE of the recoil electron is very nearly equal to the energy lost by the photon.

Abbildung in dieser Leseprobe nicht enthalten

Two extreme cases can be identified:

(i) A grazing angle scattering, i.e. ćfeo. In this case Eq. (1.8) and Eq. (1.9) predict that A ׳«A, and Ae-~0. In this extreme, the recoil electron has very little energy and the scattered photon has nearly the same energy as the incident photon.

(ii) A head-on collision or backscattering collision, i.e. θ=π. In this case, the incident photon is scattered towards the direction of its origin, whereas the electron recoils along the direction of incidence. In this case, the scattered photon has minimum energy, and hence maximum energy has transferred to the recoiled electron. By inserting θ=π in Eq. (1.8) andEq. (1.9) gives

Abbildung in dieser Leseprobe nicht enthalten

In normal circumstances, all scattering angles will occur in the medium. Therefore, a continuum of energies can be transferred to the electron, ranging from zero to the maximum predicted by the Eq. (1.11). Klein and Nishina, assuming the electron to be initially free and at rest, formulated the basic theory of Compton-scattering (Heitler, 1954).2 Departures from the Klein-Nishina (KN) theory occur at low energies because of electron binding effects. The angular distribution of scattered radiation has predicted by the KN formula as the differential scattering cross-section (having the dimensions of the area per unit solid angle) per electron. For un-polarized photons, the free electron Compton-scattering cross-section is given by KN formula (Klein and Nishina, 1929):

Where, a=Elmo0r, r״=e7471s״m״c2 =2.818x 10־l5 m represents the classical radius of the electron, and d/2 represents the solid angle element. Study of Eq. (1.12) indicates that there is a strong tendency for the forward scattering for photon of higher energy. Thus, as the value of a approaches to zero, the Eq. (1.12) reduces to the classical differential cross-section i.e. Thomson scattering.

Abbildung in dieser Leseprobe nicht enthalten

Integration of Eq. (E12) over all angles gives the total KN cross-section per electron, as:

Abbildung in dieser Leseprobe nicht enthalten

Thus, as a approach to zero, KN cross-section becomes the Thomson cross­section, Gj.

Abbildung in dieser Leseprobe nicht enthalten

It should be noted that the extrapolation cr7KN->Gj for a->0 is valid only for free electrons. For bound electrons, еаш->0 foralo. For an atom containing z electrons, Compton cross-section per atom (erc) is given by:

Abbildung in dieser Leseprobe nicht enthalten

At lower energies, where B.E. is a significant fraction of the incident photon energy, the KN differential cross-section can be modified by the use of the function for incoherent scattering S(q,Z), where q represents the magnitude of the transferred momentum, which further depends on the incident energy of the photon and the angle of deflection for the scattered photon and the atomic-number of the target atom.

Abbildung in dieser Leseprobe nicht enthalten

The factor S(q,Z) represents the probability that an atom be raised to any excited or ionized state as a result of a sudden impulsive action, which imparts a recoil momentum q to an atomic electron. The momentum transferred, q is given as:

Abbildung in dieser Leseprobe nicht enthalten

where, k' and к represent the wave-vectors of scattered and incident γ-rays. Since binding effects are important mainly for small momentum transfers, the approximation k'ttk is usually used, thus:

Abbildung in dieser Leseprobe nicht enthalten

The Compton-scattering is a predominant interaction process at the ermediate gamma-energies, 0.05-5MeV. The Compton-scattering cross­section decreases as the incident photon energy increases and varies linearly with the atomic-number, z. The interaction probability depends on the electron density, which is proportional to ZIA, and nearly constant for all materials.

The incoherent scattering functions, S(g,Z), based on the non-relativistic Hartree-Fock model for the elements, Z=1 to 100, have been tabulated by Hubbell et al., (1975). Kahane (1998) has used the Ribberfors and Berggren (1982) relativistic treatment to compute and tabulate the relativistic Dirac-Hartree-Fock photon incoherent scattering functions, S(q,z), for all elements 1< z <110.

The к-matrix theory with its claim for higher accuracy is available for Compton-scattering (Hubbell, 1999). Compilations of /4! such as XCOM, a computer program of Berger and Hubbell (1987), the tabulations of Hubbell-Seltzer (1995), and the database of Cullen et al, (1997) and Chadwick et al, (2006) rely on the incoherent scattering function S(q,Z) approach.

1.8.1.3 Pair-production (χ; e^e*). The creation of an electron-positron pair (e~, e+), when a gamma-photon interacts with the Coulomb field of a nucleus is called pair-production. In this process, the incident photon is completely absorbed and an electron-positron pair appears in its place.

Abbildung in dieser Leseprobe nicht enthalten

Pair-production is an example of materialization of energy. This interaction has threshold energy of 1.022MeV (i.e. twice the electron/positron rest mass energy: 2m0c ), since this is the minimum energy required to produce an electron-positron pair. For the exceeding value of photon energy than 1.022MeV, the excess energy is equally shared between the electron and positron as their KE. The total KE of the resultant particles is equal to the incident photon energy minus the rest mass energy of the two particles which have been created. Fig. 1.9 illustrates the pair- production.

Abbildung in dieser Leseprobe nicht enthalten

An electron and a positron produced from a pair-production are rapidly slowed down in the shielding-material. After losing its KE, the positron will eventually encounter one of the atomic-electrons (the free electron), and these two particles will annihilate each other (positron interaction), converting their mass directly into energy which produces two gamma photons, each of energy equal to the electron rest mass energy (approximately 511keV). These two 511keV photons travel exactly in opposite directions (180°) to each other. These lower energy γ-ray photons

[...]


1 The process is named in honor of Arthur H. Compton (1892-1962), US physicist. His experimental verification of the Compton Effect, in 1923, was a convincing evidence for the quantum nature of EM radiation.

2 The Swedish theoretical physicist Oskar Klein (1894-1977) and the Japanese physicist Yoshio Nishina (1890-1951) have published their formula in 1929.

3 The momentum transfer is hq.

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Title
Shielding Behaviour Analysis of Double Layered Slabs. Gamma Ray Shielding
Grade
9.99
Author
Year
2016
Pages
223
Catalog Number
V437837
ISBN (eBook)
9783668780125
ISBN (Book)
9783668780132
Language
English
Tags
Gamma Rays, radiological, Radiation Shielding, Cost effective shielding of gamma-rays
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Kulwinder Singh Mann (Author), 2016, Shielding Behaviour Analysis of Double Layered Slabs. Gamma Ray Shielding, Munich, GRIN Verlag, https://www.grin.com/document/437837

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