Introduction to Nuclear Reactions

PREFACE
CLASSICAL AND QUANTUM SCATTERING 
Experiments with Nuclear Particles
Theories and Experiments
Reactions Channels
Conservation Laws
Kinematics of Nuclear Reactions
Cross Sections, Center of Mass and Laboratory Frames 
Classical Scattering 
The Classical Cross Section
Example: Rutherford scattering
Orbiting, rainbow and glory scattering
Stationary scattering of a plane wave
Appendix 1.A - Systems of units
Appendix 1.B - Useful constants and conversion factors
Exercises 
References
THE PARTIAL-WAVE EXPANSION METHOD 
The Scattering Wave Function 
Radial Equation 
Free Particle in Spherical Coordinates 
Phase Shifts 
Scattering Amplitude and Cross Sections 
Integral Formulae for the Phase-Shifts 
Hard Sphere Scattering 
Resonances 
Scattering from a Square-Well 
Low Energy Scattering: Scattering Length 
Scattering Length for Nucleon-Nucleon Scattering 
The Effective Range Formula
Effective Range for Nucleon-Nucleon Scattering 
Coulomb Scattering
An Illustration: a - a Scattering 
Appendix 2.A - Absolute Phase Shifts and Levinson Theorem 
Exercises
References
FORMAL SCATTERING THEORY 
Introduction: Green`s Functions 
Free Particle`s Green`s Functions 
Scattering Amplitude 
Born Approximation 
Transition and Scattering Matrices 
The Two-Potential Formula 
Distorted Wave Born Approximation 
Partial-Wave Expansion of the S-Matrix 
Partial-Wave Free Particle`s Green`s Functions
Collision of Particles with Spin
Collisions of Identical Particles 
Scattering of Clusters of Identical Fermions 
Imaginary Potentials: Absorption Cross Section
Appendix 3.A - Analytical Properties of the S-Matrix 
Exercises 
References 
COMPOUND NUCLEUS REACTIONS 
Introduction 
The Nucleon-Nucleon Interaction 
The Nucleus as a Strongly Absorbing Medium 
Mean Free Path of a Nucleon in Nuclei 
Fermi Gas Model 
Formal Theory of the Optical Potential 
Empirical Optical Potential 
Compound Nucleus Formation 
R-Matrix 
Average of the Cross Sections 
Level Densities in Nuclei 
Compound Nucleus Decay: The Weisskopf-Ewing Theory 
Reciprocity Theorem 
The Hauser-Feshbach Theory 
Appendix 4.A - The Shell Model 
Exercises
References 
FUSION AND FISSION 
Introduction 
The Liquid Drop Model 
General Considerations on Fusion Reactions 
The One Dimensional WKB Approximation 
Connection Formulas in WKB
The Three-Dimensional WKB Approximation 
Heavy Ion Fusion Reactions
Sub-Barrier Fusion 
Superheavy Elements 
Occurrence of Fission 
Mass Distribution of the Fragments 
Neutrons Emitted in Fission 
Cross Sections for Fission
Energy Distribution in Fission 
Isomeric Fission 
The Nuclear Reactor 
Appendix 5.A - The Nilsson Model 
Exercises
References 
DIRECT REACTIONS 
Introduction
Level Width and Fermi`s Golden Rule 
Direct Reactions: A Simple Approach 
Direct Reactions: Detailed Calculations 
Applications of the Shell Model 
Direct Reactions as Probe of the Shell Model 
Nuclear Vibrations 
Photonuclear Reactions - Giant Resonances 
Coulomb Excitation 
Electromagnetic Transition Probabilities for Nuclear Vibrations
Nuclear Excitation in the Deformed Potential Model 
Appendix 6.A - Multipole Moments and the Electromagnetic
Interaction
Exercises
References 
NUCLEAR REACTIONS IN THE COSMOS 
Cosmic Rays
Stellar Evolution: Hydrogen and CNO Cycles 
White Dwarfs and Neutron Stars
Synthesis of Heavier Elements
Supernovae Explosions
Thermonuclear Cross Sections and Reaction Rates 
Reaction Networks 
Models for Astrophysical Nuclear Cross Sections 
Slow and Rapid Capture Processes 
Tests of the Solar Models 
Indirect Methods for Nuclear Astrophysics Reactions 
Exercises 
References
HIGH ENGERGY COLLISIONS 
Introduction 
Nucleons as Billiard Balls 
Applications of the Classical Model 
The Eikonal Wavefunction 
Elastic Scattering 
Coulomb Amplitude and Coulomb Eikonal Phase
Total Reaction Cross Sections
Scattering of Particles with Spin 
The Optical Limit of Glauber Theory 
Pauli Blocking of Nucleon-Nucleon Scattering
Glauber Theory of Multiple Scattering 
Coulomb Excitation 
Inelastic Scattering 
Charge-Exchange Reactions 
Exercises 
References
RELAVISTIC COLLISIONS
Unpacking the Nucleus 
The Boltzmann-Uehling-Uhlenbeck Equation 
Wigner Function 
Numerical Treatment of Transport Equations 
Structure of Hadrons
Quantum Chromodynamics 
The Quark-Gluon Plasma 
Exercises 
References