Radiation Shielding
by J. Kenneth Shultis and Richard E. Faw
American Nuclear Society, La Grange Rark, IL, 1999. ISBN 0-89448-456-7
Radiation Shielding
by J. Kenneth Shultis and Richard E. Faw
Prentice Hall, Upper Saddle River, NJ, 1996. ISBM 0-13-125691-2
Out of Print. Republished with same title by the American Nuclear Society
TABLE OF CONTENTS
Preface
Chapter 1 Introduction
1.1 Historical Roots
1.1.1 The Early Years
1.1.2 The Origins of Modern Shielding Practice
1.1.3 Modern Developments
1.1.4 Regulatory Development
1.2 Radiation Shielding Institutions
1.2.1 Professional Societies and Journals
1.3 Radiation Protection Institutions
1.3.1 United Nations Organizations
1.3.2 Governmental Organizations in the United States
1.4 Important Sources of Shielding Information
1.5 Final Remarks
Chapter 2 Characterization of Radiation Fields and Sources
2.1 Directions and Solid Angles
2.2 Fundamental Radiation Field Variables
2.2.1 Fluence and Fluence Rate
2.2.2 Net Flow and Net Flow Rate
2.2.3 Other Definitions
2.3 Directional Properties of the Radiation Field
2.3.1 Properties of the Fluence
2.3.2 Transformation of Variables
2.3.3 Angular Properties of the Flow and Flow Rate
2.4 Representations of Angular Dependence
2.5 General Specification of Radiation Sources
2.6 Distributed and Discrete Variables
Chapter 3 Interaction of Radiation with Matter
3.1 Interaction Coefficient
3.2 Microscopic Cross Section
3.3 Conservation Laws for Scattering Reactions
3.3.1 Conservation of Momentum
3.3.2 Conservation of Energy
3.3.3 Application of the Conservation Laws
3.3.4 Scattering of Photons by Free Electrons
3.3.5 Scattering of Neutrons by Atomic Nuclei
3.3.6 Limiting Cases in Classical Mechanics of Elastic Scattering
3.3.7 Elastic Scattering of Electrons and Heavy Charged Particles
3.4 Photon Cross Sections
3.4.1 Thomson Cross Section for Incoherent Scattering
3.4.2 Klein-Nishina Cross Section for Incoherent Scattering
3.4.3 Incoherent Scattering Cross Sections for Bound Electrons
3.4.4 Coherent (Rayleigh) Scattering
3.4.5 Photoelectric Effect
3.4.6 Pair Production
3.4.7 Photon Attenuation Coefficients
3.4.8 Compton Absorption and Scattering Cross Sections
3.4.9 Photoelectric Absorption Cross Section
3.4.10Absorption Cross Section for Pair Production
3.4.11Corrections for Radiative Energy Loss
3.5 Neutron Interactions
3.5.1 Classification of Types of Interactions
3.5.2 Cross Sections for Neutron Scattering
3.5.3 Average Energy Transfer in Neutron Scattering
3.5.4 Radiative Capture of Neutrons
3.6 Charged-Particle Interactions
3.6.1 Collisional Energy Loss
3.6.2 Electron Radiative Energy Loss
3.6.3 Charged-Particle Range
3.6.4 Residual-Range Concept
3.6.5 Electron Radiation Yield
Chapter 4 Common Radiation Sources Encountered in Shield Design
4.1 Neutron Sources
4.1.1 Fission Neutrons
4.1.2 Photoneutrons
4.1.3 Neutrons from (alpha,n) Reactions
4.1.4 Activation Neutrons
4.1.5 Fusion Neutrons
4.2 Sources of Gamma Photons
4.2.1 Radioactive Sources
4.2.2 Prompt Fission Gamma Photons
4.2.3 Gamma Photons from Fission Products
4.2.4 Capture Gamma Photons
4.2.5 Gamma Photons from Inelastic Neutron Scattering
4.2.6 Activation Gamma Photons
4.2.7 Annihilation Radiation
4.3 Sources of X Rays
4.3.1 Characteristic X Rays
4.3.2 Bremsstrahlung
4.3.3 X-Ray Machines
Chapter 5 Response Functions
5.1 Dosimetric Quantities
5.1.1 Energy Imparted, Specific Energy, and Lineal Energy
5.1.2 Deterministic Quantities
5.1.3 Absorbed Dose
5.1.4 Kerma
5.1.5 Exposure
5.1.6 Linear Energy Transfer
5.2 Dose Equivalent
5.3 Response Function Concept
5.4 Local Response Functions
