Basdevant J.-L., Rich J., Spiro M. Fundamentals in Nuclear Physics: From Nuclear Structure to Cosmology
Подождите немного. Документ загружается.
Fundamentals in Nuclear Physics
The Ecole Polytechnique, one of France’s top academic institutions, has a long-
standing tradition of producing exceptional scientific textbooks for its students.
The original lecture notes, the Cours de l’Ecole Polytechnique, which were written
by Cauchy and Jordan in the nineteenth century, are considered to be landmarks
in the development of mathematics.
The present series of textbooks is remarkable in that the texts incorporate the
most recent scientific advances in courses designed to provide undergraduate
students with the foundations of a scientific discipline. An outstanding level of
quality is achieved in each of the seven scientific fields taught at the Ecole: pure
and applied mathematics, mechanics, physics, chemistry, biology, and econom-
ics. The uniform level of excellence is the result of the unique selection of aca-
demic staff there which includes, in addition to the best researchers in its own
renowned laboratories, a large number of world-famous scientists, appointed as
part-time professors or associate professors, who work in the most advanced
research centers France has in each field.
Another distinctive characteristics of these courses is their overall consistency;
each course makes appropriate use of relevant concepts introduced in the other
textbooks. This is because each student at the Ecole Polytechnique has to acquire
basic knowledge in the seven scientific fields taught there, so a substantial link
between departments is necessary. The distribution of these courses used to be
restricted to the 900 students at the Ecole. Some years ago we were very success-
ful in making these courses available to a larger French-reading audience. We
now build on this success by making these textbooks also available in English.
Jean-Louis Basdevant
James Rich
Michel Spiro
Fundamentals
In Nuclear Physics
From Nuclear Structure to Cosmology
With 184 Figures
Prof. Jean-Louis Basdevant
Ecole Polytechnique
De
´
partement de Physique
Laboratoire Leprince-Ringuet
91128 Palaiseau
France
jean-louis.basdevant@polytechnique.edu
Dr. James Rich
Dapnia-SPP
CEA-Saclay
91191 Gif-sur-Yvette
France
rich@hep.saclay.cea.fr
Dr. Michel Spiro
IN2P3-CNRS
3 Rue Michel-Ange
75794 Paris cedex 16
France
mspiro@admin.in2p3.fr
Cover illustration: Background image—Photograph of Supernova 1987A Rings. Photo credit Chris-
topher Burrows (ESA/STScI) and NASA, Hubble Space Telescope, 1994. Smaller images, from top
to bottom—Photograph of Supernova Blast. Photo credit Chun Shing Jason Pun (NASA/GSFC),
Robert P. Kirshner (Harvard-Smithsonian Center for Astrophysics), and NASA, 1997. Interior of
the JET torus. Copyright 1994 EFDA-JET. See figure 7.6 for further description. The combustion
chamber at the Nova laser fusion facility (Lawrence Livermore National Laboratory, USA). Inside
the combustion chamber at the Nova laser fusion facility (Lawrence Livermore National Labora-
tory, USA) The Euratom Joint Research Centres and Associated Centre.
Library of Congress Cataloging-in-Publication Data
Basdevant, J.-L. (Jean-Louis)
Fundamentals in nuclear physics / J.-L. Basdevant, J. Rich, M. Spiro.
p. cm.
Includes bibliographical references and index.
ISBN 0-387-01672-4 (alk. paper)
1. Nuclear physics. I. Rich, James, 1952– II. Spiro, M. (Michel) III. Title.
QC173.B277 2004
539.7—dc22 2004056544
ISBN 0-387-01672-4 Printed on acid-free paper.
©2005 Springer Science+Business Media, Inc.
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring Street, New
York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis.
Use in connection with any form of information storage and retrieval, electronic adaptation, com-
puter software, or by similar or dissimilar methodology now known or hereafter developed is for-
bidden.
The use in this publication of trade names, trademarks, service marks and similar terms, even if
they are not identified as such, is not to be taken as an expression of opinion as to whether or not
they are subject to proprietary rights.
