Introduction to Nuclear Reactions: 1st Edition (Paperback) book cover

Introduction to Nuclear Reactions

1st Edition

By C.A. Bertulani, P. Danielewicz

CRC Press

542 pages

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Paperback: 9780750309325
pub: 2004-05-01
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Description

Until the publication of Introduction to Nuclear Reactions, an introductory reference on nonrelativistic nuclear reactions had been unavailable. Providing a concise overview of nuclear reactions, this reference discusses the main formalisms, ranging from basic laws to the final formulae used to calculate measurable quantities.

Well known in their fields, the authors begin with a discussion of scattering theory followed by a study of its applications to specific nuclear reactions. Early chapters give a framework of scattering theory that can be easily understood by the novice. These chapters also serve as an introduction to the underlying physical ideas. The largest section of the book comprises the physical models that have been developed to account for the various aspects of nuclear reaction phenomena. The final chapters survey applications of the eikonal wavefunction to nuclear reactions as well as examine the important branch of nuclear transport equations.

By combining a thorough theoretical approach with applications to recent experimental data, Introduction to Nuclear Reactions helps you understand the results of experimental measurements rather than describe how they are made. A clear treatment of the topics and coherent organization make this information understandable to students and professionals with a solid foundation in physics as well as to those with a more general science and technology background.

Reviews

"… the book brilliantly fills a sort of gap in the field, one side of which we can find somehow more basic introductory books with only a limited development of the formalism … and, on the other side, more specialised monographic studies. … useful exercises were added for each subject."

- Riccardo Raabe, Katholieke Universiteit Leuven

"This book has the possibility of becoming a standard textbook in a graduate nuclear physics course. I like the mix of formalism and practical details and that physics is always kept in the forefront. … each chapter has problems set at the end. Both researchers and students will find the book useful."

- Subal Das Gupta, McGill University, Montreal, Canada

Table of Contents

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

About the Series

Graduate Student Series in Physics

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Subject Categories

BISAC Subject Codes/Headings:
SCI051000
SCIENCE / Nuclear Physics