5.5 Charged-Particle Equilibrium
5.6 Local Neutron Dose
5.7 Local Photon Dose
5.7.1 Photon Energy Deposition Coefficients
5.7.2 Photon Kerma, Absorbed Dose, and Dose Equivalent
5.7.3 Photon Exposure
5.7.4 Selection of Proper Mass Energy Deposition Coefficients
5.8 Human as Target
5.8.1 Characterization of Ambient Radiation
5.8.2 Response Functions Based on Simple Geometric Phantoms
5.8.3 Response Functions Based on Anthropomorphic Phantoms
5.8.4 Comparison of Response Functions
Chapter 6 Basic Methods for Radiation Dose Calculations
6.1 Uncollided Radiation
6.1.1 Exponential Attenuations
6.1.2 Mean-Free-Path Length
6.1.3 Uncollided Dose from a Point Source
6.1.4 Point Kernel for the Uncollided Dose
6.2 Uncollided Doses from Distributed Sources
6.2.1 Line Source
6.2.2 Disk Source
6.2.3 Rectangular Area Source
6.2.4 Spherical Surface Source
6.2.5 Frustrum of a Cone
6.2.6 Infinite Slab Source
6.2.7 Cylindrical Volume Source
6.3 Point-Kernel Concept for Total Dose
6.3.1 Dose in Terms of the Green's Function of Transport Theory
6.3.2 Point Kernel for the Total Dose
6.3.3 Isotropic Detector Without Spatial Dependence
6.3.4 Infinite Homogeneous Medium
6.3.5 Examples of Point Kernels
6.4 Generalized Method for an Infinite Homogeneous Medium
6.4.1 Volumetric Sources
6.4.2 Absorbed Fraction and Reduction Factor
6.4.3 Advantages of the Generalized Approach
6.4.4 Limiting Source or Target Volumes
6.4.5 Reciprocity Theorem
6.4.6 Extension to Nonuniform and Surface Sources
6.4.7 Infinite Cylindrical Sources
6.5 Calculation of Geometric Factors
6.5.1 Analytical Calculation of Geometry Factors
6.5.2 Examples of Geometry Factors and Point-Pair Distributions
6.5.3 Uncollided Dose Examples Using Geometry Factors
6.5.4 Monte Carlo Evaluation of Geometry Factors and Point-Pair Distance Distributions
6.5.5 Multiregion Geometries
6.5.6 Basic Geometry Factors for One-Dimensional Problems
6.5.7 Examples of Multiple Regions
6.6 Effect of Density Variations
6.6.1 Theorems for Density Variations
6.6.2 Point Kernels in Media with Density Variations
6.6.3 Modified Point-Pair Distance Distributions
6.6.4 Modified Geometry Factors
6.6.5 Example of a Modified Point-Pair Distance Distribution
6.6.6 Example Problem Using Modified Geometry Factors
6.7 Geometric Transformations
6.7.1 Circular Area (Disk)-to-Point Source Transformation
6.7.2 Volume-to-Surface Source Transformation
Chapter 7 Special Techniques for Photons
7.1 Photon Buildup
7.1.1 Isotropic, Monoenergetic Sources in Infinite Media
7.1.2 Comparison of Buildup Factors for Point and Plane Sources
7.1.3 Empirical Approximations for Point-Source Buildup Factors
7.1.4 Point-Kernel Applications of Buildup Factors
7.2 Buildup in Heterogeneous Media
7.2.1 Boundary Effects in Finite Media
7.2.2 Treatment of Stratified Media
7.3 Broad-Beam Attenuation
7.3.1 Attenuation Factors for Monoenergetic Photon Beams
7.3.2 Attenuation of Oblique Beams of Monoenergetic Photons
7.3.3 Attenuation Factors for X-Ray Beams
7.3.4 The Half-Value Thickness
7.4 Photon Albedo
7.4.1 Differential Number Albedo
7.4.2 Integrals of Albedo Functions
7.4.3 Application of the Albedo Method
7.4.4 Single-Scatter Albedo
7.4.5 Approximation for the Single-Scatter Dose Albedo
7.4.6 Chilton-Huddleston Formula
7.4.7 Photon Albedo Data
7.5 Photon Streaming
7.5.1 Characterization of Incident Radiation
7.5.2 Line-of-Sight Component for Straight Ducts
7.5.3 Wall-Penetration Component for Straight Ducts
7.5.4 Single-Scatter Wall-Reflection Component
7.5.5 Transmission of Gamma Rays Through Two-Legged Rectangular Ducts
7.6 Shield Heterogeneities