Printed in the United States of America. (EB)
987654321 SPIN 10925645
springeronline.com
Preface
Nuclear physics began one century ago during the “miraculous decade” be-
tween 1895 and 1905 when the foundations of practically all modern physics
were established. The period started with two unexpected spinoffs of the
Crooke’s vacuum tube: Roentgen’s X-rays (1895) and Thomson’s electron
(1897), the first elementary particle to be discovered. Lorentz and Zeemann
developed the the theory of the electron and the influence of magnetism on
radiation. Quantum phenomenology began in December, 1900 with the ap-
pearance of Planck’s constant followed by Einstein’s 1905 proposal of what
is now called the photon. In 1905, Einstein also published the theories of
relativity and of Brownian motion, the ultimate triumph of Boltzman’s sta-
tistical theory, a year before his tragic death. For nuclear physics, the critical
discovery was that of radioactivity by Becquerel in 1896.
By analyzing the history of science, one can be convinced that there is
some rationale in the fact that all of these discoveries came nearly simul-
taneously, after the scientifically triumphant 19th century. The exception is
radioactivity, an unexpected baby whose discovery could have happened sev-
eral decades earlier.
Talented scientists, the Curies, Rutherford, and many others, took the ob-
servation of radioactivity and constructed the ideas that are the subject of this
book. Of course, the discovery of radioactivity and nuclear physics is of much
broader importance. It lead directly to quantum mechanics via Rutherford’s
planetary atomic model and Bohr’s interpretation of the hydrogen spectrum.
This in turn led to atomic physics, solid state physics, and material science.
Nuclear physics had the important by-product of elementary particle physics
and the discovery of quarks, leptons, and their interactions. These two fields
are actually impossible to dissociate, both in their conceptual and in their
experimental aspects.
The same “magic decade” occurred in other sectors of human activity. The
second industrial revolution is one aspect, with the development of radio and
telecommunications. The automobile industry developed at the same period,
with Daimler, Benz, Panhard and Peugeot. The Wright brothers achieved a
dream of mankind and opened the path of a revolution in transportation.
Medicine and biology made incredible progress with Louis Pasteur and many
others. In art, we mention the first demonstration of the “cin´ematographe”
VI Preface
by Auguste and Louis Lumi`ere on december 28 1895, at the Grand Caf´e, on
Boulevard des Capucines in Paris and the impressionnist exhibition in Paris
in 1896.
Nowadays, is is unthinkable that a scientific curriculum bypass nuclear
physics. It remains an active field of fundamental research, as heavy ion
accelerators of Berkeley, Caen, Darmstadt and Dubna continue to produce
new nuclei whose characteristics challenge models of nuclear structure. It
has major technological applications, most notably in medicine and in en-
ergy production where a knowledge of some nuclear physics is essential for
participation in decisions that concern society’s future.
Nuclear physics has transformed astronomy from the study of planetary
trajectories into the astrophysical study of stellar interiors. No doubt the most
important result of nuclear physics has been an understanding how the ob-
served mixture of elements, mostly hydrogen and helium in stars and carbon
and oxygen in planets, was produced by nuclear reactions in the primordial
universe and in stars.
This book emerged from a series of topical courses we delivered since the
late 1980’s in the Ecole Polytechnique. Among the subjects studied were the
physics of the Sun, which uses practically all fields of physics, cosmology for
which the same comment applies, and the study of energy and the environ-
ment. This latter subject was suggested to us by many of our students who
felt a need for deeper understanding, given the world in which they were
going to live. In other words, the aim was to write down the fundamentals
of nuclear physics in order to explain a number of applications for which we
felt a great demand from our students.
Such topics do not require the knowledge of modern nuclear theory that
is beautifully described in many books, such as The Nuclear Many Body
Problem by P. Ring and P Schuck. Intentionally, we have not gone into such
developments. In fact, even if nuclear physics had stopped, say, in 1950 or
1960, practically all of its applications would exist nowadays. These appli-
cations result from phenomena which were known at that time, and need
only qualitative explanations. Much nuclear phenomenology can be under-
stood from simple arguments based on things like the Pauli principle and the
Coulomb barrier. That is basically what we will be concerned with in this
book. On the other hand, the enormous amount of experimental data now
easily accesible on the web has greatly facilitated the illustration of nuclear
systematics and we have made ample use of these resources.
