Polarization Theory of Nuclear Reactions

Description

This book provides the reader with a modern and comprehensive overview of nuclear polarization theory. The understanding of polarization phenomena greatly enriches data obtained from scattering and nuclear reactions by providing information on the interaction that can change spin orientation as well as important verification data for the study of nuclear structures and reaction mechanisms. The author methodically derives the polarization theory of nuclear reactions for various types of elastic scattering and two-body direct reactions between particles of different spin and unpolarized target nuclei with arbitrary spin, as well as the reactions between two polarized light particles and the polarization theory for photon beams. In addition, the polarization theories of relativistic nuclear reactions are rigorously covered in great scope and detail. A chapter on polarized particle transport theory presents the Monte-Carlo method for describing the transport of polarized particles and formalizes the polarized particle transport equation. Here, the author also illustrates a novel and concrete scheme for establishing a polarization nuclear database. Nuclear polarization is important not only for microscopic nuclear structure and reaction studies but also for nuclear engineering, applied nuclear physics, and medical physics. With the development of radioactive beam facilities and, on the theoretical side, the development of consistent microscopic nuclear reaction and structure theories, this book on the polarization theory of nuclear reactions serves as a timely source of reference for students and researchers alike. Summary Introduction Contents About the Author Chapter 1: Basic Knowledge of Polarization Theory of Nuclear Reactions 1.1 Introduction 1.2 Spin Operators 1.3 Irreducible Tensors 1.4 Polarization Operators 1.5 Density Matrices References Chapter 2: Polarization Theory of Nuclear Reactions for Spin Particles 2.1 Pauli Matrices 2.2 Polarization of the Spin Particle Beams 2.3 Polarization Theory of Elastic Scattering of Unpolarized Spin Particles with Spinless Targets 2.4 Polarization Theory of Elastic Scattering of Polarized Spin Particles with Spinless Targets 2.5 Polarization Theory of Triple Elastic Scatterings Between Spin Particles and Spinless Nuclei 2.6 Two Theoretical Methods to Study the Polarization Phenomena of Nuclear Reactions 2.7 Polarization Theory for Reactions 2.8 Polarization Theory of Nuclear Reactions of Spin Particle with Polarized Target and Residual Nucleus 2.9 Polarization Theory for Reactions References Chapter 3: Polarization Theory of Nuclear Reactions for Spin 1 Particles 3.1 Spin Operators and Polarization Operators of Spin 1 Particles 3.1.1 General Expressions of S = 1 Spin Operators and Polarization Operators 3.1.2 Specific Expressions in the Spherical Basis Representation 3.1.3 Specific Expressions in the Cartesian Basis Representation 3.1.4 Transformation Relations Between the Spherical Basis and Cartesian Coordinate Systems 3.1.5 Transformation Relations Between the Spherical Basis and Cartesian Basis Representations 3.2 Some Mathematical Formulas Related to Spin Operators and Polarization Operators of Spin 1 Particles 3.2.1 Coordinate Rotation of S = 1 Spin Wave Function and Spin Operator 3.2.2 Action of the S = 1 Spin Operators and Polarization Operators on Basis Spin Functions 3.2.3 Products of S = 1 Spin Operators and Polarization Operators 3.2.4 Traces of the S = 1 Spin Operators and Polarization Operators 3.2.5 General Spin Wave Functions and Density Matrices for S = 1 Particles 3.3 Vector Polarization Rate and Tensor Polarization Rate of Spin 1 Incident Particles 3.4 Elastic Scattering Amplitude of Spin 1 Particles with Spinless Targets 3.5 Polarization Theory of Elastic Scattering of Unpolarized Spin 1 Particles with Spinless Targets 3.6 Polarization Theory of Elastic Scattering of Spin 1 Particle with both Vector Polarization and Tensor Polarization from a ... 