7.6.1 Limiting Case for Small Discontinuities
7.6.2 Small Randomly Distributed Discontinuities
7.6.3 Large Well-Defined Heterogeneities
7.7 Gamma-Ray Skyshine
7.7.1 Open Silo Example
7.7.2 Shielded Skyshine Sources
Chapter 8 Special Techniques for Neutrons
8.1 Differences Between Neutron and Photon Calculations
8.1.1 Buildup Factors
8.1.2 Neutron Dose Units
8.2 Fission Neutron Attenuation by Hydrogen
8.3 Removal Cross Sections
8.3.1 Extensions of the Removal-Cross-Section Model
8.4 Fast-Neutron Attenuation Without Hydrogen
8.5 Calculation of the Intermediate and Thermal Fluences
8.5.1 Diffusion Theory for Thermal Neutron Calculations
8.5.2 Fermi Age Treatment for Thermal and Intermediate-Energy Neutrons
8.5.3 Removal-Diffusion Techniques
8.6 Capture-Gamma-Photon Attenuation
8.6.1 Response from Uncollided Photons
8.6.2 Response from Scattered Photons
8.7 Neutron Shielding with Concrete
8.7.1 Concrete Slab Shields
8.8 Neutron Albedo
8.8.1 Fast Neutron Albedo
8.8.2 Intermediate-Energy Neutron Albedo
8.8.3 Thermal Neutron Albedo
8.8.4 Emission of Secondary Photons During Neutron Reflection
8.9 Duct Streaming for Neutrons
8.9.1 Straight Ducts
8.9.2 Ducts with Bends
8.9.3 Empirical and Experimental Results
8.10 Neutron Skyshine
Chapter 9 Special Techniques for Charged Particles
9.1 Introduction
9.2 Alpha and Beta Decay
9.2.1 Alpha Decay
9.2.2 Beta Decay
9.3 Spatial Distribution of the Absorbed Dose
9.3.1 Point and Plane Kernels Defined
9.3.2 Electron and Beta-Particle Dose Distributions
9.4 Point-Kernel Applications
9.4.1 Line Source of Electrons
9.4.2 Plane Isotropic Source of Electrons
9.4.3 Volume Source of Electrons
9.5 Energy Spectrum of the Fluence
9.5.1 CSDA Approximation
9.5.2 Fluence Energy Spectra for Electron Sources
Chapter 10 Deterministic Transport Theory
10.1 Transport Equation
10.1.1 Explicit Form for the Three Basic Geometries
10.1.2 Integral Form of the Transport Equation
10.1.3 Transport Equation for Photons
10.1.4 Transport Equation for Neutrons
10.2 Implications of the Transport Equation
10.2.1 Existence and Uniqueness
10.2.2 Spatially Uniform Flux Density
10.2.3 Plane-Density Variations
10.2.4 Scaling of Radiation Fields
10.2.5 Volume-to-Surface Source Transformation
10.3 Approximations to the Transport Equation
10.3.1 Exponential Attenuation
10.3.2 Diffusion Approximation
10.3.3 Multigroup Approximation
10.4 Method of Moments
10.5 Discrete-Ordinates Method
10.6 Integral Transport Method
10.6.1 Direct Integration of the Scattering Source Term
10.6.2 Implementation
Chapter 11 Monte Carlo Methods for Radiation Transport Calculations
11.1 Random Numbers
11.2 Selection Techniques for Stochastic Variables
11.2.1 Selection of Discrete Variables
11.2.2 Cumulative Distribution Method for Continuous Variables
11.2.3 Rejection Method
11.2.4 Composition Method
11.2.5 Composition-Rejection Method
11.3 Analog Calculations
11.3.1 Geometric Transformations
11.3.2 Particle Tracking
11.3.3 Scoring
11.4 Variance Reduction
11.4.1 Central-Limit Theorem
11.4.2 Importance Sampling
11.4.3 Truncation Methods
11.4.4 Splitting and Russian Roulette
11.4.5 Interaction Forcing
11.4.6 Exponential Transformation
11.4.7 Deterministic Scoring Methods
Appendices
A. Constants and Conversion Factors
B.1 Elliptic Integrals
B.2 Sievert or Secant Integral
B.3 Exponential Integral Function
B.4 Legendre Polynomials
B.5 Chandrasekhar's H Function
B.6 Dirac Delta Function
C. Cross Sections and Related Data
E. Photon Buildup Factors and Neutron Attenuation Factors
F. Skyshine Response Functions
G. Fission-Product Source Parameters
H. Photons Emitted by Selected Radionuclides
Index