This book is an introduction to a large variety of scientific and techno-
logical fields. It is a first step to pursue further in the study of such or such
an aspect. We have taught it at the senior undergraduate level at the Ecole
Polytechnique. We believe that it may be useful for graduate students, or
more generally scientists, in a variety of fields.
In the first three chapters, we present the “scene” , i.e. we give the basic
notions which are necessary to develop the rest. Chapter 1 deals with the
Preface VII
basic concepts in nuclear physics. In chapter 2, we describe the simple nu-
clear models, and discuss nuclear stability. Chapter 3 is devoted to nuclear
reactions.
Chapter 4 goes a step further. It deals with nuclear decays and the fun-
damental electro-weak interactions. We shall see that it is possible to give a
comparatively simple, but sound, description of the major progress particle
physics and fundamental interactions made since the late 1960’s.
In chapter 5, we turn to the first important practical application, i.e.
radioactivity. We shall see examples of how radioactivity is used be it in
medicine, in food industry or in art.
Chapters 6 and 7 concern nuclear energy. Chapter 6 deals with fission and
the present aspects of that source of energy production. Chapter 7 deals with
fusion which has undergone quite remarkable progress, both technologically
and politically in recent years with the international ITER project.
Fusion brings us naturally, in chapter 8 to the subject of nuclear as-
trophysics and stellar structure and evolution. Finally, we present an intro-
duction to present ideas about cosmology in chapter 9. A more advanced
description can be found in Fundamentals of Cosmology,writtenbyoneof
us (J. R.).
We want to pay a tribute to the memory of Dominique Vautherin, who
constantly provided us with ideas before his tragic death in December 2000.
We are grateful to Martin Lemoine, Robert Mochkovitch, Hubert Flocard,
Vincent Gillet, Jean Audouze and Alfred Vidal-Madjar for their invaluable
help and advice throughout the years. We also thank Michel Cass´e, Bertrand
Cordier, Michel Cribier, David Elbaz, Richard Hahn, Till Kirsten, Sylvaine
Turck-Chi`eze, and Daniel Vignaud for illuminating discussions on various
aspects of nuclear physics.
Palaiseau, France Jean-Louis Basdevant, James Rich, Michel Spiro
April, 2005
Contents
Introduction .................................................. 1
1. Basic concepts in nuclear physics ......................... 9
1.1 Nucleonsand leptons ................................... 9
1.2 Generalpropertiesofnuclei.............................. 11
1.2.1 Nuclear radii.................................... 12
1.2.2 Binding energies ................................. 14
1.2.3 Mass units and measurements...................... 17
1.3 Quantum states of nuclei ............................... 25
1.4 Nuclear forces and interactions........................... 29
1.4.1 The deuteron .................................... 31
1.4.2 The Yukawa potentialanditsgeneralizations ........ 35
1.4.3 Origin of theYukawapotential..................... 38
1.4.4 From forces to interactions ........................ 39
1.5 Nuclear reactions and decays............................. 41
1.6 Conservation laws ...................................... 43
1.6.1 Energy-momentum conservation.................... 44
1.6.2 Angular momentum and parity (non)conservation .... 46
1.6.3 Additive quantum numbers........................ 46
1.6.4 Quantum theory of conservation laws ............... 48
1.7 Charge independence and isospin......................... 51
1.7.1 Isospin space .................................... 51
1.7.2 One-particle states ............................... 52
1.7.3 The generalized Pauli principle..................... 55
1.7.4 Two-nucleonsystem .............................. 55
1.7.5 Origin of isospin symmetry; n-p mass difference ...... 56
1.8 Deformed nuclei........................................ 58
1.9 Bibliography........................................... 62
Exercises .................................................. 62
2. Nuclear models and stability.............................. 67
2.1 Mean potentialmodel................................... 69
2.2 The Liquid-DropModel ................................. 74
2.2.1 The Bethe–Weizs¨acker mass formula ............... 74
XContents
2.3 The Fermigasmodel ................................... 77
2.3.1 Volume and surface energies ....................... 79
2.3.2 The asymmetry energy............................ 81
2.4 The shell model andmagicnumbers ...................... 81
2.4.1 The shell model and the spin-orbit interaction ....... 85
2.4.2 Some consequencesof nuclear shell structure......... 88
2.5 β-instability ........................................... 90
2.6 α-instability ........................................... 94