3.7 General Form of Nuclear Reaction Polarization Theory of Spin 1 Particles with Non-zero Spin Target 3.8 Polarization Theory for Reactions 3.9 Polarization Theory for Reactions 3.10 Polarization Theory for Reactions 3.11 Polarization Theory for Reactions 3.12 Polarization Theory for Reactions 3.13 Deuteron Phenomenological Optical Potentials with Tensor Terms and Corresponding Radial Equations 3.13.1 Deuteron Phenomenological Optical Potentials Containing Tensor Terms 3.13.2 Deuteron Radial Equations for the Spherical Nuclei when Containing Tensor Potentials 3.14 Folding Model Describing the Reaction Between Deuteron and Nucleus 3.14.1 Deuteron Folding Model Without Breakup Channel 3.14.2 Deuteron Folding Optical Potentials Containing Break Channel 3.15 The Spherical Nucleus CDCC Theory Describing the Breakup Reaction for Incident Loosely Bound Light Complex Particles 3.15.1 Development of CDCC Theory 3.15.2 Spherical Nucleus CDCC Equation 3.15.3 Angular Distribution of Deuteron Elastic Scattering 3.15.4 Double Differential Cross Section of the Ejected Nucleons After Deuteron Breaking 3.16 Axis Symmetric Rotational Nucleus CDCC Theory Describing the Breakup Reaction for Incident Loosely Bound Light Complex Pa... 3.16.1 Axis-Symmetric Rotational Nucleus CDCC Equation 3.16.2 Angular Distribution of Deuteron Elastic and Inelastic Scattering 3.16.3 Double Differential Cross Section of the Ejected Nucleons After Deuteron Breaking References Chapter 4: Polarization Theory of Nuclear Reactions for Spin Particles and Polarization Theory for Photon Beams 4.1 Polarization Theory of Nuclear Reactions for Spin Particles 4.2 Polarization Theory for Photon Beams 4.2.1 Classic Electromagnetic Field Theory 4.2.2 Hamilton Canonical Equation 4.2.3 Quantization of Electromagnetic Fields 4.2.4 Polarization Theory of Photon Beams References Chapter 5: Polarization Theory of Relativistic Nuclear Reactions 5.1 Basic Theory of Relativistic Quantum Mechanics 5.1.1 Klein-Gordon Equation 5.1.2 Dirac Equation 5.1.3 Pauli Metric and Bjorken-Drell Metric 5.1.4 Plane Wave Solution of the Dirac Equation 5.1.5 Lorentz Covariant of the Dirac Equation 5.1.6 The Trace Formulas for γ Matrix Products 5.2 Transformation of Relativistic Coordinate Systems 5.3 Relativistic Optical Model and Phenomenological Optical Potential 5.4 Dirac S Matrix Theory of the Relativistic Nuclear Reactions 5.5 Dirac Coupling Channel Theory Including Elastic Scattering and Collective Inelastic Scattering Channels 5.6 Relativistic Collective Deformation RDWBA Method and Calculation of Nucleon Polarization Quantities 5.7 Relativistic Impulse Approximation of Elastic Scattering and Calculation of Nucleon Polarization Quantities 5.8 Relativistic Impulse Approximation of Inelastic Scattering and Calculation of Nucleon Polarization Quantities 5.8.1 Relativistic Distorted Wave Impulse Approximation of Single Particle State Inelastic Scattering 5.8.2 Relativistic Distorted Wave Impulse Approximation of Collective State Inelastic Scattering 5.9 Relativistic Impulse Approximation of (p, n) Reactions and Calculation of Nucleon Polarization Quantities 5.10 Relativistic Classical Field Theory and Lagrangian Density in Quantum Hadron Dynamics 5.10.1 Relativistic Classical Field Theory 5.10.2 Lagrangian Density in Quantum Hadron Dynamics 5.10.3 Relativistic Mean Field Equations 5.11 Relativistic Green Function Theory at Zero Temperature 5.11.1 The Propagator of Neutral Scalar Bosons with Spinless 5.11.2 The Propagator of Fermions with Spin 5.11.3 The Propagator of Neutral Vector Bosons with Spin 1 5.11.4 Feynman Rules of Nucleon-Meson Interaction in Momentum Representation 5.12 Real Part of Nucleon Relativistic Microscopic Optical Potential and Relativistic Nuclear Matter Properties 5.12.1 Self-Energy Operator and Green Function