2.7 Nucleon emission....................................... 98
2.8 The productionofsuper-heavyelements................... 100
2.9 Bibliography........................................... 101
Exercises .................................................. 101
3. Nuclear reactions ......................................... 107
3.1 Cross-sections .......................................... 108
3.1.1 Generalities...................................... 108
3.1.2 Differential cross-sections .......................... 111
3.1.3 Inelastic and total cross-sections .................... 112
3.1.4 The uses of cross-sections .......................... 113
3.1.5 General characteristics of cross-sections ............. 115
3.2 Classical scattering on a fixed potential ................... 121
3.2.1 Classical cross-sections ............................ 122
3.2.2 Examples ....................................... 123
3.3 Quantum mechanical scattering on a fixed potential ........ 126
3.3.1 Asymptotic states and their normalization ........... 127
3.3.2 Cross-sections in quantum perturbation theory ....... 129
3.3.3 Elastic scattering ................................. 132
3.3.4 Quasi-elastic scattering ............................ 135
3.3.5 Scattering of quantum wavepackets ................ 136
3.4 Particle–particle scattering .............................. 143
3.4.1 Scattering of two free particles ..................... 143
3.4.2 Scattering of afree particle on aboundparticle ...... 146
3.4.3 Scattering on acharge distribution ................. 149
3.4.4 Electron–nucleus scattering ........................ 151
3.4.5 Electron–nucleon scattering ........................ 153
3.5 Resonances ............................................ 157
3.6 Nucleon–nucleus and nucleon–nucleon scattering............ 161
3.6.1 Elastic scattering ................................. 161
3.6.2 Absorption ...................................... 167
3.7 Coherent scattering and the refractive index ............... 169
3.8 Bibliography........................................... 171
Exercises .................................................. 171
Contents XI
4. Nuclear decays and fundamental interactions ............. 175
4.1 Decay rates, generalities................................. 175
4.1.1 Natural width, branching ratios .................... 175
4.1.2 Measurementof decayrates ....................... 176
4.1.3 Calculation of decay rates ........................ 178
4.1.4 Phase space and two-body decays .................. 183
4.1.5 Detailed balance and thermal equilibrium ........... 184
4.2 Radiativedecays ....................................... 187
4.2.1 Electric-dipole transitions ......................... 188
4.2.2 Higher multi-pole transitions....................... 190
4.2.3 Internal conversion ............................... 193
4.3 Weakinteractions ...................................... 195
4.3.1 Neutron decay ................................... 196
4.3.2 β-decay of nuclei ................................. 202
4.3.3 Electron-capture ................................. 207
4.3.4 Neutrino mass and helicity ........................ 209
4.3.5 Neutrino detection................................ 214
4.3.6 Muon decay ..................................... 218
4.4 Families of quarks and leptons ........................... 221
4.4.1 Neutrino mixing and weak interactions .............. 221
4.4.2 Quarks.......................................... 228
4.4.3 Quark mixing and weak interactions ................ 232
4.4.4 Electro-weak unification........................... 235
4.5 Bibliography........................................... 241
Exercises .................................................. 241
5. Radioactivity and all that ................................ 245
5.1 Generalities............................................ 245
5.2 Sources of radioactivity ................................. 246
5.2.1 Fossil radioactivity ............................... 247
5.2.2 Cosmogenic radioactivity .......................... 252
5.2.3 Artificial radioactivity ............................ 254
5.3 Passage of particles through matter ....................... 256
5.3.1 Heavy charged particles ........................... 257
5.3.2 Particle identification ............................. 263
5.3.3 Electrons and positrons ........................... 265
5.3.4 Photons......................................... 266
5.3.5 Neutrons ........................................ 269
5.4 Radiationdosimetry .................................... 270
5.5 Applicationsofradiation ................................ 273
5.5.1 Medical applications .............................. 273
5.5.2 Nuclear dating ................................... 274
5.5.3 Other uses of radioactivity ........................ 280
5.6 Bibliography........................................... 281
Exercises .................................................. 282