in Nuclear Matter 5.12.2 Real Part of Nucleon Relativistic Microscopic Optical Potential 5.12.3 Relativistic Nuclear Matter Properties 5.13 Imaginary Part of Nucleon Relativistic Microscopic Optical Potential 5.13.1 Contribution of σ - σ Meson Exchange Processes to the Imaginary Part of the Optical Potential 5.13.2 Contribution of ω - ω Meson Exchange Processes to the Imaginary Part of the Optical Potential 5.13.3 Contribution of σ - ω Meson Exchange Processes to the Imaginary Part of the Optical potential 5.13.4 Contribution of πps - πps Meson Exchange Processes to the Imaginary Part of Optical Potential 5.13.5 Contribution of πpv - πpv Meson Exchange Processes to the Imaginary Part of the Optical Potential 5.13.6 Contribution of ρV - ρV Meson Exchange Processes to the Imaginary Part of the Optical Potential 5.13.7 Contribution of ρT - ρT Meson Exchange Processes to the Imaginary Part of Optical Potential 5.13.8 Contribution of ρV - ρT Meson Exchange Processes to the Imaginary Part of Optical Potential 5.14 Contribution to Imaginary Part of Nucleon Relativistic Microscopic Optical Potential by Fourth Order Exchange Diagrams 5.15 Relativistic Bethe-Salpeter Equation 5.16 Bonn One Boson Exchange Potential 5.17 Nucleon Relativistic Microscopic Optical Potential Based on the Dirac-Brueckner-Hartree-Fock Theory 5.17.1 Relativistic Brueckner Theory 5.17.2 Relativistic Pauli Incompatibility Operators 5.17.3 Calculation Formulas for T Matrix Elements and Nuclear Matter Properties in Symmetric Nuclear Matter 5.17.4 Nucleon Self-Energy in Asymmetric Nuclear Matter 5.17.5 Nucleon Relativistic Microscopic Optical Potential Based on DBHF Theory 5.18 Proca Relativistic Dynamics Equation of Spin 1 Particle and Its Application in Elastic Scattering Calculations 5.18.1 Proca Equation of Free Particles 5.18.2 Proca Equation with Interaction Potential 5.18.3 Some Expressions Related to S=1 Spin Operators 5.18.4 Proca Equation in the Form of Schrodinger-like Equation 5.18.5 Discussion on the Application of the Proca Equation to Calculate the Elastic Scatterings Between Deuteron and Nucleus 5.19 Weinberg Relativistic Dynamics Equation with Spin 1 Particles and Discussion on its Application 5.19.1 Weinberg Equation of Free Particles 5.19.2 Weinberg Equation with Interaction Potential 5.19.3 Discussion on the Application of the Weinberg Equation to Calculate the Elastic Scatterings Between Deuteron and Nucleus 5.20 The Relativistic Nuclear Reaction Theory Considering the Internal Structure of the Incident Deuterons References Chapter 6: Basis of the Polarized Particle Transport Theory 6.1 Introduction to the Polarized Particle Transport Theory 6.2 Polarized Particle Transport Theory for Reactions 6.2.1 Polarization Theory of Spin Particles Related to Azimuthal Angle 6.2.2 Polarization Nuclear Database of Spin Particles 6.2.3 Main Points of Polarized Particle Transport Theory for Spin Particles 6.3 Polarized Particle Transport Theory for Reactions 6.3.1 Polarization Quantities of Spin 1 Particles Related to Azimuthal Angle 6.3.2 Polarization Nuclear Database of Spin 1 Particles 6.3.3 Main Points of Polarized Particle Transport Theory for Spin 1 Particles 6.4 Polarized Particle Transport Theory for Reactions 6.4.1 Polarization Quantities for Reactions Related to Azimuthal Angle 6.4.2 Polarization Nuclear Database for Reactions 6.4.3 Polarization Quantities for Reactions Related to Azimuthal Angle 6.4.4 Polarization Nuclear Database for Reactions 6.4.5 Main Points of Polarized Particle Transport Theory for Reactions 6.5 Polarized Particle Transport Equation 6.6 Prospect of the Polarized Particle Transport Theory 6.6.1 To Perfect the Polarization Theory of Nuclear Reactions 6.6.2 To Establish a Polarization Nuclear Database 6.6.3 To Research the Polarized Particle Transport Theory References Appendix: Clebsch-Gordan Coefficients, Racah Coefficients, and 9j Symbols References Index